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Claims  |
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What is claimed is:
1. An image-processing system comprising:
a substantially non-ringing, non-aliasing, localized transform spectrum
analyzer responsive to an input image-representing signal defined in at
least one dimension of the represented image by a spectrum of spatial
frequencies within a range extending downward from a maximum frequency
f.sub.m to zero, said analyzer separating said input-signal spectrum in
descending spatial frequency order starting from f.sub.m into a group of
one or more contiguous bandpass subspectra output signals each of which
subspectrum has a nominal bandwidth no greater than one octave within said
range, and into a remnant subspectrum output signal contining all those
spatial frequencies of said input-signal spectrum which are below those
contained in the lowest spatial frequency bandpass subspectrum
output-signal;
means for coring at least one of said bandpass subspectra output signals
and remnant subspectrum output signal, thereby introducing spurious
out-of-band spatial frequency components into each cored subspectrum
output signal; and
a spectrum synthesizer coupler to said analyzer through said coring means
and responsive to all of said subspectra signals from said analyzer being
applied thereto for deriving an output image-representing signal;
wherein said synthesizer is comprised of substantially non-ringing,
non-aliasing filter means individually associated with the subspectrum of
at least each cored signal that is lower than the highest spatial
frequency bandpass subspectrum output signal, for substantially removing
at least those spurious frequency components therefrom which are
above-band with regard to that subspectrum, and means for summing all said
subspectra signals, including both any that has been cored and/or filtered
and any that has been neither cored nor filtered, thereby to derive said
output image representing signal;
whereby any noise component originally present in the spectrum of said
input image-representing signal has been reduced in the spectrum of said
output image-representing signal without introducing any signifficant
amount of aliasing or other spurious spatial frequency component in the
spectrum of said output image-representing signal.
2. The system defined in claim 1, wherein:
said output image-representing signal is to be employed to display an image
on a display device having a resolution capability insufficient to
noticeably display any spatial frequency higher than f.sub.m ; and
said highest spatial frequency octave output signal from said spectrum is
coupled through said coring means to said summing means without having any
of said synthesizer filter means individually associated therewith.
3. The system defined in claim 1, wherein each of said synthesizer filter
means is comprised of a low-pass filter having a gradual rolloff about a
nominal cutoff frequency equal to the upper spatial frequency of the
subspectrum with which that filter means is individually associated.
4. The system defined in claim 3, wherein said synthesizer comprises:
at least two of said low-pass filters that are coupled in cascade through a
summer, a first of said filters being individually associated with a
relatively lower one of said subspectra and a second of said filters being
individually associated with a relatively higher one of said subspectra;
means for applying said relatively lower one of said subspectra signals as
an input to said first of said low-pass filters;
means for applying the output of said first of said low-pass filters as a
first input to said summer;
means for applying said relatively higher one of said subspectra signals as
a second input to said summer; and
means for applying the output of said summer as an input to said second of
said low-pass filters;
whereby said lower one of said subspectra signals is filtered by both said
first and second of said cascaded low-pass filters.
5. The system defined in claim 4, wherein both said lower and higher ones
of said subspectra signals are cored subspectra signals.
6. The system defined in claim 5, wherein said lower and higher ones of
said subspectra are contiguous subspectra.
7. The image-processing system defined in claim 1, wherein:
said input image-representing signal is a video signal representing an
image that has been scanned in at least said one dimension; said video
signal contains no temporal frequency corresponding to an image spatial
frequency greater than f.sub.m, and said video signal is sampled at a
temporal sampling frequency corresponding to at least twice f.sub.m ;
said spectrum analyzer is a Burt Pyramid spectrum analyzer including one
stage for deriving the highest one of said subspectra output signals
therefrom, said one stage inlcuding (1) convolution filter-decimation
means responsive to said sampled video signal for deriving a first
filtered output signal therefrom at one-half the sample frequency of said
video signal, (2) expander-interpolation means having said first filtered
output signal applied as an input thereto for deriving a second filtered
output signal therefrom at the same sample frequency as said video signal,
and (3) means for subtracting the level value of each sample of said
second filtered output signal from the level value of the corresponding
sample of said video signal to thereby derive said highest one of said
subspectra output signals as the output from said subtraction means; and
each of the convolution filter and interpolation filter of said one stage
exhibits a filter spatial frequency characteristic in accordance with a
symmetrical, equal-contribution kernel weighting function that includes at
least seven multiplier-coefficients having respective values such that the
product of the respective filter spatial frequency characteristics of said
convolution and interpolation filters is a given spatial frequency
characteristic (a) which is substantially unity over a spatial frequency
range extending from zero to f.sub.m /4(b) which has a gradual rolloff
over a spatial frequency range extending from f.sub.m /4 to 3f.sub.m /4,
and (c) which is substantially zero over a spatial frequency range
extending from 3f.sub.m /4 to f.sub.m.
