Fast wavelet estimation of weak bio-signals using novel algorithms for generating multiple additional data frames

• US 20030185408A1
• Filed: 03/29/2002
• Published: 10/02/2003
• Est. Priority Date: 03/29/2002
• Status: Active Grant

• Current Assignee: Brainscope SPV LLC, Washington University In St Louis
• Original Assignee: Washington University In St Louis
• Inventors: Causevic, Elvir, Wickerhauser, Mladen Victor, Causevic, Eldar
• Granted Patent: US 7,054,454 B2
• Time in Patent Office: Days
• US Class Current: 381/94.1
• CPC Class Codes: A61B 5/121 evaluating hearing capacity
• CPC Class Codes: A61B 5/38 Acoustic or auditory stimuli
• CPC Class Codes: A61B 5/7203 for noise prevention, reduction or removal
• CPC Class Codes: A61B 5/726 using Wavelet transforms
• CPC Class Codes: G06F 2218/06 by applying a scale-space analysis, e.g. using wavelet analysis
• CPC Class Codes: G10L 21/0208 Noise filtering
• CPC Class Codes: G10L 25/27 characterised by the analysis technique
• CPC Class Codes: H03G 3/007 Control dependent on the supply voltage

Abstract

A method and apparatus for de-noising weak bio-signals having a relatively low signal to noise ratio utilizes an iterative process of wavelet de-noising a data set comprised of a new set of frames of wavelet coefficients partially generated through a cyclic shift algorithm. The method preferably operates on a data set having 2^N frames, and the iteration is performed N−1 times. The resultant wavelet coefficients are then linearly averaged and an inverse discrete wavelet transform is performed to arrive at the de-noised original signal. The method is preferably carried out in a digital processor.

Claims

1. A signal processor for de-noising an input signal, said signal processor including a memory for storing said input signal as an array A1 of a plurality of component frames, and a processor configured to:

(a) perform a wavelet transform on each of said component frames to thereby create a corresponding array of wavelet coefficients;

(b) iteratively for at least one repetition (i) combine multiple numbers of said wavelet coefficients into a plurality of resultant wavelet coefficients forming an array A2 of a like number 2^N of wavelet coefficients, each of said resultant wavelet coefficients being formed from a different combination of wavelet coefficients determined from the original set of wavelet coefficients or the previous iteration, as appropriate; and

(ii) wavelet de-noising each resultant wavelet coefficient of array A2; and

(c) combine the resultant wavelet coefficients resulting from the last iteration to form a combined resultant wavelet coefficient.

2. The signal processor of claim 1 wherein said input signal is characterized by a relatively low signal to noise ratio, and wherein said processor is configured to combine different wavelet coefficients to create each resultant wavelet coefficient.

3. The signal processor of claim 2 wherein said processor is configured to use a different threshold for discrete wavelet de-noising in each iteration.

4. The signal processor of claim 2 wherein said processor is configured to combine adjacent pairs of wavelet coefficients in a cyclic manner to create at least some of the resultant wavelet coefficients.

5. The signal processor of claim 2 wherein the processor is configured to combine the final array of iterated wavelet coefficients by averaging them.

6. The signal processor of claim 2 wherein the processor is configured to combine said wavelet coefficients by Euler-Fermat reordering.

7. The signal processor of claim 2 wherein the processor is configured to combine said wavelet coefficients by creating all mathematical permutations thereof to produce N! frames of wavelet coefficients.

8. A method for de-noising an input signal, said method utilizing a signal processor including a memory for storing said input signal as an array A1 of 2^N component frames, said method comprising the steps of:

(a) performing a discrete wavelet transform on each of said component frames to thereby determine a corresponding array of wavelet coefficients;

(b) iteratively for N−

1 repetitions (i) combining multiple numbers of the wavelet coefficients determined from the previous step or iteration, as appropriate, into a plurality of resultant wavelet coefficients forming an array A2 of a like number 2^N of wavelet coefficients, each of said resultant wavelet coefficients being formed from a different combination of wavelet coefficients; and

(ii) wavelet de-noising each wavelet coefficient of array A2; and

(c) combining the resultant wavelet coefficients resulting from the iteration to form a combined resultant wavelet coefficient; and

(d) performing an inverse discrete wavelet transform on the combined resultant wavelet coefficient to thereby produce the de-noised input signal.

9. The method of claim 8 wherein said input signal is characterized by a relatively low signal to noise ratio, and further comprising the step of combining different wavelet coefficients to create each resultant wavelet coefficient.

10. The method of claim 9 further comprising the step of using a different threshold for discrete wavelet de-noising in each iteration.

11. The method of claim 9 further comprising the step of combining adjacent pairs of wavelet coefficients in a cyclic manner to create at least some of the resultant wavelet coefficients.

