Matching pursuits subband coding of data

1. A method for coding multi-dimensional data using a codebook of basis functions, comprising:

(a) applying a transform to the multi-dimensional data to create transform coefficients, wherein the multi-dimensional data has a total number of dimensions greater than a total number of dimensions of the codebook of basis functions;

(b) forming groups of the transform coefficients; and

(c) coding different ones of the groups of the transform coefficients using matching pursuits coding with non-identical dictionaries of basis functions from the codebook of basis functions.

2. The method of claim 1 , wherein step (c) comprises using subsets of a master basis dictionary in the non-identical dictionaries of basis functions.

3. The method of claim 2 , wherein step (c) comprises using non-overlapping subsets of the master basis dictionary in the non-identical dictionaries of basis functions.

4. The method of claim 2 , wherein step (c) comprises using overlapping subsets of the master basis dictionary in the non-identical dictionaries of basis functions.

5. The method of claim 2 , wherein step (c) comprises using data indicative of the subsets of the master basis dictionary.

6. The method of claim 2 , further comprising:

(d) communicating the subsets with a decoder.

7. The method of claim 2 , further comprising:

(d) communicating the subsets in a form of a sampled value of a function with a decoder.

8. The method of claim 2 , further comprising:

(d) communicating data indicative of the subsets with a decoder.

9. The method of claim 2 , further comprising:

(d) using a mask applied to the master basis dictionary to identify the subsets.

10. The method of claim 1 , wherein:

step (a) comprises using two-dimensional data for the multi-dimensional data; and

step (c) comprises using two-dimensional dictionaries as the non-identical dictionaries of basis functions.

11. The method of claim 10 , wherein step (a) comprises using a digital image as the two-dimensional data.

12. The method of claim 1 , wherein:

step (a) comprises using three-dimensional data as the multi-dimensional data; and

step (c) comprises using three-dimensional dictionaries as the non-identical dictionaries of basis functions.

13. The method of claim 12 , wherein step (a) comprises using data having two spatial dimensions and one temporal dimension as the multi-dimensional data.

14. The method of claim 12 , wherein step (a) comprises using three-dimensional data having three spatial dimensions.

15. The method of claim 1 , wherein:

step (a) comprises using three-dimensional data as the multi-dimensional data; and

step (c) comprises using dictionaries having more than three dimensions as the non-identical dictionaries of basis functions.

16. The method of claim 15 , wherein step (a) comprises using data having at least one temporal dimension as the multi-dimensional data.

17. The method of claim 1 , further comprising:

wherein step (c) further comprises performing a matching pursuits process on the multi-dimensional data; and

(d) applying a transform to at least one dimension of the multi-dimensional data prior to step (c).

18. The method of claim 17 , wherein step (a) comprises using a wavelet transform as the transform.

19. The method of claim 18 , wherein step (c) comprises using transform coefficient groupings that comprise sub-bands of the wavelet transform.

20. The method of claim 18 , wherein step (a) comprises using a multi-dimensional wavelet transform as the wavelet transform.

21. The method of claim 20 , wherein step (a) comprises using a discrete cosine transform as the multi-dimensional wavelet transform.

22. The method of claim 20 , wherein the non-identical dictionaries of basis functions in step (c) further comprise a transpose of basis functions applied to at least one other transform coefficient grouping.

23. The method of claim 1 , further comprising:

(d) using audio data as the multi-dimensional data.

24. The method of claim 1 , further comprising:

(d) using video data as the multi-dimensional data.

25. A method for decoding multi-dimensional data using a codebook of basis functions, comprising:

(a) decoding different groupings of transform coefficients with non-identical dictionaries of basis functions having more than three dimensions from the codebook to create decoded multi-dimensional data having more than three dimensions; and

(b) applying a transform to the decoded multi-dimensional data.

26. The method of claim 25 , wherein step (a) comprises using subsets of a master basis dictionary in the non-identical dictionaries of basis functions.

27. The method of claim 26 , further comprising:

(c) communicating the subsets of the master basis dictionary in a form of a sampled value of a function with a coder.

28. The method of claim 26 , further comprising:

(c) communicating the subsets of the master basis dictionary with a coder.

29. The method of claim 26 , further comprising:

(c) communicating data indicative of the subsets of the master basis dictionary with a coder.

30. The method of claim 26 , further comprising:

(c) applying a mask to the master basis dictionary to identify the subsets of the master basis dictionary.

31. The method of claim 25 , wherein step (a) comprises using two-dimensional data as the multi-dimensional data and two-dimensional dictionaries as the non-identical dictionaries of basis functions.

32. The method of claim 31 , wherein step (a) comprises using two-dimensional data that comprises a digital image as the multi-dimensional data.

33. The method of claim 25 , wherein step (a) comprises using three-dimensional data as the multi-dimensional data and three-dimensional dictionaries as the non-identical dictionaries of basis functions.

34. The method a claim 33 , wherein step (a) comprises using data having two spatial dimensions and one temporal dimension as the multi-dimensional data.

35. The method of claim 25 , wherein step (a) comprises using data having three spatial dimensions as the multi-dimensional data.

36. The method of claim 25 , wherein step (a) comprises using data having at least one temporal dimension as the multi-dimensional data.

37. The method of claim 25 , wherein step (a) comprises using data having a total number of dimensions that is higher than a total number of dimensions of the codebook as the multi-dimensional data; and the decoding further comprises applying a matching pursuits process to the multi-dimensional data.