8. The image-processing system defined in claim 7, in which each of said
convolution and interpolation filters exhibits said given spatial
frequency characteristic.
9. The image-processing system defined in claim 8, wherein:
said Burt Pyramid analyzer includes N stages where N is a plural integer
and said one stage is the first ordinal one of said N stages, for
respectively deriving each of said bandpass subspectra output signals, and
at least each of said second to (N-1)th stage includes (1) a convolution
filter decimation means responsive to the first filtered output signal
from the convolution filter decimation means of the immediately preceding
stage for deriving a first filtered output therefrom at one-half the
sample frequency of that of the first filtered output signal from the
convolution filter-decimation means of the immediately preceding stage,
(2) expander-interpolation filter means having said first filtered output
of that stage applied as an input thereto for deriving a second filtered
output signal therefrom at the sampling frequency of the first filtered
output signal of the immediately preceding stage, and (3) means for
subtracting the level value of each sample of said second filtered output
signal of a stage from the corresponding sample of the first filtered
output signal of the immediately preceding stage to thereby derive an
octave-bandpass subspectra output signal corresponding to that stage; and
each of the convolution filter and interpolation filter of each of said
second to (N-1)th stage exhibits a filter spatial frequency characteristic
in accordance with a symmetrical, equal contribution kernel weighting
function that includes at least seven multiplier-coefficients having
respective values such that the respective spatial frequency
characteristic of said convolution filter and interpolation filter of a
stage (a) is substantially unity over a range extending from zero to
f.sub.m /4, where f.sub.m is the nominal upper frequency of the spatial
frequency spectrum of the first filtered output signal of the immediately
preceding stage, (b) has a gradual rolloff over a spatial frequency range
extending from f.sub.m /4 to 3f.sub.m /4, and (c) is substantially zero
over a spatial frequency range extending from 3f.sub.m /4 to f.sub.m.
10. The image-processing system defined in claim 9, wherein:
wherein all of the second to Nth stages include the elements (1) (2) and
(3) defined in claim 9 and have the spatial frequency characteristics (a),
(b) and (c) defined in claim 9, and
said remnant subspectra output signal of said analyzer is the first
filtered output signal of said Nth stage.
11. The image-processing system defined in claim 10, wherein said
synthesizer is a Burt Pyramid synthesizer including:
an ordinal set of N expander-interpolation filter means and summers that
individually correspond with each of the N stages of said Burt Pyramid
analyzer, said expander-interpolation filter means and summers being
intercoupled in cascade in reverse order with the output of each
expander-interpolation filter means being applied as a first input to a
summer and the output of that summer being applied as an input to the
immediately preceding ordinal one of said expander-interpolation filter
means in said set, said remnant subspectrum signal being applied as an
input to the Nth expander-interpolation filter means of said set, the
bandpass subspectrum signal associated with each of said N stages of said
analyzer being applied as a second input to the corresponding summer of
said set, whereby the output of the summer of said set corresponding to
the first stage of said analyzer constitutes said output
image-representing signal; and
wherein each of the interpolation filters exhibits a filter spatial
frequency characteristic in accordance with a symmetrical, equal
contribution kernel weighting function that includes at least seven
multiplier-coefficients having respective values such that the respective
spatial frequency characteristic of said interpolation filter of a stage
(a) is substantially unity over a range extending from zero to f.sub.m /4,
where f.sub.m is the nominal upper frequency of the spatial frequency
spectrum of the first filtered output signal of the immediately preceding
stage, (b) has a gradual rolloff over a spatial frequency range extending
from f.sub.m /4 to 3f.sub.m /4, and (c) is substantially zero over a
spatial frequency range extending from 3f.sub.m /4 to f.sub.m.
12. The image-processing system defined in claim 11, wherein said
input-image-representing signal is a video signal representing a
two-dimensional image that has been scanned in both of said two
dimensions.
13. The image-processing system defined in claim 1, wherein said
input-image-representing signal is a video signal representing a
two-dimensional image that has been scanned in both of said two
dimensions.
14. The image-processing system defined in claim 13, wherein:
said video signal is a television raster-scanned video signal comprised of
successively-occurring scanning fields, each of said scanning fields
including a blanking portion followed by an active video portion; and
each of said coring means includes first means comprised of switch means
and time-constant means for deriving an adjustable threshold control
signal having a magnitude during the active video portion of each scanning
field which is a direct function of the noise level of the subspectrum
output signal applied as an input to that coring means solely during the
blanking portion of that scanning field, and second means controlled by
said threshold control signal for deriving an output from that coring
means only if the level of the input signal to that coring means during
each scanning field exceeds the magnitude of said threshold control signal
during that scanning field.