12. The method of claim 9 further comprising the step of combining the final array of iterated wavelet coefficients by averaging them.

13. The method of claim 9 further comprising the step of combining said wavelet coefficients by Euler-Fermat reordering.

14. The method of claim 9 further comprising the step of combining said wavelet coefficients by creating all mathematical permutations thereof to produce N! wavelet coefficients.

15. A signal de-noiser, said signal de-noiser comprising a processor configured to process a plurality of 2^N frames of sampled data comprising the signal, said processor being further configured to

(a) perform a discrete wavelet transform operation on each of said sampled data frames to thereby create a corresponding frame of wavelet coefficients;

(b) iteratively (i) construct a plurality of frames of wavelet coefficients; and

(ii) de-noise each constructed plurality of frames of wavelet coefficients;

(d) combine the final plurality of frames of wavelet coefficients into a final frame of wavelet coefficients; and

(e) inverse discrete wavelet transform said final frame of wavelet coefficients.

16. The signal de-noiser of claim 15 wherein the processor is further configured to use cyclic tree re-cycling to construct the plurality of frames of wavelet coefficients.

17. The signal de-noiser of claim 16 wherein the processor is further configured to perform N−

1 iterations.

18. The signal de-noiser of claim 17 wherein the processor is further configured to use a different threshold for each de-noising step.

19. The signal de-noiser of claim 18 wherein the processor is further configured to combine the final plurality of wavelet coefficient frames by averaging them.

20. The signal de-noiser of claim 15 wherein the processor is configured to iteratively construct and de-noise frames of wavelet coefficients a plurality of times.

21. A method of de-noising a signal by using a processor, said signal comprising a plurality of 2^N frames of sampled data, the method comprising the steps of:

(a) performing a discrete wavelet transform operation on each of said sampled data frames to thereby create a corresponding frame of wavelet coefficients;

(b) iteratively (i) constructing a plurality of frames of wavelet coefficients; and

(ii) de-noising each constructed plurality of frames of wavelet coefficients;

(d) combining the final plurality of frames of wavelet coefficients into a final frame of wavelet coefficients; and

(e) inverse discrete wavelet transforming said final frame of wavelet coefficients.

22. The method of claim 21 further comprising the step of using cyclic tree re-cycling to construct the plurality of frames of wavelet coefficients.

23. The method of claim 22 wherein the step of iteratively constructing and de-noising includes performing N-I iterations.

24. The method of claim 23 further comprising the step of using a different threshold for each de-noising step.

25. The method of claim 24 wherein the step of combining the final plurality of wavelet coefficients includes averaging them.

26. A signal processor for de-noising an input signal, said signal processor including a memory for storing said input signal as an array Al of a plurality of component frames, and a processor configured to:

(a) perform a wavelet transform on each of said component frames to thereby create a corresponding array of wavelet coefficients;

(b) iteratively for at least one repetition (i) combine multiple numbers of said wavelet coefficients into a plurality of resultant wavelet coefficients forming an array A2 of wavelet coefficients, each of said resultant wavelet coefficients being formed from a different combination of wavelet coefficients determined from the original set of wavelet coefficients or the previous iteration, as appropriate; and

(ii) wavelet de-noising each resultant wavelet coefficient of array A2; and

(c) combine the resultant wavelet coefficients resulting from the last iteration to form a combined resultant wavelet coefficient.

27. The signal processor of claim 26 wherein said processor is further configured to use a different threshold in different iterations of de-noising.

28. The signal processor of claim 26 wherein said processor is further configured to decrease the threshold by a factor of (½

)^K between iterations.

29. The signal processor of claim 26 wherein the processor is further configured to perform an inverse wavelet transform on the combined resultant wavelet coefficient to thereby produce the de-noised input signal.

30. The signal processor of claim 26 wherein said input signal is characterized by a relatively low signal to noise ratio, and wherein said processor is configured to combine different wavelet coefficients to create each resultant wavelet coefficient.

31. The signal processor of claim 26 wherein said processor is configured to use a different threshold for discrete wavelet de-noising in each iteration.

32. The signal processor of claim 26 wherein said processor is configured to combine adjacent pairs of wavelet coefficients in a cyclic manner to create at least some of the resultant wavelet coefficients.

33. The signal processor of claim 26 wherein the processor is configured to combine the final array of iterated wavelet coefficients by averaging them.

34. The signal processor of claim 26 wherein the processor is configured to combine said wavelet coefficients by Euler-Fermat reordering.

35. The signal processor of claim 26 wherein the processor is configured to combine said wavelet coefficients by creating all mathematical permutations thereof to produce N! frames of wavelet coefficients.

