Signal separating device, signal separating method, information recording medium, and program

A signal separating method executed by a signal separating device having an iterative estimator, a repeating calculator, and a result output unit that separates an observed signal matrix X having m rows and T columns into matrices A, S and N such that

• X=c(A,S)+N
• is satisfied for a predefined matrix operation c(•, •), wherein A is a mixing matrix having m rows and n columns, S is a source signal matrix having n rows and T columns, and N is a noise matrix having m rows and T columns, and wherein the signal separating method comprises:
• an iterative estimation step, wherein the iterative estimator operates with respect to a matrix function J(•, •, •) that takes a matrix having m rows and T columns, a matrix having m rows and n columns, and a matrix having n rows and T columns, and returns a scalar value, wherein, upon receiving a matrix having m rows and T columns, a matrix having m rows and n columns, and a matrix having n rows and T columns, the iterative estimator iteratively estimates, through a predetermined number of repetitions, a combination of arguments, which are a matrix having m rows and n columns, and a matrix having n rows and T columns, whereby the scalar value returned by the matrix function J(•, •, •) is extremized when the matrix having m rows and T columns is fixed;
• a repeating calculation step, wherein the repeating calculator calculates, by repetition, L number of matrices A1, A2, A3, . . . , AL such that
• c(A1,c(A2,c(A3,c( . . . , c(AL-1,AL) . . . ))))
• yields a matrix of m rows and n columns, wherein the repeating calculator defines a matrix
• S0=X
• wherein, during the i-th repetition (i=1, 2, 3, . . . , L), the repeating calculator supplies to the iterative estimator a matrix Si-1 having m rows and T columns, a predefined initial value matrix having m rows and n columns, and a predefined initial value matrix having n rows and T columns for a matrix function Ji(•, •, •) of the i-th repetition, thereby causing the iterative estimator to make iterative estimations with respect to the matrix function Ji(•, •, •) that takes a matrix having m rows and T columns, a matrix having m rows and n columns, and a matrix having n rows and T columns, and returns a scalar value, with the repeating calculator then taking the resulting matrix of m rows and n columns to be Ai, and also taking the matrix of n rows and T columns to be Si;
• and
• a result output step, wherein the result output unit calculates a mixing matrix A of m rows and n columns by evaluating
• A=c(A1,c(A2,c(A3,c( . . . , AL) . . . ))))
• using the calculated L number of matrices A1, A2, A3, AL, takes the calculated matrix SL of n rows and T columns to be the source signal matrix S of n rows and T columns, and then outputs the matrices A and S.

A non-transitory computer readable information recording medium storing a program that causes a computer to separate an observed signal matrix X having m rows and T columns into matrices A, S and N such that

• X=c(A,S)+N
• is satisfied for a predefined matrix operation c(•, •), wherein A is a mixing matrix having m rows and n columns, S is a source signal matrix having n rows and T columns, and N is a noise matrix having m rows and T columns, and wherein the program causes the computer to function as:
• an iterative estimator that operates with respect to a matrix function J(•, •, •) that takes a matrix having m rows and T columns, a matrix having m rows and n columns, and a matrix having n rows and T columns, and returns a scalar value, wherein, upon receiving a matrix having m rows and T columns, a matrix having m rows and n columns, and a matrix having n rows and T columns, the iterative estimator iteratively estimates, through a predetermined number of repetitions, a combination of arguments, which are a matrix having m rows and n columns, and a matrix having n rows and T columns, whereby the scalar value returned by the matrix function J(•, •, •) is extremized when the matrix having m rows and T columns is fixed;
• a repeating calculator that calculates, by repetition, L number of matrices A1, A2, A3, . . . , AL such that
• c(A1,c(A2,c(A3,c( . . . , c(AL-1,AL) . . . ))))
• yields a matrix of m rows and n columns, wherein the repeating calculator defines a matrix
• S0=X
• wherein, during the i-th repetition (i=1, 2, 3, . . . , L), the repeating calculator supplies to the iterative estimator a matrix Si-1 having m rows and T columns, a predefined initial value matrix having m rows and n columns, and a predefined initial value matrix having n rows and T columns for a matrix function Ji(•, •, •) of the i-th repetition, thereby causing the iterative estimator to make iterative estimations with respect to the matrix function J(•, •, •) that takes a matrix having m rows and T columns, a matrix having m rows and n columns, and a matrix having n rows and T columns, and returns a scalar value, with the repeating calculator then taking the resulting matrix of m rows and n columns to be Ai, and also taking the matrix of n rows and T columns to be Si;
• and
• a result output unit that calculates a mixing matrix A of m rows and n columns by evaluating
• A=c(A1,c(A2,c(A3,c( . . . , c(AL-1,AL) . . . ))))
• using the calculated L number of matrices A1, A2, A3, . . . , AL, takes the calculated matrix SL of n rows and T columns to be the source signal matrix S of n rows and T columns, and then outputs the matrices A and S.