Data processing: artificial intelligence – Neural network – Learning task
Reexamination Certificate
2000-03-10
2003-09-23
Starks, Jr., Wilbert L. (Department: 2121)
Data processing: artificial intelligence
Neural network
Learning task
C706S021000, C706S024000
Reexamination Certificate
active
06625587
ABSTRACT:
BACKGROUND OF THE INVENTION
1. Field of the Invention
The present invention relates to methods and apparatus for recovering original signal information or content by processing multiple measurements of a set of mixed signals. More specifically, the invention relates to adaptive systems for recovering several original signals from received measurements of their mixtures.
2. Discussion of Related Art
The recovery and separation of independent sources is a classic but difficult signal processing problem. The problem is complicated by the fact that in many practical situations, many relevant characteristics of both the signal sources and the mixing media are unknown.
To best understand the problem, the following problem statement is helpful: With reference to
FIG. 1
of the drawings, consider N independent signals
102
, s
1
(t), . . . , and s
N
(t). Independent signals
102
may represent any of, or a combination of, independent speakers or speeches, sounds, music, radio-based or light based wireless transmissions, electronic or optic communication signal, still images, videos, etc. Independent signals
102
may be delayed and superimposed with one another by means of natural or synthetic mixing in the medium or environment
104
through which they propagate. A signal separation process
106
transforms the mixture of independent signals
102
into output signals
108
, u
1
(t), . . . , and u
N
(t).
Two main categories of methods are often used for the recovery and separation of independent sources: neurally inspired adaptive algorithms and conventional discrete signal processing.
Neurally inspired adaptive architectures and algorithms follow a method originally proposed by J. Herault and C. Jutten, now called the Herault-Jutten (or HJ) algorithm. The suitability of this set of methods for CMOS integration have been recognized. However, the standard HJ algorithm is at best heuristic with suggested adaptation laws that have been shown to work mainly in special circumstances. The theory and analysis of prior work pertaining to the HJ algorithm are still not sufficient to support or guarantee the success encountered in experimental simulations. Herault and Jutten recognize these analytical deficiencies and they describe additional problems to be solved. Their proposed algorithm assumes a linear medium and no filtering or no delays. Specifically, the original signals are assumed to be transferred by the medium via a matrix of unknown but constant coefficients. To summarize, the Herault-Jutten method (i) is restricted to the full rank and linear static mixing environments, (ii) requires matrix inversion operations, and (iii) does not take into account the presence of signal delays. In many practical applications, however, filtering and relative signals delay so occur. Accordingly, previous work fails to successfully separate signals in many practical situations and real world applications.
Conventional signal processing approaches to signal separation originate mostly in the discrete domain in the spirit of traditional digital signal processing methods and use the statistical properties of signals. Such signal separation methods employ computations that involve mostly discrete signal transforms and filter/transform function inversion. Statistical properties of the signals in the form of a set of cumulants are used to achieve separation of mixed signals where correlation of these cumulants are mathematically forced to approach zero. This constitutes the crux of the family of algorithms that search for the parameters of transfer functions that recover and separate the signals from one another. Calculating all possible cumulants, on the other hand, would be impractical and too time consuming for real time implementation.
Conventional signal processing approaches to signal separation originate mostly in the discrete domain in the spirit of traditional digital signal processing methods and use the statistical properties of signals. Such signal separation methods employ computations that involve mostly discrete signal transforms and filter/transform function inversion. Statistical properties of the signals in the form of a set of cumulants are used to achieve separation of mixed signals where these cumulants are mathematically forced to approach zero. This constitutes the crux of the family of algorithms that search for the parameters of transfer functions that recover and separate the signals from one another. Calculating all possible cumulants, on the other hand, would be impractical and too time consuming for real time implementation.
The specifics of these two methods are elaborated on below.
Neurally Inspired Architecture and Algorithms for Signal Separation
These sets of neurally inspired adaptive approaches to signal separation assume that the “statistically independent” signal vector S(t)=[s
1
(t), . . . , and s
N
(t)]
T
is mixed to produce the signal vector M(t). The vector M(t) is received by the sensors (e.g. microphones, antenna, etc.).
Let the mixing environment be represented by the general (static or dynamic) operator &tgr;. Then,
M
(
t
)=&tgr;(
S
(
t
) Equation (1)
There are several formulations that can be used to invert the mixing process, i.e. operator &tgr;, in a “blind” fashion where no a priori knowledge exists as to the nature or content of the mixing operator &tgr; or the original sources S(t). We group these into two categories, static and dynamic. Additional distinctions can be made as to the nature of the employed adaptation criteria, e.g. information maximization, minimization of high order cumulants, etc.
The static case. The static case is limited to mixing by a constant nonsingular matrix. Let us assume that the “statistically independent” signal vector S(t)=[s
1
(t), . . . , and s
N
(t)]
T
is mixed to produce the signal vector M(t). Specifically, let the mixing operator &tgr; be represented by a constant matrix A, namely
M
(
t
)=
AS
(
t
) Equation (2)
FIGS. 2A and 2B
show two architectures of the signal separation and recovery network in case of static mixing by a mixing matrix A. U(t) is the output which approximates the original source signals S(t). Y(t) contains the values that are used in updating the parameters of the unmixing process, i.e., W in
FIG. 2A and D
in FIG.
2
B. The architecture in
FIG. 2A
necessarily computes the inverse of the constant mixing matrix A, which requires that A is invertible, i.e. A
−1
exists. The Architecture of
FIG. 2B
does not impose the restriction in that upon convergence of off diagonal elements of the matrix D are exactly those of off diagonal elements of the matrix A. In this case, however, diagonal elements of the matrix A are restricted to equal “1.0.” By setting the elements of D to zero, one essentially concludes that the mixing process may be invertible even if the mixing matrix is not. A shown in
FIGS. 2A and 2B
, the weight update utilizes a function of the output U(t). The update of the entries of these tow matrices is defined by the criteria used for signal separation, discrimination or recovery, e.g., information maximization, minimization of higher order cumulants, etc.
As an example, one possible weight update rule for the case where
U
(
t
)=
WM
(
t
) Equation (3)
could be
w
.
ij
=
η
[
W
-
T
+
g
″
(
u
)
g
′
(
u
)
M
T
]
ij
Equation (4)
where &eegr; is sufficiently small, g is an odd function, and M is the set of mixtures, U is the set of outputs which estimate the source signals, subscript T denotes transpose, and −T denotes inverse of transpose. Note that the function g plays an additional role in the update which can be related to the above, diagram as
Y
(
t
)=
g
(
U
(
t
)) Equation (5)
One uses Equation (4) to update the entries of W in Equation (3). Through this iterative update procedure, the entries of W converge so that the product WA is nearly equal to the identity matrix or a permutation of the identity matrix.
On the other hand, in
Erten Gamze
Salam Fathi M.
Brooks & Kushman P.C.
Clarity, LLC
Hirl Joseph P.
Starks, Jr. Wilbert L.
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