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Description  |
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BACKGROUND OF THE INVENTION
1. Field of the Invention
The invention relates to a source separation system for processing input
signals formed by mixtures of primary signals originating from various
sources and for estimating the primary signals, the system comprising a
first source separation sub-assembly which, with the aid of separation
coefficients, produces estimates of the primary signals, while a second
sub-assembly adaptively determining the separation coefficients.
2. Description of the Related Art
There are systems which receive on their inputs signals which present
themselves in the form of mixed signals formed by a superpositioning of
contributions originating from various signal sources. This is shown, for
example, with an antenna that receives signals originating from various
transmitters, or when a microphone produces a desired speech signal mixed
with undesired disturbing signals. Generally, one wishes to perfectly
extract all the source signals which occur in the mixture, either
completely or by an optimization of a signal-to-noise ratio.
When using various sensors which produce various mixed signals, one has
sought to obtain reliable estimates of the source signals. Known
techniques work with unknown mixed signals and unknown source signals, so
that the separation techniques are called blind source separation
techniques.
Among the known source separation structures, one may cite, for example,
the prior art document "Multi-layer neural networks with a local adaptive
learning rule for blind separation of source signals", A. CICHOCKI, W.
KASPRZAK, S. AMARI, International Symposium on nonlinear theory and its
applications (NOLTA'95) LAS VEGAS, Dec. 10-14, 1995, 1Ce-5, pages 61 to
65.
This document relates to mixtures which are hard to process, for example,
because the mixed signals are very much alike or when the mixed signals
have highly different levels.
Nonetheless, the structures described in this document are not suitable
when the source signals are non-stationary signals. This forms a
considerable drawback, because these types of signals are very often found
in the concrete applications such as speech signal processing or, more
generally, audio signal processing.
SUMMARY OF THE INVENTION
It is an object of the invention to propose a source separation system
which permits of handling the case of non-stationary signals even if these
signals enter the category of mixtures that were previously called
"hard-to-process" mixtures.
This object is achieved with a source separation system for processing
input signals formed by mixtures of primary signals originating from
various sources and for estimating the primary signals, the system
comprising a first source separation sub-assembly having first inputs
connected to the input signals, second inputs for receiving separation
coefficients and outputs for producing first estimates of the primary
signals, and a second sub-assembly for adaptively determining the
separation coefficients, characterized in that the source separation
system further comprises a third sub-assembly which receives the first
estimates for detecting a maximum estimate with a maximum amplitude level
and which standardizes the first estimates relative to the maximum
estimate to produce second estimates for application to the second
sub-assembly for the calculation of the separation coefficients.
Thus, when the primary signals originating from various sources exhibit
considerable amplitude level variations during a transition period, it is
impossible that a temporary excessive amplitude level of the second
estimates occurs during this transition period. The level of the second
estimates always remains inside a given amplitude window.
However, when the level of the input signal is relatively constant, be it
either a strong or a weak input signal, the first estimates which are
produced on the output exhibit an average level that is substantially the
same on the output. This means that the separation coefficients calculated
by the system are adapted to maintain the first estimates produced in
standardized manner with predefined energy. This may form a handicap in
certain applications, because in this manner, the strong or weak nature of
an input signal is lost. For example, in the case of speech signals, it
may be useful differentiating a weak voice from a strong voice.
For remedying this drawback, according to the invention the third
sub-assembly comprises an output module which divides each first estimate
by a specific separation coefficient to produce third estimates which are
proportional to the primary signals with a proportionality factor that is
independent of said primary signals.
In certain particular applications, it may appear that a primary signal is
temporarily absent. The situation deserving of attention is that of
speakers speaking alternately. Thus, there are moments at which each
speaker stops speaking, that is to say, that his source signal is
interrupted for a moment to be resumed several instants later. Thus, the
estimate of this absent signal is to be zero on the output during these
periods. In the case where primary signals are zero or very weak, the
separation system will have a tendency of duplicating one of the other
non-zero estimates on the unused output. To avoid this situation,
according to the invention, the third sub-assembly comprises a selection
module which prevents an estimate from being duplicated on a channel
assigned to a primary signal that is absent.