15. An image processing system for processing an input spectrum-analyzed
image-representing signal, wherein said image-representing signal that has
been spectrum-analyzed defines, in at least one dimension of the
represented image spectrum, spatial frequencies within a range extending
from a maximum frequency f.sub.m down to zero, and wherein said
spectrum-analyzed image-representing signal, starting with f.sub.m, is
comprised, in descending spatial frequency order, of a group of one or
more separate contiguous bandpass subspectra signals, each of which has a
nominal bandwith no greater than one octave within said range, and a
remnant subspectrum signal containing all those spatial frequencies of
said image-representing signal spectrum which are below those contained in
the lowest spatial frequency bandpass spectrum signal; said system
including:
means for coring at least one of said bandpass subspectra signals, thereby
introducing spurious out-of-band spatial frequency components into each
cored subspectrum signal; and
a spectrum synthesizer coupled to said coring means and having all analyzed
subspectra signals, including both those that have been cored and those
that have not been cored, applied thereto for deriving an output
image-representing signal;
wherein said synthesizer is comprised of substantially non-ringing,
non-aliasing filter means individually associated with the subspectrum of
at least each cored signal that is lower than the highest spatial
frequency bandpass subspectrum output signal, for substantially removing
at least those spurious frequency components therefrom which are
above-band, and means for summing all said subspectra signals, including
both any that has been cored and/or filtered and any that has been neither
cored nor filtered, thereby to derive said output image-representing
signal;
whereby any noise component originally present in said spectrum analyzed
image-representing signal has been reduced in the spectrum of said output
image-representing signal without introducing any significant amount of
aliasing or other spurious spatial frequency component in the spectrum of
said output image-representing signal.
16. The system defined in claim 15, wherein:
said output image-representing signal is to be employed to display an image
on a display device having a resolution capability insufficient to
noticeably display any spatial frequency higher than f.sub.m ; and
said highest spatial frequency octave output signal from said spectrum is
coupled through said coring means to said summing means without having any
of said synthesizer filter means individually associated therewith.
17. The system defined in claim 15, wherein each of said synthesizer filter
means is comprised of a low-pass filter having a gradual rolloff about a
nominal cutoff frequency equal to the upper spatial frequency of the
subspectrum with which that filter means is individually associated.
18. The system defined in claim 17, wherein said synthesizer comprises:
at least two of said low-pass filters that are coupled in cascade through a
summer, a first of said filters being individually associated with a
relatively lower one of said subspectra and a second of said filters being
individually associated with a relatively higher one of said subspectra;
means for applying said relatively lower one of said subspectra signals as
an input to said first of said low-pass filters;
means for applying the output of said first of said low-pass filters as a
first input to said summer;
means for applying said relatively higher one of said subspectra signals as
a second input to said summer; and
means for applying the output of said summer as an input to said second of
said low-pass filters;
whereby said lower one of said subspectra signals is filtered by both said
first and second of said cascaded low-pass filters.
19. The system defined in claim 18, wherein both said lower and higher ones
of said subspectra signals are cored subspectra signals.
20. The system defined in claim 19, wherein said lower and higher ones of
said subspectra are contiguous subspectra.
21. The image-processing system defined in claim 15, wherein:
said image-representing signal which has been spectrum analyzed is a video
signal representing an image that has been scanned in at least said one
dimension; said video signal contains no temporal frequency corresponding
to an image spatial frequency greater than f.sub.m, and said video signal
is sampled at a temporal sampling frequency corresponding to at least
twice f.sub.m ;
said group of bandpass subspectra signal is comprised of N bandpass
subspectra signals, where N is a plural integer;
said synthesizer is a Burt Pyramid synthesizer that includes an ordinal set
of N expander-interpolation filter means and summers, said
expander-interpolation filter means and summers being intercoupled in
cascade in reverse order with the output of each expander-interpolation
filter means being applied as a first input to a summer and the output of
that summer being applied as an input to the immediately preceding ordinal
one of said expander-interpolation filter means in said set, said remnant
subspectrum signal being applied as an input to the Nth
expander-interpolation filter means of said set, the bandpass subspectrum
signal associated with each of said N bandpass subspectra signals being
applied as a second input to the corresponding summer of said set, whereby
the output of the summer of said set corresponding to the first stage of
said analyzer constitutes said output image-representing signal; and
wherein each of the interpolation filters exhibits a filter spatial
frequency characteristic in accordance with a symmetrical, equal
contribution kernel weighting function that includes at least seven
multiplier-coefficients having respective values such that the respective
spatial frequency characteristic of said interpolation filter of a stage
(a) is substantially unity over a range extending from zero to f.sub.m /4,
where f.sub.m is the nominal upper frequency of the spatial frequency
spectrum of the first filtered output signal of the immediately preceding
stage, (b) has a gradual rolloff over a spatial frequency range extending
from f.sub.m /4 to 3f.sub.m /4, and (c) is substantially zero over a
spatial frequency range extending from 3f.sub.m /4 to f.sub.m.
