Method and apparatus for performing linear filtering in wavelet based domain

• US 6,643,406 B1
• Filed: 03/29/2000
• Issued: 11/04/2003
• Est. Priority Date: 07/28/1999
• Status: Expired due to Term

• Current Assignee: Intellectual Ventures I LLC (Intellectual Ventures LLC)
• Original Assignee: Polaroid Corporation (PLR IP Holdings LLC)
• Inventors: Wober, Munib, Hajjahmad, Ibrahim, Cottrell, F. Richard
• Primary Examiner(s): Couso, Jose L.
• Application Number:
  US09/537,734
• Time in Patent Office: 1,315 Days
• Field of Search: 382/232, 382/233, 382/236, 382/238, 382/240, 382/242, 382/248, 382/250, 348/384.1, 348/394.1, 348/395.1, 348/400--40, 348/407--41, 348/420.1, 348/421.1, 348/425.2, 348/430.1, 348/431.1, 375/240-2-2, 375/240-1-2, 375/240-8-2, 375/240-2-2, 341/51, 341/63, 341/65, 341/67, 341/107, 364/724.011, 364/724.04, 364/724.05, 364/724.13, 364/724.14, 364/725.01, 364/725.02
• US Class Current: 382/240
• CPC Class Codes: G06F 17/148 Wavelet transforms
• CPC Class Codes: G06T 2207/20064 Wavelet transform [DWT]
• CPC Class Codes: G06T 5/00 Image enhancement or restoration
• CPC Class Codes: G06T 5/10 using non-spatial domain filtering
• CPC Class Codes: H03H 17/0211 using specific transformation algorithms, e.g. WALSH functions, Fermat transforms, Mersenne transforms, polynomial transforms, Hilbert transforms correlation computation G06F17/156

Abstract

Disclosed herein are a method, apparatus and computer usable medium for linear filtering with filters of any desired shape and length using the wavelet transform as the computation engine by modifying the basis functions. Specifically, the method and apparatus modifies the basis function of the wavelet and/or inverse wavelet transform(s) by convolving it with the desired filter, thereby forming a modified wavelet and/or inverse wavelet transform(s). The linear filtering is performed in the signal processing and image processing related fields using the wavelet transform with a method that is mathematically equivalent to the filtering operation in the spatial domain. Linear filtering in the wavelet based domain eliminates the need for another program for software support or additional silicon area or real estate to accommodate more functions in hardware. The modified wavelet and/or inverse wavelet transform harnesses and leverages the wavelet and/or inverse wavelet basis function of the wavelet and/or inverse wavelet transform so as to perform the desired linear filtering of the digital or analog signals, without incurring extra cost in terms of software computations or hardware modifications.

Claims

1. A method for linear filtering digital signals from a data source using desired filters of various shape and length to establish a desired filtered effect, the filtering method comprising the steps of:

wavelet transforming said digital signals with modified wavelet filter bank functions during a wavelet decomposition analysis using said wavelet transform as a computation engine; and

forming said modified wavelet filter bank functions from the filter bank functions of said wavelet transform in accordance with said desired filtering effect, said modification of said filter bank functions comprising;

convolving each filter bank function of at least one stage level of said wavelet transform with said desired filter, thereby forming a modified wavelet transform.

2. The method of claim 1, further comprising:

storing said digital signals from said data source in a computer readable memory, wherein said digital signals being at least one-dimensional;

performing said modified wavelet transformation for analysis decomposition on said digital signals in a first stage level to generate one or more sub-bands of modified wavelet coefficients at said first stage level.

3. The method of claim 2, further comprising:

sequentially performing one or more designated wavelet transformations for analysis decomposition at recursively ascending stage levels, wherein at each of said stage levels said designated wavelet transformations are performed on said wavelet coefficients that are present at immediately preceding stage level to generate wavelet coefficients as a succession of sub-bands.

4. The method of claim 2, wherein said first stage level modified wavelet transformations performed on one-dimensional said digital signals further comprises:

performing said modified wavelet transformation on said digital signals to produce modified wavelet coefficients in a low(L)-frequency portion and a high(H)-frequency portion to generate one or more sub-bands of modified wavelet coefficients at said first stage level.

5. The method of claim 4, further comprising:

sequentially performing one or more designated wavelet transformations on said one-dimensional digital signals for analysis decomposition at recursively ascending stage levels, wherein said designated wavelet transformation comprises;

performing said designated wavelet transformation on said low(L)-frequency portion wavelet coefficients that are present at immediately preceding stage level to generate designated wavelet coefficients as a succession of sub-bands.

