Deflation and decomposition of data signals using reference signals
A system processes data signals consisting of sums of independent signal terms, zero or more of which signal terms may already have been identified, in order to generate one or more additional terms. Deflated versions of the data signals are created by subtracting from the data signals any previously identified signal terms. Additional independent signal terms are computed using a set of reference signals organized into mutually independent partioning support sets. The images of each support set are computed on the data signals. Computed images on a data signal that are non-zero are identified as additional independent signal terms of that data signal.
1. A method for generating additional independent signal terms (ISTs) of a data signal given an initial set of ISTs of that data signal and at least one mutually independent partitioning support set of reference signals, the initial set of ISTs including zero or more ISTs, the method comprising:
(1) generating a deflated data signal by subtracting the sum of all of the ISTs in the initial set of ISTs from the data signal;
(2) generating an optimal image of each of the at least one mutually independent partitioning support sets on the deflated data signal;
(3) testing each generated optimal image so as to identify each non-zero optimal image; and
(4) identifying each non-zero optimal image as an additional independent signal term of the data signal.
2. The method of claim 1 , wherein the initial set of ISTs consists of zero ISTs, and wherein the method further comprises:
(5) generating additional independent signal terms of the data signal by performing the following steps at least once:
a. creating an augmented set of ISTs by adding any previously-generated additional independent signal terms to the initial set of ISTs; and
b. generating additional independent signal terms of the data signal, using the augmented set of ISTs as the initial set of ISTs.
3. The method of claim 1 , further comprising:
(5) before (1), generating at least one of the reference signals in the at least one mutually independent partitioning set of reference signals by linearly filtering signals generated by a blind source separation algorithm.
4. The method of claim 3 , wherein the additional independent signal terms (ISTs) of the data signal represents a response of a sensor.
5. The method of claim 4 , wherein the sensor comprises an acoustic sensor.
6. A system comprising at least one non-transitory computer readable medium having stored thereon computer program instructions executable by at least one computer processor to perform a method for generating additional independent signal terms (ISTs) of a data signal given an initial set of ISTs of that data signal and at least one mutually independent partitioning support set of reference signals, the initial set of ISTs including zero or more ISTs, the method comprising:
(1) generating a deflated data signal by subtracting the sum of all of the ISTs in the initial set of ISTs from the data signal;
(2) generating an optimal image of each of the at least one mutually independent partitioning support sets on the deflated data signal;
(3) testing each generated optimal image so as to identify each non-zero optimal image; and
(4) identifying each non-zero optimal image as an additional independent signal term of the data signal.
7. The system of claim 6 , wherein the initial set of ISTs consists of zero ISTs, and wherein the method further comprises:
(5) generating additional independent signal terms of the data signal by performing the following steps at least once:
c. creating an augmented set of ISTs by adding any previously-generated additional independent signal terms to the initial set of ISTs; and
d. generating additional independent signal terms of the data signal, using the augmented set of ISTs as the initial set of ISTs.
8. The system of claim 6 , wherein the method further comprises:
(5) before (1), generating at least one of the reference signals in the at least one mutually independent partitioning set of reference signals by linearly filtering signals generated by a blind source separation algorithm.
9. The system of claim 8 , wherein the additional independent signal terms (ISTs) of the data signal represents a response of a sensor.
10. The system of claim 9 , wherein the sensor comprises an acoustic sensor.