22. The image-processing system defined in claim 21, wherein said
input-image-representing signal is a video signal representing a
two-dimensional image that has been scanned in both of said two
dimensions.
23. The image-processing system defined in claim 15, wherein said
input-image-representing signal is a video signal representing a
two-dimensional image that has been scanned in both of said two
dimensions.
24. The image-processing system defined in claim 23, wherein:
said video signal is a television raster-scanned video signal comprised of
successively-occurring scanning fields, each of said scanning fields
including a blanking portion followed by an active video portion; and
each of said coring means includes first means comprised of switch means
and time-constant means for deriving an adjustable threshold control
signal having a magnitude during the active video portion of each scanning
field which is a direct function of the noise level of the subspectrum
output signal applied as an input to that coring means solely during the
blanking portion of that scanning field, and second means controlled by
said threshold control signal for deriving an output from that coring
means only if the level of the input signal to that coring means during
each scanning field exceeds the magnitude of said threshold control signal
during that scanning field. |
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Claims |
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Description |
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BACKGROUND OF THE INVENTION
1. Field of the Invention:
This invention relates to an image-processing system employing coring
techniques for reducing the noise component of an image-representing
signal, such as a television video signal. More particularly, this
invention relates to such a system which reduces this noise component
without introducing any significant amount of aliasing or other spurious
spatial frequency components into the image-representing signal.
2. Description of the Prior Art:
Coring is a well known technique for reducing the noise component of an
image-representing signal. Coring consists of selectively passing only
those portions of the image-representing signal which have an absolute
amplitude level exceeding a selected threshold magnitude. Coring is a
non-linear process that inherently introduces spurious harmonic and
intermodulation spatial frequency components into the image-representing
signal. The relative power of these spurious spatial frequency components
increase as the selected threshold magnitude increases. Therefore, the
selection of the coring threshold magnitude is a tradeoff between that
which is high enough to substantially reduce the noise component and yet
is not so high as to introduce an intolerable amount of spurious spatial
frequency components.
The noticeability of a noise component, to an observer of a displayed image
derived from an image-representing signal, depends on both (1) the spatial
frequency spectrum of the noise component relative to the spatial
frequency spectrum of the signal component of the displayed image and (2)
on the operation of the human visual system in perceiving noise.
It has been found that human visual system appears to compute a primitive
spatial-frequency decomposition of luminous images, by partitioning
spatial frequency information into a number of contiguous, overlapping
spatial-frequency bands. Each band is roughly an octave wide and the
center frequency of each band differs from its neighbors by roughly a
factor of two. Research suggests that there are approximately seven bands
or "channels" that span the 0.5 to 60 cycle/degree spatial-frequency range
of the human visual system. The importance of these findings is that
spatial frequency information more than a factor of two away from other
spatial frequency information will be independently processed by the human
visual system. It has been further found that the spatial-frequency
processing that occurs in the human visual system is localized in space.
Thus, the signals within each spatial-frequency channel are computed over
small subregions of the image. These subregions overlap each other and are
roughly two cycles wide at a particular frequency. If a sine wave grating
image is employed as a test pattern, it is found that the threshold
contrast-sensitivity function for the sine wave grating image rolls-off
rapidly as the spatial frequency of the sine wave grating image is
increased. That is, high spatial frequencies require high contrast to be
seen (.perspectiveto.20% at 30 cycle/degree) but lower spatial frequencies
require relatively low contrast to be seen (.perspectiveto.0.2% at 3
cycle/degree). It has been found that the ability of the human visual
system to detect a change in the contrast of a sine wave grating image
that is above threshold also is better at lower spatial frequencies than
at higher spatial frequencies. Specifically, an average human subject, in
order to correctly discriminate a changing contrast 75% of the time,
requires roughly a 12% change in contrast for a 3 cycle/degree sine wave
grating, but requires a 30% change in contrast for a 30 cycle/degree
grating.