6. The method of claim 2, wherein said analysis decomposition on two-dimensional said digital signals includes N number (N=1,2,3,4 . . . ) of stage levels, and wherein said first stage level modified wavelet transformation further comprises:

performing said modified wavelet transformation on said two-dimensional digital signals in a first direction to produce modified wavelet coefficients in a first direction low(L)-frequency portion and a first direction high(H)-frequency portion; and

performing said modified wavelet transformation in a second direction on said first direction low(L)-frequency portion of said first stage to produce modified wavelet coefficients in a second direction low-low(LL) frequency portion and a second direction low-high(LH) frequency portion; and

performing said modified wavelet transformation in a second direction on said first direction high(H)-frequency portion of said first stage to produce modified wavelet coefficients in a second direction high-low(HL) frequency portion and a second direction high-high(HH) frequency portion.

7. The method of claim 6, further comprising:

sequentially performing one or more designated wavelet transformations on said two-dimensional digital signals for analysis decomposition at recursively ascending analysis stage levels, wherein said designated wavelet transformation comprises;

performing said designated wavelet transformation at subject recursive stage level on the wavelet coefficients that are present at immediately preceding stage level low-low(LL)-frequency portion to produce designated wavelet coefficients in a first direction low(L)-frequency portion and a first direction high(H)-frequency portion of subject stage level;

performing said designated wavelet transformation at subject recursive stage level in a second direction on said first direction low(L)-frequency portion to produce designated wavelet coefficients in a second direction low-low(LL) frequency portion and a second direction low-high(LH) frequency portion; and

performing said designated wavelet transformation at subject recursive stage level in a second direction on said first direction high(H)-frequency portion to produce designated wavelet coefficients in a second direction high-low(HL) frequency portion and a second direction high-high(HH) frequency portion.

8. The method of claims 3, 5, or 7, further comprising steps for compressing said digital signals as follows:

quantizing said modified wavelet coefficients or said designated wavelet coefficients existing at the highest said stage level using a quantizer at a selected quantization level; and

entropy encoding said quantized coefficients using an encoder to obtain the compressed data.

9. A method for linear filtering digital signals from a data source using desired filters of various shape and length to establish a desired filtered effect, the filtering method comprising the steps of:

inverse wavelet transforming said digital signals with modified inverse wavelet filter bank functions during an inverse wavelet reconstruction synthesis using said inverse wavelet transform as a computation engine; and

forming said modified inverse wavelet filter bank functions from the filter bank functions of said inverse wavelet transform in accordance with said desired filtering effect, said modification of filter bank functions comprising;

convolving each filter bank function of at least one stage level of said inverse wavelet transform with said desired filter, thereby forming a modified inverse wavelet transform.

10. The method of claim 9, wherein said digital signals from said data source are stored in a computer readable memory;

wherein said digital signals have been decomposed in a wavelet transform decomposition analysis having N number (N=1,2,3,4 . . . ) of recursively ascending analysis stage levels;

wherein said decomposed analysis digital signals are reconstructed in an inverse wavelet transform reconstruction synthesis having a corresponding and equal N number (N=1,2,3,4 . . . ) of recursively descending synthesis stage levels, and

if the N number of stage levels is greater than one, then the method further comprises;

sequentially performing one or more designated inverse wavelet transformations for synthesis reconstruction at the recursively descending synthesis stage levels at each of the first through (N−

1) synthesis stage levels, wherein at each of said synthesis stage levels said designated inverse wavelet transformations are performed on said coefficients that are present at immediately preceding synthesis stage level or at corresponding analysis stage level to generate inverse wavelet coefficients as a succession of full bands, and

performing said modified inverse wavelet transformation in said last synthesis stage level, Nth level, for synthesis reconstruction;

wherein said modified inverse wavelet transformation being performed on coefficients that are present at immediately preceding synthesis stage level or at corresponding analysis stage level to generate one or more full bands of modified inverse wavelet coefficients at said last stage level, N^th level.

