Method of noise reduction using instantaneous signal-to-noise ratio as the principal quantity for optimal estimation

1. A method of identifying an estimate for a clean signal random variable representing a portion of a clean signal found within a noisy signal, the method comprising:

defining a mapping random variable as a function of at least the clean signal random variable and a noise random variable;

determining a model parameter that describes at least one aspect of a distribution of values for the mapping random variable, wherein determining a model parameter comprises approximating a function of the mapping random variable using a Taylor series expansion; and

using the model parameter to determine an estimate for the clean signal random variable from an observed value.

2. The method of claim 1 wherein defining the mapping random variable as a function of at least the clean signal random variable and the noise random variable comprises defining the mapping variable as a ratio of the clean signal random variable to the noise random variable.

3. The method of claim 2 wherein determining a model parameter comprises determining a mean of the mapping random variable.

4. The method of claim 1 further comprising using the model parameter to determine an estimate of the mapping random variable.

5. The method of claim 4 wherein defining the mapping random variable as a function of at least the clean signal random variable and the noise random variable comprises defining the mapping variable as a ratio of the clean signal random variable to the noise random variable.

6. The method of claim 1 further comprising performing an iteration comprising steps of:

calculating a mean for the mapping random variable using a Taylor series expansion;

setting a new expansion point for the Taylor series expansion equal to the mean of the mapping random variable; and

repeating the iteration steps using the new expansion point.

7. The method of claim 1 further comprising;

determining a clean signal model parameter that describes at least one aspect of a distribution of values for the clean signal random variable; and

using the clean signal model parameter to determine the estimate for the clean signal random variable.

8. The method of claim 7 further comprising:

determining a noise model parameter that describes at least one aspect of a distribution of values for the noise random variable; and

using the noise model parameter to determine the estimate for the clean signal random variable.

9. The method of claim 8 wherein determining the noise model parameter comprises determining the noise model parameter from noise estimates collected from the noisy signal.

10. A computer-readable storage medium storing computer-executable instructions for performing steps comprising:

defining a random variable as a function of a signal-to-noise ratio variable;

determining a mean for a distribution of the signal-to-noise ratio variable based on the defined function; and

using the mean to determine an estimate of a value for the signal-to-noise ratio variable for a frame of an observed signal.

11. The computer-readable storage medium of claim 10 wherein the random variable comprises a clean signal random variable representing a portion of a clean signal.

12. The computer-readable storage medium of claim 10 wherein the random variable comprises a noise signal random variable representing a noise in an observed signal.

13. The computer-readable storage medium of claim 10 wherein defining a random variable further comprises defining the random variable as a function of an observed value.

14. The computer-readable storage medium of claim 10 wherein determining a mean further comprises approximating at least a portion of the defined function with an approximation function.

15. The computer-readable storage medium of claim 14 wherein the approximation function comprises a Taylor series approximation.

16. The computer-readable storage medium of claim 15 wherein determining a mean further comprises performing an iteration.

17. The computer-readable storage medium of claim 16 wherein performing an iteration comprises performing steps of:

using the Taylor series approximation to determine a mean for the signal-to-noise ratio;

setting a new expansion point equal to the mean for the signal-to-noise ratio; and

repeating the step of using the Taylor series approximation to determine a mean while using the new expansion point.

18. The computer-readable storage medium of claim 10 further comprising using the mean to determine an estimate of the random variable.

19. The computer-readable storage medium of claim 18 wherein the random variable is a clean signal random variable representing a portion of a clean signal.

20. The computer-readable storage medium of claim 10 wherein determining a mean further comprises determining the mean based on a model parameter that describes a distribution of clean signal values, each clean signal value representing a portion of a clean signal.

21. The computer-readable storage medium of claim 10 wherein determining a mean further comprises determining the mean based on a model parameter that describes a distribution of noise values.

22. The computer-readable storage medium of claim 21 further comprising determining the mean from an observed signal.

23. A computer-readable storage medium storing computer-executable instructions for performing steps comprising:

defining a random variable as a function of a signal-to-noise ratio variable;

determining distribution parameters for the signal-to-noise ratio based on the defined function wherein determining a distribution parameter comprises approximating at least a portion of the defined function with a Taylor Series approximation; and

using the distribution parameters to determine an estimate of the signal-to-noise ratio.