Based on the operation of the human visual system, it becomes clear that a
relatively high signal-to-noise (S/N) ratio within an octave spatial
frequency band tends to mask the noise (i.e. the noise becomes
unnoticeable to an observer) and that this masking effect is more
effective for a higher spatial frequency octave than it is for a lower
spatial frequency octave. This is true because of the relative decrease in
both contrast sensitivity and change-in-contrast sensitivity of the human
visual system at higher spatial frequencies. On the other hand, a
relatively small high spatial frequency noise component superimposed on a
nearly uniform background, which is comprised of dc (zero) or very low
spatial frequency video components, is easily noticed by the human visual
system. This is significant because real-world images, for the most part,
have a spatial frequency spectrum in two dimensions which contains a large
amount of relatively low spatial frequency signal energy and only a small
amount of high frequency signal energy. This makes any high spatial
frequency noise particularly noticeable.
If only a single coring means is employed to core the entire spatial
frequency spectrum of an input image-representing signal, the selected
threshold magnitude is likely to be too small to satisfactorily reduce the
noticeable noise component in one or more octave portions of this spatial
frequency spectrum, while at the same time being so high in one or more
other octave portions of this spatial frequency spectrum that an
intolerable amount of spurious spatial-frequency component artifact is
introduced in the displayed image.
This problem can be avoided by first spectrum analyzing the input
image-representing signal into a plurality of contiguous subspectra bands,
then separately coring each of these bands with a different appropriate
selected threshold magnitude, and finally synthesizing these cored bands
into a single output image-representing signal which is employed to derive
the displayed image.
Reference is made to U.S. Pat. No. 4,442,454, which issued Apr. 10, 1984 to
Powell, and is entitled "Image Processing Method Using a Block Overlap
Transformation Procedure." This Powell patent discloses a spectrum
analyzer for separating the spatial frequency spectrum of an applied
sampled two-dimensional image-manifesting signal input into three
contiguous subspectra. The spectrum analyzer disclosed in Powell includes
predetermined direct transform networks for deriving a fine-detailed
(relatively high spatial frequency) subspectrum output at the sampling
density of the input signal, an intermediate detail (relatively
intermediate spatial frequency) subspectrum output at a reduced sampling
density, and a coarse detail (relatively low spatial frequency)
subspectrum output at a further reduced sampling density. Each of the
respective subspectra output signals from the analyzer is individually
first cored and then operated on by an inverse transform network. An
expand/interpolation filter is used to increase the sampling density of
each of the coarse-detail and intermediate-detail subspectra back to the
sampling density of the fine-detail subspectrum, after which the
respective cored subspectra signals are summed to derive an output
image-representing signal used to provide a reduced-noise display of the
represented image.
Powell is aware that image processing of image-representing signals, for
the purpose of reducing noise, tends to result in some distortion of local
image values (i.e. an artifact of the processing itself is generated that
is noticeable in the display of the processed image). In fact, the block
overlap transformation procedure of Powell is intended to prevent a
noticeable boundary from existing between adjacent blocks in the displayed
image. These boundaries are undesirable because they lead to a
checkerboard appearance in the displayed image that is unacceptable for
high quality image reproduction. Powell also realizes that some distortion
of local image values necessarily results from the non-linear coring
process, and that this produces an artifact that noticeably affects both
the displayed image signal and the residue of unwanted noise.
Nevertheless, Powell believes that such an artifact of the coring process
has to be tolerated in order to realize the desired noise reduction.
SUMMARY OF THE INVENTION
The image processing system of the present invention permits any noise
component originally present in the spectrum of an input
image-representing signal to be reduced in the spectrum of the output
image-representing signal without introducing any significant amount of
aliasing or other spurious spatial frequency component in the spectrum of
the output image-representing signal. Thus, the present invention does not
require that noticeable artifacts of the processing itself be tolerated in
order to realize the desired noise reduction.
More specifically, the image processing system of the present invention is
comprised of a substantially non-ringing, non-aliasing, localized
transform spectrum analyzer that is responsive to an input
image-representing signal defined in at least one dimension of the
represented image by a spectrum of spatial frequencies within a range
extending from a maximum frequency f.sub.m down to zero. The analyzer
separates the input-signal spectrum in descending spatial frequency order
starting from f.sub.m into a group of one or more contiguous bandpass
subspectra output signals each of which has a nominal bandwidth no greater
than one octave within the f.sub.m to zero range, and into a remnant
subspectrum output signal containing all those spatial frequencies of the
input signal spectrum which are below those contained in the lowest
spatial frequency bandpass subspectrum output signal. The image processing
system further comprises means for coring at least one of the bandpass
subspectra output signals, thereby introducing spurious out-of-band
spatial frequency components into each cored subspectrum output signal.