11. The method of claim 10, wherein said one-dimensional digital signals from the decomposition analysis have been decomposed in said wavelet transform at a last ascended analysis stage level, N^th level, of said decomposition analysis forming wavelet coefficients in a low(L)-frequency portion and high(H) frequency portion, and wherein

if the N number of stage levels of said inverse wavelet reconstruction synthesis is greater than one, then said method further comprises:

sequentially performing one or more designated inverse wavelet transformations on said one-dimensional digital signals for synthesis reconstruction at recursively descending synthesis stage levels to produce inverse wavelet coefficients in a low(L)-frequency portion and a high(H) frequency portion, wherein;

said designated inverse wavelet transformation at first synthesis stage level comprises;

performing said designated inverse wavelet transformation on corresponding low-pass and high-pass wavelet coefficients received from corresponding analysis stage level; and

said designated inverse wavelet transformation for each of the second through the (N−

1) synthesis stage levels comprises;

performing said designated inverse wavelet transformation on the low-pass inverse wavelet coefficients filters received from said immediately preceding synthesis stage level, and on the high-pass wavelet coefficients received from the corresponding analysis stage level, and

whereby said designated inverse wavelet transformation produces inverse wavelet coefficients that reconstructs the signal to recombine the sub-bands in to a succession of full bands.

12. The method of claim 11, having said modified inverse wavelet transformations performed on said one-dimensional signals, wherein:

if said inverse wavelet reconstruction synthesis includes only one stage level, said modified method comprises;

performing said modified inverse wavelet transformation on the corresponding low-pass and high-pass wavelet coefficients that are outputted from corresponding analysis stage level; and

alternatively, if said inverse wavelet reconstruction synthesis includes more than one stage level, said modified method shall be performed in said last synthesis stage level, Nth stage level, wherein said modified method comprises;

performing said modified inverse wavelet transformation on the low-pass inverse wavelet coefficients that are present at said immediately preceding synthesis stage level, and on the high-pass wavelet coefficients from the corresponding analysis stage level,

whereby said modified inverse wavelet transformation produces inverse wavelet coefficients that reconstructs the signal to recombine the sub-bands into a full band.

13. The method of claim 10, wherein said digital signals being two-dimensional digital signals, wherein

said two-dimensional digital signals from the decomposition analysis has been decomposed in said wavelet transform through the last recursively ascended analysis stage level, Nth level, whereby having formed wavelet coefficients in:

a first direction low(L)frequency and a second direction low(L)-frequency portion resulting in a low-low(LL)-frequency portion;

a first direction low(L)frequency and a second direction high(H)-frequency portion resulting in a low-high(LH)-frequency portion;

a first direction high(H)frequency and a second direction low(L)-frequency portion resulting in a high-low(HL)-frequency portion; and

a first direction high(H)frequency and a second direction high(H)-frequency portion resulting in a high-high(HH)-frequency portion, and wherein

if the N number of stage levels of said inverse wavelet reconstruction synthesis is greater than one, then said method further comprises;

sequentially performing one or more designated inverse wavelet transformations on said two-dimensional digital signals for synthesis reconstruction at recursively descending synthesis stage levels, wherein;

said designated inverse wavelet transformation at the first synthesis stage level comprises;

performing said designated inverse wavelet transformation at the first synthesis stage level in a second direction on the coefficients of said low-low(LL) frequency portion and said low-high(LH) frequency portion received from the corresponding analysis stage level to produce designated inverse wavelet coefficients that are reconstructed into a second direction low(L)-frequency portion at the first synthesis stage level,

performing said designated inverse wavelet transformation at the first synthesis stage level in a second direction on the coefficients of said high-low(HL) frequency portion and said high-high(HH) frequency portion received from the corresponding analysis stage level to produce designated inverse wavelet coefficients that are reconstructed into a second direction high(H)-frequency portion of the first synthesis stage level, and

performing said designated inverse wavelet transformation at said first synthesis stage level in a first direction on said second direction reconstructed coefficients of said low-pass and high-pass frequency portions to produce designated inverse wavelet coefficients that reconstructs the signal to recombine the sub-bands into a full band; and

said designated inverse wavelet transformation at each of the second through the (N−

1) synthesis stage levels comprises;

performing said designated inverse wavelet transformation at subject recursive synthesis stage level in a second direction on the coefficients received from said immediately preceding synthesis stage level, and on said low-high(LH) frequency portion received from the corresponding analysis stage level to produce designated inverse wavelet coefficients that are reconstructed into a second direction low(L)-frequency portion of the subject synthesis stage level,

performing said designated inverse wavelet transformation at subject recursive synthesis stage level in a second direction on the coefficients of said high-low(HL) frequency portion and said high-high(HH) frequency portion at the subject synthesis stage level received from the corresponding analysis stage level to produce designated inverse wavelet coefficients that are reconstructed in a second direction high(H)-frequency portion of the subject synthesis stage level, and

performing said designated inverse wavelet transformation at subject recursive synthesis stage level in a first direction on said second direction reconstructed coefficients of said low-pass and high-pass frequency portions that are present at subject recursive synthesis stage level to produce designated inverse wavelet coefficients that reconstructs the signal to recombine the sub-bands into a full band.