These and other aspects of the invention will be apparent from and
elucidated with reference to the embodiments described hereinafter.
BRIEF DESCRIPTION OF THE DRAWINGS
In the drawings:
FIG. 1 shows a general circuit diagram of a source separation system;
FIG. 2 shows a particular diagram of a prior art separation system for
separating two input signals;
FIG. 3 shows curves of an input signal exhibiting considerable level
variations;
FIG. 4 shows a general circuit diagram of a prior-art source separation
system;
FIG. 5 shows a general circuit diagram of a source separation system
according to the invention;
FIG. 6 shows a source separation system according to the invention
permitting the estimates not to diverge on the output;
FIG. 7 shows a diagram of source separation according to the invention
permitting the estimates not to diverge and to remain proportioned to the
input signals;
FIG. 8 shows a diagram of a source separation system according to the
invention permitting estimates not to diverge, to remain proportioned to
the input signals and preventing an estimate being duplicated on a channel
assigned to a primary signal that is absent; and
FIG. 9 shows a diagram of a particular example of a source separation
system with two input signals in the case of FIG. 8.
DESCRIPTION OF THE PREFERRED EMBODIMENTS
FIG. 1 represents primary sources S1 to Sn formed, for example, by voices
of passengers in a vehicle, by various noise sources (engine, bodywork,
air circulation through the windows, etc.) and by a car radio. The primary
sources produce primary signals X.sub.i (t). It will be noticed that these
primary signals are mixed in the transmission space. For identifing the
voices, sensors C1 to Cn, for example, microphones, are placed inside the
compartment. The sensors produce mixed signals E.sub.i (t).
Similarly, this may relate to the reception of radio waves transmitted by
sources S1 to Sn and detected by sensors formed by antennas C1 to Cn. In
the air, the primary signals X.sub.i (t) produced by the transmitters will
arrive at the antennas in mixed form. These antennas then supply mixed
signals E.sub.i (t) which are the only accessible signals for reception.
To obtain estimated signals, called estimates X.sub.i (t), where i is a
current index varying from 1 to n corresponding to each source based on
mixed signals E.sub.i (t), a source separation system 10 is known to be
used.
According to the known prior art (FIG. 4), the input signals E.sub.i (t)
enter a source separation sub-assembly 12 which produces first estimates
X.sub.i (t). A second sub-assembly 14 determines separation coefficients
W.sub.i,j based on the first estimates X.sub.i (t). For this purpose, it
calculates correction factors .DELTA.W.sub.ij for updating the separation
coefficients. These are then inserted into the next cycle in the first
sub-assembly 12 for determining subsequent estimates X.sub.i (t).
For clarity, a simple case of a system will be described having a direct
structure comprising a single processing layer for separating two source
signals X.sub.1 (t) and X.sub.2 (t) according to the above-mentioned prior
art (FIG. 2). Two sensors produce mixed signals E.sub.1 (t) and E.sub.2
(t). These signals are linked with the primary signals by the following
relations:
E.sub.1 (t)=a.sub.11 X.sub.1 (t)+a.sub.12 X.sub.2 (t) (1)
E.sub.2 (t)=a.sub.21 X.sub.1 (t)+a.sub.22 X.sub.2 (t) (2)
in which the terms a.sub.11, a.sub.12, a.sub.21 and a.sub.22 are
coefficients of unknown mixtures. The signals which occur in these
relations are centered signals, that is to say, that the DC components
which could occur therein have been eliminated, for example, by a suitable
filter operation.
The diagram of the prior art represented in FIG. 2 permits of determining
the estimates X.sub.1 (t) and X.sub.2 (t) based on mixed signals E.sub.1
(t) and E.sub.2 (t) based on the relations:
X.sub.1 (t)=W.sub.11 E.sub.1 (t)+W.sub.12 E.sub.2 (t) (3)
X.sub.2 (t)=W.sub.21 E.sub.1 (t)+W.sub.22 E.sub.2 (t) (4)
in which the terms W.sub.11, W.sub.12, W.sub.21, W.sub.22 are adaptive
separation coefficients.
