Blind signal processing system employing information maximization to recover unknown signals through unsupervised minimization of output redundancy

A neural-network implemented method for recovering one or more of a plurality I of independent source signals (S.sub.i) from a plurality J>I of sensor signals (X.sub.j) each including a combination of at least some of said source signals (S.sub.i) wherein 0<i<I>1 and 0<j.ltoreq.J>I are integers, said method comprising:

• (a) selecting a plurality I of bias weights (W.sub.i0) and a plurality I.sup.2 of scaling weights (W.sub.ij);
• (b) adjusting said bias weights (W.sub.i0) and said scaling weights (W.sub.ij) by repeatedly performing the steps of:
• (b.1) producing a plurality I of estimation signals (U.sub.i) responsive to said sensor signals (X.sub.j) such that (U.sub.i)=(W.sub.ij)(X.sub.j)+(W.sub.i0),
• (b.2) producing a plurality I of training signals (Y.sub.i) responsive to a transformation of said sensor signals (X.sub.j) such that Y.sub.i =g(U.sub.i), wherein g(x) is a nonlinear function and the Jacobian of said transformation is J=det(.differential.Y.sub.i /.differential.X.sub.j) when J=I, and
• (b.3) adjusting each said bias weight W.sub.i0 and each said scaling weight W.sub.ij responsive to one or more samples of said training signals (Y.sub.i) such that said each bias weight W.sub.i0 is changed proportionately to a bias measure .DELTA.W.sub.i0 accumulated over said one or more samples and said each scaling weight W.sub.ij is changed proportionately to a corresponding scaling measure .DELTA.W.sub.ij =.epsilon..multidot..differential.(ln.vertline.J.vertline.)/.differential. W.sub.ij accumulated over said one or more samples, wherein .epsilon.>0 is a learning rate;
• and
• (c) producing said estimation signals (U.sub.i) to represent said one or more recovered source signals (S.sub.i).

A method implemented in a transversal filter having an input for receiving a sensor signal X that includes a combination of multipath reverberations of a source signal S and having a plurality I of delay line tap output signals (T.sub.i) distributed at intervals of one or more time delays .tau., said source signal S and said sensor signal X varying with time over a plurality J.gtoreq.I of said time delay intervals .tau. such that said sensor signal X has a value X.sub.j at time .tau.(j-1) and each said delay line tap output signal T.sub.i has a value X.sub.j+1-i representing said sensor signal value X.sub.j delayed by a time interval .tau.(i-1), wherein .tau.>0 is a predetermined constant and 0<i.ltoreq.I>1 and 0<j.ltoreq.J.gtoreq.I are integers, said method recovering said source signal S from said sensor signal X and comprising:

• (a) selecting a plurality I of filter weights (W.sub.i);
• (b) adjusting said filter weights (W.sub.i) by repeatedly performing the steps of
• (b.1) producing a plurality K=I of weighted tap output signals (V.sub.k) by combining said delay line tap output signals (T.sub.i) such that (V.sub.k)=(F.sub.ki) (T.sub.i), wherein 0<k.ltoreq.K=I>1 are integers, and wherein F.sub.ki =W.sub.k+1-i when 1.ltoreq.k+1-i.ltoreq.I and F.sub.ki =0 otherwise,
• (b.2) summing a plurality K=I of said weighted tap signals (V.sub.k) to produce an estimation signal ##EQU24## wherein said estimation signal U has a value U.sub.j at time .tau.(j-1), (b.3) producing a plurality J of training signals (Y.sub.j) responsive to a transformation of said sensor signal values (X.sub.j) such that Y.sub.j =g(U.sub.j) wherein g(x) is a nonlinear function and the Jacobian of said transformation is J=det(.differential.Y.sub.i /.differential.X.sub.j) when J=I, and
• (b.4) adjusting each said filter weight W.sub.i responsive to one or more samples of said training signals (Y.sub.j) such that said each filter weight W.sub.i is changed proportionately to a corresponding leading measure .DELTA.W.sub.1 accumulated over said one or more samples when i=1 and a corresponding scaling measure .DELTA.W.sub.i =.epsilon..multidot..differential.(ln.vertline.J.vertline.)/.differential. W.sub.i accumulated over said one or more samples otherwise;
• and
• (c) producing said estimation signal U to represent said recovered source signal S.