Coupled to the analyzer through the coring means is a spectrum synthesizer
that is responsive to all of the subspectra signals from the analyzer
being applied thereto for deriving an output image-representing signal.
This synthesizer is comprised of substantially non-ringing, non-aliasing
filter means individually associated with the subspectrum of at least each
cored signal that is lower than the highest spatial frequency bandpass
output signal. The filter means individually associated with a subspectrum
substantially removes at least those spurious frequency components
therefrom which are above-band with regard to that subspectrum. The
synthesizer is further comprised of means for summing all of the
subspectra signals, including both any that has been cored and/or filtered
and any that has been neither cored nor filtered, thereby to derive the
aforesaid output image representing signal.
A practical implementation of the present invention, for operating in real
time on an input video signal representing a scanned television image, may
employ a so-called Burt Pyramid spectrum analyzer and Burt Pyramid
synthesizer of a type disclosed in co-pending U.S. patent application Ser.
No. 596,817, filed Apr. 4, 1984 by Carlson et al., and assigned to the
same assignee as the present invention.
BRIEF DESCRIPTION OF THE DRAWING
FIG. 1 comprises respective graphs comparing a "brickwall" filter
characteristic to a gradual rolloff filter characteristic;
FIG. 2 is a functional block diagram of an idealized embodiment of the
present invention;
FIG. 2a illustrates an alternative embodiment of the spectrum synthesizer
of FIG. 2;
FIG. 3a illustrates a Burt Pyramid spectrum analyzer which is useful in a
practical implementation of the spectrum analyzer of FIG. 2;
FIG. 3b illustrates a Burt Pyramid synthesizer which is useful in a
practical implementation of the spectrum synthesizer of FIG. 2a;
FIG. 4 is a graph of the baseband envelope of a seven
multiplier-coefficient kernel weighting function having the respective
values shown in FIGS. 4 and 4a of the convolution or interpolation filter
of a Burt Pyramid analyzer and/or synthesizer useful in implementing the
present invention; and
FIG. 5 is a block diagram of a preferred embodiment of the coring means of
FIG. 2, which coring means is suitable for coring a video signal defining
a scanned two-dimensional television image.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
The distinctive feature of the present invention is that its spectrum
analyzer and synthesizer each incorporates only filters having gradual
rolloff filter characteristics, rather than "brickwall" filter
characteristics. FIG. 1 illustrates the distinction between an idealized
"brickwall" filter characteristic and a generalized gradual rolloff filter
characteristic. As indicated by graph 100, within a passband extending
from a lower cutoff frequency f.sub.L to an upper cutoff frequency
f.sub.h, a "brickwall" filter passes frequency components of a signal
without attenuation, while all out-of-band frequency components of this
signal below f.sub.L or above f.sub.h are completely attenuated. The
center frequency f.sub.c of the band is equal to the average of the
respective cutoff frequencies f.sub.h and f.sub.L, while the bandwidth is
equal to the difference between the respective cutoff frequencies f.sub.h
and f.sub.L. If the filter is a bandpass filter, the value of the lower
cutoff frequency f.sub.L is greater than zero. However, if the filter is a
low-pass filter, the value of the lower cutoff frequency f.sub.L is zero.
In a spectrum analyzer for separating the frequency spectrum of an input
signal into a plurality of contiguous subspectra signals, a "brickwall"
filter characteristic completely prevents frequency components within one
subspectrum from contaminating an adjacent subspectrum. However, the
problem with a "brickwall" filter is that it rings when shock-excited by
the energy of an out-of-band high-frequency pulse. For example, consider a
video signal representing a horizontally scanned image comprised of a
bright narrow light stripe surrounded by a relatively dark, substantially
large uniform background area. The relatively dark background will contain
spatial frequencies that fall within a relatively low spatial frequency
subspectra. However, when the horizontal scan passes across the edge of
the narrow bright light vertical stripe, a short, high-amplitude pulse is
generated in the video signal that shock-excites a low spatial frequency
subspectrum "brickwall" filter into ringing. This causes a high spatial
frequency bright ringing artifact to be generated which is superimposed on
the portion of the dark background immediately following the bright
vertical stripe. Such an artifact is quite noticeable because, as
mentioned earlier, the human visual system is quite sensitive to a high
spatial frequency spurious component superimposed on a low spatial
frequency background. The present inventors point out it is undesirable to
remove noticeable noise present in the original input signal by a process
which, in itself, adds noticeable artifacts to the displayed image.