For updating the separation coefficients, one may apply the following
adaptation rules:
W.sub.ii (t1)=W.sub.ii (t)-.mu.{.function.[X.sub.i (t)]g[X.sub.i (t)]-1}(5)
W.sub.ij (t+1)=W.sub.ij (t)-.mu..function.{X.sub.i (t)]g[X.sub.j (t)],
i.noteq.j (6)
in which .mu. is a positive adaptation step while f and g are preferably
nonlinear functions. More particularly, one may choose f(x)=x.sup.3 and
g(x)=x. In FIG. 4, the signals X.sub.1 (t) and X.sub.2 (t) arrive at the
sub-assembly 14 which calculates the correction factors .DELTA.W.sub.ij to
be applied to the coefficients W.sub.ij between the instants t and t+1
according to the relations:
.DELTA.W.sub.ii =W.sub.ii (t+1)-W.sub.ii (t)=-.mu.{.function.[X.sub.i
(t)]g[X.sub.i (t)]-1} (7)
.DELTA.W.sub.ij =W.sub.ij (t+1)-W.sub.ij (t)=-.mu..function.[X.sub.i
(t)]g[X.sub.j (t)], i.noteq.j (8)
The new values of W.sub.ij are loaded in separation coefficient memories in
the first sub-assembly 12.
The adaptation rule (6) is used for updating the crossed coefficients
W.sub.12 and W.sub.21, intended to eliminate the component X.sub.2 (t) in
X.sub.1 (t) and the component X.sub.1 (t) in X.sub.2 (t).
The adaptation rule (5) is used for updating the direct coefficients
W.sub.1 and W.sub.22 intended to standardize the shells of the signals
X.sub.1 (t) and X.sub.2 (t), respectively. These direct coefficients adapt
themselves to the nature of the signals to be processed.
In the case of two signals represented in FIG. 2, the mixed signal E.sub.1
(t) enters multipliers 141 and 142 and the mixed signal E.sub.2 (t) enters
multipliers 143, 144. The outputs of the multipliers 141 and 143 are added
together in an adder 150, whereas the outputs of the multipliers 142 and
144 are added together in an adder 151 to produce, respectively, the
estimates X.sub.1 (t) and X.sub.2 (t). The module 161 receives the
estimate X.sub.1 (t) and the module 162 receives the estimates X.sub.1 (t)
and X.sub.2 (t). The modules 161 and 162 calculate the correction factors
.DELTA.W.sub.11 and .DELTA.W.sub.21 respectively, according to the
equations 7 and 8 and produce updated separation coefficients W.sub.11 and
W.sub.21. A similar processing is carried out in the modules 163 and 164
for the correction factors .DELTA.W.sub.12 and .DELTA.W.sub.22.
Let us consider the case of source signals which have a relatively constant
scale (or a constant envelope) during a given period, wherein the mixing
coefficient a.sub.ij is furthermore constant or varying very slowly. In
this case, the coefficients W.sub.11 and W.sub.22 converge to the
relatively constant values ensuring predefined energies for the estimates
X.sub.1 (t) and X.sub.2 (t). In the case where f(x)=x.sup.3 and g(x)=x,
the predefined energy is expressed by <X.sup.4 >. This predefined value
is, for example, equal to 1 in the case of equations 5 and 6. Updating the
separation coefficients is carried out at each unit of time t, t+1, t+2 .
. .
When the scale of the source signals suddenly varies considerably, it
brings about a rapid and strong variation of the mixed signals. This case
is represented in FIG. 3. At point A, there is a sudden variation in the
envelope of the mixed signals E(t). Still, at the instants immediately
thereafter, according to the previously updated algorithm, the separation
coefficients W.sub.11 and W.sub.22 will retain values near to those which
they had just before this considerable increase, because their adaptation
requires a duration which stretches out over several hundred to several
thousand time units. Thus, the strong scale increase of the mixed signals
also brings about a considerable increase of the estimates X.sub.1 (t) and
X.sub.2 (t) by the relations (3) and (4) which, in its turn, causes the
modifications of the coefficients W.sub.11 and W.sub.22 to become
considerable because of the relation (5). Thus, the values of these
separation coefficients become very high as a result of which a
considerable rise of the output signals causes again a rise of the
separation coefficients which makes that the outputs may diverge when
there are non-stationary signals.