14. The method of claim 12, having said modified inverse wavelet transformations performed on said two-dimensional signals, wherein:

if said inverse wavelet reconstruction synthesis includes only one synthesis stage level then the method further comprises performing modified inverse wavelet transformation on said two-dimensional digital signals for synthesis reconstruction at said only synthesis stage level, whereby said only synthesis stage level being the first synthesis stage level, said modified method comprises;

performing said modified inverse wavelet transformation at said first synthesis stage level in a second direction on the coefficients of said low-low(LL) frequency portion and said low-high(LH) frequency portion received from the corresponding analysis stage level to produce modified inverse wavelet coefficients that are reconstructed in a second direction low(L)-frequency portion of said first synthesis stage level,

performing said modified inverse wavelet transformation at said first synthesis stage level in a second direction on the coefficients of said high-low(HL) frequency portion and said high-high(HH) frequency portion received from the corresponding analysis stage level to produce modified inverse wavelet coefficients that are reconstructed in a second direction high(H)-frequency portion of said first synthesis stage level, and

performing said modified inverse wavelet transformation at said first synthesis stage level in a first direction on the second direction reconstructed coefficients of said low-pass and high-pass frequency portions at said first synthesis stage level to produce modified inverse wavelet coefficients that reconstructs the signal to recombine the sub-bands into a full band; and

alternatively, if said inverse wavelet reconstruction synthesis includes more than one synthesis stage level then the method comprises performing modified inverse wavelet transformation on said two-dimensional digital signals for synthesis reconstruction at the last synthesis stage level, N^th level, said modified method comprises;

performing said modified inverse wavelet transformation at the last synthesis stage level in a second direction on the coefficients received from said immediately preceding synthesis stage level, and on the coefficients of said low-high(LH) frequency portion received from the corresponding analysis stage level to produce modified inverse wavelet coefficients that are reconstructed in a second direction low(L)-frequency portion of the last synthesis stage level,

performing said modified inverse wavelet transformation at the last synthesis stage level in a second direction on the coefficients of said high-low(HL) frequency portion and said high-high(HH) frequency portion received from the corresponding analysis stage level to produce modified inverse wavelet coefficients that are reconstructed in a second direction high(H)-frequency portion of said last synthesis stage level, and

performing said modified inverse wavelet transformation at the last synthesis stage level in a first direction on the second direction reconstructed coefficients of said low-pass and high-pass frequency portions at said last synthesis stage level to produce modified inverse wavelet coefficients that reconstructs the signal to recombine the sub-bands into a full band.

15. The method of claims 10, 12, or 14, further comprising steps for decompressing said digital signals as follows:

dequantizing said modified inverse wavelet coefficients at the highest synthesis stage level, Nth level, using a dequantizer at a selected dequantization level; and

entropy decoding said dequantized coefficients using an decoder to obtain the decompressed data.

16. A method for linear filtering digital signals from a data source using desired filters of various shape and length to establish a desired filtered effect, the filtering method comprising the steps of:

wavelet transforming and inverse wavelet transforming said digital signals with modified filter bank functions using said wavelet and inverse wavelet transforms as a computation engines;

forming said modified filter bank functions from the filter bank functions of said wavelet and inverse wavelet transforms in accordance with said desired filtering effect; and

splitting said desired filter in a first part and a second part, said modification of said filter bank functions of said wavelet and inverse wavelet transforms comprising;

convolving each filter bank function of at least one stage level of said wavelet transform with said first part of said desired filter, thereby forming a modified wavelet transform; and

convolving each filter bank function of at least one stage level of said inverse wavelet transform with said second part of said desired filter, thereby forming a modified inverse wavelet transform.