A generalized gradual rolloff filter characteristic for a bandpass filter
is shown in graph 102 that has a center frequency f.sub.c. Since the
rolloff is gradual, there are no distinct lower and upper cutoff
frequencies f.sub.L and f.sub.h to define the bandwidth of the passband of
the filter. Instead, the nominal lower and upper cutoff frequencies
f.sub.L and f.sub.h are defined by those frequencies at which the filter
attenuates an input signal by a preselected amount (e.g. the half-power
points shown in FIG. 1). The nominal bandwidth of the filter is then the
difference between the nominal upper cutoff frequency f.sub.h and the
nominal lower cutoff frequency f.sub.L. However, as indicated by the
shaded regions 104 in FIG. 1, a small amount of the energy in a given
subspectrum band of a spectrum analyzer employing gradual rolloff filters
will result in the contamination of adjacent subspectrum bands. This has a
tendency to produce spurious aliasing spatial frequencies in an
image-processing system employing sampled and subsampled signals. However,
the image-processing system of the present invention, described in detail
below, minimizes the effect of any aliasing.
In the case of a gradual rolloff bandpass filter, shown generally by graph
102 of FIG. 1, rolloff usually occurs on both the higher and lower
frequency sides of the center frequency f.sub.c. In the case of a gradual
rolloff low-pass filter, however, only the high frequency side of the
center frequency f.sub.c actually rolls off. The exact shape of the
roll-off of any specific gradual rolloff filter characteristic is a matter
of design. Design criteria suitable for gradual rolloff filters employed
by the image-processing system of the present invention is discussed in
more detail below.
FIG. 2 is a functional block diagram of an idealized embodiment of the
present invention. A non-ringing, non-aliasing localized transform,
octave-band spectrum analyzer 200 has an image-representing signal I
supplied as an input thereto. In principle, input signal I can be a
continuous analog signal, a sampled analog signal (such as is employed by
CCD imagers and signal-translators) or a sampled digital signal (such as
is derived from an analog-to-digital converter). In practice, however,
image processing of the type being discussed is nearly always carried out
on a sampled image-representing signal by a spectrum analyzer employing a
digital computer in non-real time or, alternatively, employing physical
hardware that may operate either in real time or in non-real time.
Therefore, for illustrative purposes, it is assumed that input signal I is
a sampled signal, rather than a continuous signal.
As indicated in FIG. 2, the image-representing signal I is defined in at
least one dimension of the represented image by a spectrum of spatial
frequencies within a range extending from a maximum frequency f.sub.m to
zero. In order that signal I contain no spatial frequencies higher than
f.sub.m, it is assumed to have been passed through a prefilter. For
illustrative purposes, it will be assumed that input signal I is a
temporal video signal derived from a conventionally scanned
two-dimensional television image (although this is not essential). In any
case, analyzer 200 separates the spatial frequency spectrum of input
signal I into N (where N is any given integer) contiguous bandpass
subspectra output signals L.sub.0 . . . L.sub.N-1, and a remnant
subspectrum output signal G.sub.N. Bandpass subspectra output signals
L.sub.0 . . . L.sub.N-1 are arranged in descending spatial frequency
order, starting from f.sub.m, into respective nominal bandwidths of one
octave within the range f.sub.m to zero. Remnant subspectrum output signal
G.sub.0 contains all those spatial frequencies of the spectrum of input
signal I which are below those contained in the (N-1) bandpass subspectrum
(which is the lowest spatial frequency bandpass subspectrum). More
specifically, as shown in FIG. 2, octave I has a nominal bandwidth of
f.sub.m /2 and a center frequency of 3f.sub.m /4, octave 2 has a nominal
bandwidth of f.sub.m /4 and a center frequency of 3f.sub.m /8, and so
forth.
Each of coring means 202-1 . . . 202-N has a corresponding one of the
subspectra output signals L.sub.0 . . . L.sub.N- 1 and G.sub.N applied as
an input thereto. Respective outputs L.sub.0 . . . L.sub.N-1 and G.sub.N
from coring means 202-1 . . . 202-N are applied to corresponding ones of
non-ringing, non-aliasing filters 204-1 . . . 204-N of spectrum
synthesizer 206. Spectrum synthesizer 206 also includes summer 208 for
summing the respective outputs from filters 204-1 . . . 204-N to derive a
reconstructed output image-manifesting signal I.sub.R.