36. The signal processor of claim 26 wherein said input signal varies, and wherein said processor is further configured to select portions of said input signal for separate de-noising processing

37. The signal processor of claim 27 wherein said processor is further configured to assemble the combined resultant wavelet coefficients so as to reconstruct them corresponding to the input signal.

38. A signal processor for de-noising an input signal, said signal processor including a memory for storing said input signal as a plurality of component frames, and a processor configured to:

(a) separately perform a wavelet de-noising operation on each of said component frames to produce a first plurality of de-noised frames;

(b) re-order the component frames and perform a wavelet de-noising operation on each of said frames to produce a second plurality of de-noised frames; and

(b) combine the first and second pluralities of resultant de-noised frames to form a combined frame of resultant de-noised wavelet coefficients.

39. The signal processor of claim 38 wherein the processor is further configured to iteratively de-noise the individual frames for a plurality of times as part of each de-noising operation before the resultant de-noised frames are finally combined into a frame of combined resultant de-noised wavelet coefficients.

40. The signal processor of claim 39 wherein the processor is configured to combine multiple numbers of frames before each iteration.

41. The signal processor of claim 39 wherein the processor is further configured to use a different threshold for each iteration of de-noising.

42. The signal processor of claim 39 wherein the input signal is comprised of an array A1 or 2^N frames, and the processor is further configured to perform up to N−

1 de-noising iterations.

43. A method for de-noising an input signal using a signal processor, said signal processor including a memory for storing said input signal as an array A1 of a plurality of component frames, said method comprising the steps of:

(a) performing a wavelet transform on each of said component frames to thereby create a corresponding array of wavelet coefficients;

(b) iteratively for at least one repetition (i) combining multiple numbers of said wavelet coefficients into a plurality of resultant wavelet coefficients forming an array A2 of wavelet coefficients, each of said resultant wavelet coefficients being formed from a different combination of wavelet coefficients determined from the original set of wavelet coefficients or the previous iteration, as appropriate; and

(ii) wavelet de-noising each resultant wavelet coefficient of array A2; and

(c) combining the resultant wavelet coefficients resulting from the last iteration to form a frame of combined resultant wavelet coefficients.

44. The method of claim 43 wherein the step of wavelet de-noising includes using a different threshold in different iterations of de-noising.

45. The method of claim 43 wherein the step of wavelet de-noising includes decreasing the threshold by a factor of (½

)^K between iterations.

46. The method of claim 43 further comprising the step of performing an inverse wavelet transform on the frame of combined resultant wavelet coefficients to thereby produce the de-noised input signal.

47. The method of claim 43 wherein said input signal is characterized by a relatively low signal to noise ratio, and wherein the combining step includes combining different wavelet coefficients before de-noising to thereby create each resultant wavelet coefficient.

48. The method of claim 43 wherein the de-noising step includes using a different threshold for discrete wavelet de-noising in each iteration.

49. The method of claim 43 wherein the combining step includes combining adjacent pairs of wavelet coefficients in a cyclic manner before de-noising to thereby create at least some of the resultant wavelet coefficients.

50. The method of claim 43 wherein the step of combining the final array of iterated wavelet coefficients includes averaging them.

51. The method of claim 43 wherein the combining step includes combining said wavelet coefficients by Euler-Fermat reordering.

52. The method of claim 43 wherein the combining step includes combining said wavelet coefficients by creating all mathematical permutations thereof to produce N! frames of wavelet coefficients.

53. The method of claim 43 wherein said input signal varies, and further comprising the step of selecting portions of said input signal for separate de-noising processing

54. The method of claim 43 wherein further comprising the step of assembling the combined resultant wavelet coefficients so as to reconstruct them corresponding to the input signal.

55. A method for de-noising an input signal using a signal processor, said signal processor including a memory for storing said input signal as a plurality of component frames, the method comprising the steps of:

(a) separately performing a wavelet de-noising operation on each of said component frames to produce a first plurality of de-noised frames;

(b) re-ordering the component frames and performing a wavelet de-noising operation on each of said frames to produce a second plurality of de-noised frames; and

(b) combining the first and second pluralities of resultant de-noised frames to form a combined frame of resultant de-noised wavelet coefficients.

56. The method of claim 55 wherein the step of wavelet de-noising includes iteratively de-noising the individual frames for a plurality of times as part of each de-noising operation before the resultant de-noised frames are finally combined into a frame of combined resultant de-noised wavelet coefficients.

57. The method of claim 56 further comprising the step of combining multiple numbers of frames before each iteration.

58. The method of claim 56 wherein the de-noising step includes using a different threshold for each iteration of de-noising.

59. The method of claim 56 wherein the input signal is comprised of an array A1 or 2^N frames, and the step of iteratively de-noising includes performing up to N−

1 de-noising iterations.