17. The method of claim 16, wherein an analysis decomposition and a corresponding synthesis reconstruction each includes only one stage level, whereby said stage level defines a first stage level, said method further comprising:

storing said digital signals from said data source in a computer readable memory, wherein said digital signals being at least one-dimensional;

performing said modified wavelet transformation for said analysis decomposition on said digital signals in said first analysis stage level to generate one or more sub-bands of modified wavelet coefficients at said first analysis stage level; and

performing said modified inverse wavelet transformation in said first synthesis stage level for synthesis reconstruction, wherein said modified inverse wavelet transformation being performed on coefficients received from corresponding first analysis stage level to generate one or more sub-bands of modified inverse wavelet coefficients at said first synthesis stage level.

18. The method of claim 16, wherein an analysis decomposition includes N number (N=2,3,4 . . . ) of recursively ascending analysis stage levels and wherein a synthesis reconstruction includes a corresponding N number (N=2,3,4 . . . ) of recursively descending synthesis stage levels, wherein the N number of stage levels is at least two levels, said method further comprising:

storing said digital signals from said data source in a computer readable memory, wherein said digital signals being at least one-dimensional;

said analysis decomposition further comprises;

performing said modified wavelet transformation for said analysis decomposition on said digital signals in first analysis stage level to generate one or more sub-bands of modified wavelet coefficients at said first analysis stage level; and

sequentially performing one or more designated wavelet transformations for analysis decomposition at recursively ascending stage levels, wherein at each of said recursively ascending analysis stage levels said designated wavelet transformations are performed on said wavelet coefficients that are present at immediately preceding stage level to generate wavelet coefficients as a succession of sub-bands, and

said synthesis reconstruction further comprises;

sequentially performing one or more designated inverse wavelet transformations for synthesis reconstruction at the recursively descending synthesis stage levels at each of the first through (n−

1) synthesis stage levels, wherein at each of said synthesis stage levels said designated inverse wavelet transformations are performed on said coefficients that are present at immediately preceding synthesis stage level or at corresponding analysis stage level to generate inverse wavelet coefficients as a succession of sub-bands; and

performing said modified inverse wavelet transformation in last synthesis stage level, Nth level, for synthesis reconstruction, wherein said modified inverse wavelet transformation being performed on coefficients that are present at immediately preceding synthesis stage level to generate one or more sub-bands of modified inverse wavelet coefficients at said last stage level, N^th level.

19. The method of claims 17 or 18, further comprising steps for compressing and decompressing said digital signals, wherein

said compressing includes the following steps:

quantizing said modified wavelet coefficients or said designated wavelet coefficients existing at the highest said analysis stage level using a quantizer at a selected quantization level; and

entropy encoding said quantized coefficients using an encoder to obtain the compressed data, and

said decompression includes the following steps;

dequantizing said modified inverse wavelet coefficients at the highest synthesis stage level, Nth level, using a dequantizer at a selected dequantization level; and

entropy decoding said dequantized coefficients using an decoder to obtain the decompressed data.

20. A linear filtering apparatus for linear filtering digital signals using desired filters of various shape and length to establish a desired filtered effect on said digital signals, said apparatus having a control means for controlling the operation of said linear filtering apparatus, and a signal sensing means that receives said digital signals from a signal data source, said linear filtering apparatus comprising:

a wavelet transform means for wavelet transforming said digital signals with modified wavelet filter bank functions during a wavelet decomposition analysis using said wavelet transform means as a computation engine, wherein said modified wavelet filter bank functions are formed by convolving each of the filter bank functions of at least one stage level of said wavelet transform wavelet transform means.

21. The apparatus of claim 20, further comprising:

a storage device for storing digital signal arrays in a computer readable memory, said digital signal arrays having at least one-dimension representing said digital signals;

wherein said wavelet transform means performs said modified wavelet transformation for analysis decomposition on said digital signal arrays in a first analysis stage level to generate one or more sub-bands of modified wavelet coefficients at said first analysis stage level.

22. The apparatus of claim 21, wherein said wavelet transform means sequentially performs one or more designated wavelet transformations for analysis decomposition at recursively ascending analysis stage levels, wherein at each of said analysis stage levels said designated wavelet transformations are performed on said coefficients that are present at immediately preceding analysis stage level to generate wavelet coefficients as a succession of sub-bands.

23. The apparatus of claims 21 or 22, further comprising elements for compressing said digital signal arrays as follows:

a quantizer for quantizing at a selected quantization level said modified wavelet coefficients or said wavelet coefficients existing at highest said analysis stage level; and

an encoder for entropy encoding said quantized coefficients to obtain the compressed data.