38. The method of claim 25 , wherein step (b) comprises using an inverse wavelet transform as the transform.

39. The method of claim 38 , wherein step (b) comprises using an inverse discrete cosine transform as the transform.

40. The method of claim 25 , further comprising:

(c) using audio data as the multi-dimensional data.

41. The method of claim 25 , further comprising:

(c) using video data as the multi-dimensional data.

42. A computer-readable medium containing instructions that, when executed by a processor, causes the processor to:

(a) apply a transform to multi-dimensional data to create transform coefficients, wherein the multi-dimensional data has a total number of dimensions higher than a total number of dimensions of a codebook of basis functions;

(b) form groups of transform coefficients; and

(c) code different ones of the groups of transform coefficients using matching pursuits coding with non-identical dictionaries of basis functions from the codebook of basis functions.

43. The computer-readable medium of claim 42 , wherein the method further causes the processor to use subsets of a master basis dictionary in the non-identical dictionaries of basis functions.

44. The computer-readable medium of claim 43 , wherein the method further causes the processor to use overlapping subsets of the master basis dictionary in the non-identical dictionaries of basis functions.

45. The computer-readable medium of claim 42 , wherein the method further causes the processor to:

(d) communicate the subsets with a decoder.

46. The computer-readable medium of claim 42 , wherein the method further causes the processor to:

(d) communicate the subsets in a form of a sampled value of a function with a decoder.

47. The computer-readable medium of claim 42 , wherein the method further causes the processor to:

(d) communicate data indicative of the subsets with a decoder.

48. The computer-readable medium of claim 42 , wherein the method further causes the processor to:

(d) use audio data as the multi-dimensional data.

49. The computer-readable medium of claim 42 , wherein the method further causes the processor to:

(d) use video data as the multi-dimensional data.

50. A computer-readable medium containing instructions that, when executed by a processor, causes the processor to:

(a) decode different groupings of transform coefficients with non-identical dictionaries of basis functions having more than three dimensions from a codebook to create decoded multi-dimensional data having more than three dimensions; and

(b) apply a transform to the decoded multi-dimensional data.

51. The computer-readable medium of claim 50 , wherein the method further causes the processor to use subsets of a master basis dictionary in the non-identical dictionaries of basis functions.

52. The computer-readable medium of claim 51 , wherein the method further causes the processor to use overlapping subsets of the master basis dictionary in the non-identical dictionaries of basis functions.

53. The computer-readable medium of claim 50 , wherein the method further causes the processor to:

(c) communicate the subsets of the master basis dictionary with a coder.

54. The computer-readable medium of claim 50 , wherein the method further causes the processor to:

(c) communicate the subsets of the master basis dictionary in a form of a sampled value of a function with a coder.

55. The computer-readable medium of claim 50 , wherein the method further causes the processor to:

(c) use audio data as the multi-dimensional data.

56. The computer-readable medium of claim 50 , wherein the method further causes the processor to:

(c) use video data as the multi-dimensional data.

57. An apparatus, comprising:

a coder configured to encode multi-dimensional data using a codebook of basis functions, wherein the multi-dimensional data has a total number of dimensions higher than a total number of dimensions of the codebook of basis functions;

wherein said coder is configured to apply a transform to the multi-dimensional data to create transform coefficients, form groups of transform coefficients, and code different ones of the groups of transform coefficients using matching pursuits coding with non-identical dictionaries of basis functions from the codebook of basis functions.

58. The apparatus of claim 57 , wherein the coder is further configured to code the different ones of the groups of transform coefficients using subsets of a master basis dictionary in the non-identical dictionaries of basis functions.

59. The apparatus of claim 58 , wherein the coder is further configured to code the different ones of the groups of transform coefficients using overlapping subsets of the master basis dictionary in the non-identical dictionaries of basis functions.

60. The apparatus of claim 58 , wherein the coder is further configured to communicate the subsets with a decoder.

61. The apparatus of claim 58 , wherein the coder is further configured to communicate the subsets with a decoder in a form of a sampled value of a function.

62. The apparatus of claim 58 , wherein the coder is further configured to communicate data indicative of the subsets with a decoder.

63. The apparatus of claim 57 , wherein the multi-dimensional data comprises audio data.

64. The apparatus of claim 57 , wherein the multi-dimensional data comprises video data.

65. An apparatus, comprising:

a decoder configured to decode multi-dimensional data using a codebook of basis functions;

wherein said decoder decodes different groupings of transform coefficients with non-identical dictionaries of basis functions having more than three dimensions from the codebook to create decoded multi-dimensional data having more than three dimensions and applies a transform to the decoded multi-dimensional data.

66. The apparatus of claim 65 , wherein the decoder is further configured to decode the different ones of the groups of transform coefficients using subsets of a master basis dictionary in the non-identical dictionaries of basis functions.

67. The apparatus of claim 66 , wherein the decoder is further configured to decode the different ones of the groups of transform coefficients using overlapping subsets of the master basis dictionary in the non-identical dictionaries of basis functions.

68. The apparatus of claim 66 , wherein the decoder is further configured to communicate the subsets of the master basis dictionary with a coder.

69. The apparatus of claim 66 , wherein the decoder is further configured to communicate the subsets of the master basis dictionary in a form of a sampled value of a function with a coder.

70. The apparatus of claim 65 , wherein the multi-dimensional data comprises audio data.

71. The apparatus of claim 65 , wherein the multi-dimensional data comprises video data.