Spectrum analyzer 200 performs a linear transformation on the image spatial
frequency spectrum of the image-representing input signal I. Therefore, in
the ideal case in which spectrum analyzer 200 provides a substantially
non-ringing, non-aliasing localized transform, no significant amount of
baseband spatial frequency will be present in any of the respective
outputs from spectrum analyzer 200 which is not also present in the image
spatial frequency spectrum of the input image-representing signal I. Thus,
no significant amounts of spurious spatial frequency components are
introduced by spectrum analyzer 200. However, coring means 202-1 . . .
202-N, which inherently operate in a non-linear manner, do introduce
spurious spatial frequency components in each of the output signals
L'.sub.0 . . . L'.sub.N-1 and G'.sub.N. These spurious spatial frequency
components are comprised of harmonic components and intermodulation
components of the subspectrum spatial frequencies applied as an input to
each of coring means 202-1 . . . 202-N. All harmonics of any spatial
frequency within an octave-bandwidth subspectrum have spatial frequencies
above that octave-bandwidth subspectrum. Also, those intermodulation
components having a spatial frequency equal to the sum of different
spatial frequencies within an octave-bandwidth subspectrum are situated
above that octave-bandwidth subspectrum. Further, those intermodulation
components having a spatial frequency equal to the difference between
different spatial frequencies within an octave-bandwidth subspectrum are
situated below that octave-bandwidth subspectrum.
If the output from a coring means operating on an octave-bandwidth
subspectrum input were applied to a bandpass filter exhibiting a
"brickwall" characteristic (of the type shown in graph 100 of FIG. 1), all
the spurious spatial frequencies of the harmonic and intermodulation
components generated by the coring means would be rejected by the filter.
However, for the reasons discussed above, such a "brickwall"
characteristic filter would tend to introduce shock-excited spurious
spatial frequency ringing components. In order to avoid introduction of
such spurious spatial frequency ringing components, such bandpass filter
should have a gradual rolloff filter characteristic (such as shown in
graph 102 of FIG. 1) and a nominal bandwidth of an octave. In this latter
case, a small amount of out-of-band harmonic and intermodulation spatial
frequency components will not be completely rejected because of the
presence of the out-of-band portions of the gradual rolloff filter
characteristic (i.e., the shaded portions 104 shown in FIG. 1). However,
as discussed in more detail below, the amount of spurious spatial
frequency components due to a gradual rolloff characteristic can be made
insignificant (i.e. essentially unnoticeable in a displayed image) by
proper filter design.
Each of filters 204-1 . . . 204-(N-1) of spectrum synthesizer 206 may be
bandpass filters or, alternatively, low-pass filters. In the case in which
these filters are bandpass filters, each filter has a center frequency and
a nominal bandwidth corresponding to the octave subspectrum with which it
is associated. In the case in which these filters are low-pass filters,
they have a nominal bandwidth from zero to a nominal upper cutoff
frequency that is the same as that of a corresponding bandpass filter
associated with the same octave subspectrum. Filter 204-N associated with
the remnant subspectrum, is a low-pass filter having a nominal upper
cutoff frequency substantially equal to a lower cutoff frequency of the
(N-1 ) octave subspectrum.
If low-pass (rather than bandpass) filters are employed for octave filters
204-1 . . . 204-(N-1), the below-band difference (beat) spurious spatial
frequency components of the coring process will not be rejected. However,
such beat intermodulation signals tend to be low-level signals that are
not easily noticed by the human visual system if present in a displayed
image. In part this is because these lower spatial frequency beats are
de-localized and randomly overlapping, and in part this is due to the
masking effect of the relatively high-level signal content of most real
world images in the lower spatial frequency portion of the image spatial
frequency spectrum. Further, in practical systems, suitable non-ringing,
non-aliasing gradual rolloff characteristics are more easily implemented
for low-pass filters than for bandpass filters.
Although, in FIG. 2, each and every one of the subspectra output signals
from analyzer 200 has an individual coring means associated therewith, it
is not essential to the present invention that this be the case. All that
is required is that at least one of the subspectra output signals has a
coring means individually associated therewith. However, if any of the
coring means 202-2 . . . 202-N, associated with subspectra composed of
spatial frequencies below those of octave 1 (that is the highest spatial
frequency subspectrum) is present, it must have a corresponding one of
filters 204-2 . . . 204-N of spectrum synthesizer 206 individually
associated therewith in order to substantially remove therefrom at least
the above-band spacious spatial frequency components due to the non-linear
coring process. However, in the case of the octave 1 subspectrum,
corresponding filter 204-1 of spectrum synthesizer 206 often is dispensed
with. The reason for this is that most image displays are incapable of
resolving spatial frequencies higher than the maximum spatial frequency
f.sub.m of the octave 1 subspectrum. Because any above-band spurious
spatial frequencies present in the synthesized output signal I.sub.R
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