The invention comprises modifying the prior-art system represented in FIG.
4, maintaining the operations (3) and (4), but the modification of the
rules to adapt separation coefficients. To be more precise, instead of
utilizing the first estimates X.sub.1 (t) and X.sub.2 (t) for updating the
coefficients, these signals are made to pass through specific means which
limit the amplitudes according to the instant under consideration. It is
second estimates having limited amplitudes that are used then. Thus, the
modifications made in the separation coefficients are limited. In this
manner, the new coefficients progressively converge to new stable values
and no longer diverge.
This embodiment is represented in the FIGS. 5 and 6. A third sub-assembly
15 is connected to the output of the first sub-assembly 12. The third
sub-assembly transforms the first estimates X.sub.1 (t) to X.sub.n (t)
into second estimates X.sub.1 (t) to X.sub.n (t) whose amplitudes are
standardized relative to the maximum amplitude signal, as an absolute
value taken from those between X.sub.1 (t) to X.sub.n (t) at the instant
under consideration. This operation is realized in an amplitude limiting
unit 16 (FIG. 6).
Each instant, the separation coefficients are modified in the following
manner:
the outputs X.sub.i (t) of the prior-art system are calculated;
the maximum M of their absolute values is calculated which is:
M=max.vertline.X.sub.i (t).vertline.,i=1 . . . n;
a threshold value .beta.>0 is defined corresponding to the maximum value
authorized for the absolute values of the limited signals X.sub.i (t).
This threshold is freely chosen and defines the extent of the desired
limitation.
At the instant under consideration, M is compared to .beta. and the
limitation is realized so that:
if M<=.beta., the signals X.sub.i (t) have an amplitude that is low enough,
thus there is no need to limit, so that:
.A-inverted.i=1 . . . n, .sub.i (t)=X.sub.i (t);
if M>.beta., at least one signal having a high amplitude, thus all the
signals with the same reduction factor are limited, so that:
##EQU1##
The variations .DELTA.W.sub.ij are calculated in the same manner as in the
prior-art system. The second sub-assembly 14 determines the modifications
to be made to the separation coefficients W.sub.ij based on second
estimates X.sub.1 (t) to X.sub.n (t), that is to say:
.DELTA.W.sub.ii =-.mu.{.function.[.sub.i (t)]g[.sub.i (t)]-1}(9)
.DELTA.W.sub.ij =-.mu..function.[.sub.i (t)]g[.sub.j (t)], i.noteq.j.(10)
The invention may also be applied (module 12) to a source separation
structure described in the document: "Blind separation of sources, Part I:
An adaptive algorithm based on neuromimetic architecture" C. Jutten, J.
Herault, Signal Processing, 24, 1991, pages 1-10.
A second possibility which permits limiting the divergence of the output
signals consists of calculating the correction factors:
F.sub.ij (t)=-.mu.{.function.[X.sub.i (t)]g[X.sub.i (t)]-1}, i=j(11)
F.sub.ij (t)=-.mu..function.[X.sub.i (t)]g[X.sub.j (t)], i.noteq.j(12)
but instead of utilizing these correction factors just as they are used for
updating the separation coefficients, the signals corresponding to these
correction factors are made to pass through low-pass filter means to
reduce the development of these variations. This avoids sudden scale
changes. This solution is found to be less robust than the preceding one.
Preferably, this solution is associated with the first solution and, in
this case, the second sub-assembly 14 comprises a low-pass filter unit 141
which filters the correction factors F.sub.ij (t) to calculate the
variations of coefficients .DELTA.W.sub.ij to update the separation
coefficients W.sub.ij.
In this case, each separation coefficient is modified by a quantity
.DELTA.W.sub.ij (t) which results from a first-order low-pass filtering,
that is to say:
##EQU2##
Which can also be expressed by:
##EQU3##
where .alpha.>0 is a parameter of the filter defining the amplitude of the
smoothing effect caused by the filter. This parameter is predetermined.