A neural network for recovering a plurality of source signals from a plurality of mixtures of said source signals, said neural network comprising:

• input means for receiving a plurality J of input signals (X.sub.j) each including a combination of at least some of a plurality I of independent source signals (S.sub.i), wherein 0<i.ltoreq.I>1 and 0<j.ltoreq.J.gtoreq.I are integers;
• weight means coupled to said input means for storing a plurality I of bias weights (W.sub.i0) and a plurality I.sup.2 of scaling weights (W.sub.ij);
• output means coupled to said weight means for producing a plurality I of output signals (U.sub.i) responsive to said input signals (X.sub.j) such that (U.sub.i)=(W.sub.ij) (X.sub.j)+(W.sub.i0);
• training means coupled to said output means for producing a plurality I of training signals (Y.sub.i) responsive to a transformation of said input signals (X.sub.j) such that Y.sub.i =g(U.sub.i),
• wherein g(x) is a nonlinear function and the Jacobian of said transformation is J=det(.differential.Y.sub.i /.differential.X.sub.j) when J=I;
• adjusting means coupled to said training means and said weight means for adjusting said bias weights (W.sub.i0) and said scaling weights (W.sub.ij) responsive to one or more samples of said training signals (Y.sub.i) such that each said bias weight W.sub.i0 is changed proportionately to a corresponding bias measure .DELTA.W.sub.i0 accumulated over said one or more samples and each said scaling weight W.sub.ij is changed proportionately to a corresponding scaling measure .DELTA.W.sub.ij =.epsilon..multidot..differential.(ln.vertline.J.vertline.)/.differential. W.sub.ij accumulated over said one or more samples, wherein .epsilon.>0 is a learning rate.

A system for adaptively cancelling one or more interferer signals (S.sub.n) comprising:

• input means for receiving a plurality J of input signals (X.sub.j) each including a combination of at least some of a plurality I of independent source signals (S.sub.i) that includes said one or more interferer signals (S.sub.n), wherein 0<i.ltoreq.I>1, 0<j.ltoreq.J.gtoreq.I and 0<n.ltoreq.N.gtoreq.1 are integers;
• weight means coupled to said input means for storing a plurality I of bias weights (W.sub.i0) and a plurality I.sup.2 of scaling weights (W.sub.ij);
• output means coupled to said weight means for producing a plurality I of output signals (U.sub.i) responsive to said input signals (X.sub.j) such that (U.sub.i)=(W.sub.ij) (X.sub.j)+(W.sub.i0);
• training means coupled to said output means for producing a plurality I of training signals (Y.sub.i) responsive to a transformation of said input signals (X.sub.j) such that Y.sub.i =g(U.sub.i), wherein g(x) is a nonlinear function and the Jacobian of said transformation is J=det(.differential.Y.sub.i /.differential.X.sub.j);
• adjusting means coupled to said training means and said weight means for adjusting said bias weights (W.sub.i0) and said scaling weights (W.sub.ij) responsive to one or more samples of said training signals (Y.sub.i) such that each said bias weight W.sub.i0 is changed proportionately to a corresponding bias measure .DELTA.W.sub.i0 accumulated over said one or more samples and each said scaling weight W.sub.ij is changed proportionately to a corresponding scaling measure .DELTA.W.sub.ij =.epsilon..multidot..differential.(ln.vertline.J.vertline.)/.differential. W.sub.ij accumulated over said one or more samples, wherein .epsilon.>0 is a learning rate;
• and
• feedback means coupled to said output means and said input means for selecting one or more said output signals (U.sub.n) representing said one or more interferer signals (S.sub.n) for combination with said input signals (X.sub.j), thereby cancelling said interferer signals (S.sub.n).