The result of the energy standardization operation carried out with the
first estimates produced by the first sub-assembly is that these
neighboring estimates having predefined energy are maintained, and this
whatever the scale of the signal sources. The first estimates will thus
converge to the same standardized energy. This is not always acceptable in
all the applications where non-stationary source signals appear. For
example, let us consider the case where the source signals are speech
signals with periods in which the signals have much energy (loud words)
and periods in which the signals have little energy (soft words). In the
situation described previously, the first estimates would all have the
same high energy level in these two situations which narrows down to
leveling the energy.
To remedy this effect, according to the invention (FIG. 7) an after
treatment is given to the first estimates X.sub.i (t). Therefore, each
first estimate X.sub.i (t) of rank i is divided by the separation
coefficient W.sub.ii corresponding to its rank, appearing in the equations
3 and 4. This has something in common with a destandardization or with an
auto-adaptive gain control. It will easily be noticed that the three
estimates X.sub.i (t)=X.sub.i (t)/W.sub.ii thus obtained are proportional
to the source signals which correspond to X.sub.i (t) with a constant
proportionality factor. This operation is carried out in the output module
17 represented in FIG. 7.
Thus, the processing steps first consist of multiplying the mixed signals
by the separation coefficients W.sub.ij, then producing the first
standardized estimates X.sub.i (t) and after that dividing them by the
same separation coefficients W.sub.ii to obtain third destandardized
estimates X.sub.i (t)=X.sub.i (t)/W.sub.ii. It should be observed that
these operations are not redundant and do not cancel each other.
Another particular embodiment of the invention relates to the case of two
non-stationary signals for which there is only one non-zero source signal
X.sub.i (t) during a given period, or, more particularly, to the case of
two source signals where one of these signals is very strong compared with
the other. In that case, this strong source signal will give rise to an
estimate (first or second, as the case may be) which will appear on the
two output channels of the device according to the previous embodiments,
that is to say, if the signal X.sub.1 (t) is strong, then the other signal
X.sub.2 (t) will be stronger in its turn, the estimate X.sub.1 (t) will
not only appear on channel 1 (assigned to the signal X.sub.1 (t)), but
also on the channel 2. And, vice versa when the signal X.sub.2 (t) becomes
strong.
For handling this case, the third sub-assembly 15 has at the output a
selection module 19 which prevents an estimate from being duplicated on a
channel assigned to an absent source signal. The selection module 19 is
connected to the output of the output module 17 (FIG. 7) so as to obtain
the diagram represented in FIG. 8. This module 19 operates in the
following manner:
if the two signals arriving at its inputs are correlated, then the module
19 produces the signal that has the higher amplitude and keeps the other
output at zero;
if the two signals are not correlated, the processing is carried out
independently of the block as has been described previously.
For implementing the function of this module 19, one may be facing:
a sub-block which detects the proportionality of the two input signals of
this module 19 based, for example, on a correlation test which activates
the correct multiplexing of the signals arriving there;
or a source separation module similar to that used for the separation of
sources provided in the description or similar to that described in the
document by C. Jutten and J. Herault cited previously. But in that case,
the signals which are to be processed are no "hard to process"mixed
signals, because at this level they are signals which are either
correlated or not.
The case with two signals is given by way of example, while the selection
may be effected between more than two signals.
FIG. 9 represents a particular embodiment of FIG. 8 in the case where there
are only two mixed signals E.sub.1 (t) and E.sub.2 (t). The same
references are used for FIG. 9 and for FIG. 2. The unit 16 for limiting
the amplitude applies limited estimates .sub.1 (t) and .sub.2 (t) to the
modules 161 to 164 which calculate the new separation coefficients. The
output sub-units 17.sub.1 and 17.sub.2 calculate
X.sub.1 (t)=X.sub.1 (t)/W.sub.11 and X.sub.2 (t)=X.sub.2 (t)/W.sub.22,
respectively.
When one of the signals E.sub.1 (t) or E.sub.2 (t) is momentarily absent or
very weak, the selection unit 19 provides that the estimate of one signal
is not simultaneously duplicated on the channel not assigned to this
signal.
* * * * *
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