24. A linear filtering apparatus for linear filtering digital signals using desired filters of various shape and length to establish a desired filtered effect on said digital signals, said apparatus having a control means for controlling the operation of said linear filtering apparatus, and a signal sensing means that receives said digital signals from a signal data source, said linear filtering apparatus comprising:

an inverse wavelet transform means for inverse wavelet transforming said digital signals with modified wavelet filter bank functions during an inverse wavelet reconstruction synthesis using said wavelet transform as a computation engine, wherein;

said modified wavelet filter bank functions are formed by convolving the filter bank functions of at least one stage level of said inverse wavelet transform with said desired filter, thereby forming a modified inverse wavelet transform.

25. The apparatus of claim 24, further comprising:

a storage device for storing digital signal arrays in a computer readable memory, said digital signal arrays having at least one-dimension representing said digital signals;

wherein said digital signals have been decomposed in a wavelet transform decomposition analysis having N number (N=1,2,3,4 . . . ) of recursively ascending analysis stage levels;

wherein said decomposed analysis digital signals are reconstructed in an inverse wavelet transform reconstruction synthesis having a corresponding and equal N number (N=1,2,3,4 . . . ) of recursively descending synthesis stage levels, and

if the N number of stage levels is greater than one, the inverse wavelet transform means sequentially performs;

one or more designated inverse wavelet transformations for synthesis reconstruction at the recursively descending synthesis stage levels at each of the first through (n−

1) synthesis stage levels, wherein at each of said synthesis stage levels said designated inverse wavelet transformations are performed on said coefficients that are present at immediately preceding synthesis stage level or at corresponding analysis stage level to generate inverse wavelet coefficients as a succession of full bands.

26. The apparatus of claim 25, wherein said inverse wavelet transform means performs said modified inverse wavelet transformation in last synthesis stage level, Nth level, for synthesis reconstruction, wherein said modified inverse wavelet transformation is performed on coefficients that are present at immediately preceding synthesis stage level or at corresponding analysis stage level to generate one or more full bands of modified inverse wavelet coefficients at said last stage level, N^th level.

27. The apparatus of claims 25 or 26, further comprising elements for decompressing said digital signal array as follows:

a dequantizer for dequantizing said modified inverse wavelet coefficients at the highest synthesis stage level, Nth level; and

a decoder for entropy decoding said dequantized coefficients to obtain the decompressed data.

28. A linear filtering apparatus for linear filtering digital signals using desired filters of various shape and length to establish a desired filtered effect on said digital signals, said apparatus having a control means for controlling the operation of said linear filtering apparatus, and a signal sensing means that receives said digital signals from a signal data source, said linear filtering apparatus comprising:

wavelet transform means and inverse wavelet transform means for wavelet transforming and inverse wavelet transforming, respectively, said digital signals with respective modified wavelet filter bank functions and modified inverse wavelet filter bank functions, during wavelet decomposition and inverse wavelet reconstruction analyses, respectively, using said wavelet and inverse wavelet transforms as computation engines, wherein;

said desired filter is split into a first part and a second part; and

said modified wavelet filter bank functions of said wavelet transform are formed in accordance with said desired filtering effect, wherein said modification comprises;

convolving each of the wavelet filter bank functions of at least one stage level of said wavelet transform with said first part of said desired filter, thereby forming a modified wavelet transform; and

said modified inverse wavelet filter bank functions of said inverse wavelet transform are formed in accordance with said desired filtering effect, wherein said modification comprises;

convolving each of the filter bank functions of at least one stage level of said inverse wavelet transform with said second part of said desired filter, thereby forming a modified inverse wavelet transform.

29. The apparatus of claim 28, further comprising:

a storage device for storing digital signal arrays in a computer readable memory, said digital signal arrays having at least one-dimension representing said digital signals, wherein an analysis decomposition and a corresponding synthesis reconstruction each includes only one stage level, whereby said stage level defines a first stage level, and wherein;

said wavelet transform means performs said modified wavelet transformation for said analysis decomposition on said digital signals in said first analysis stage level to generate one or more sub-bands of modified wavelet coefficients at said first analysis stage level; and

said inverse wavelet transform means performs said modified inverse wavelet transformation in said first synthesis stage level for synthesis reconstruction on coefficients received from corresponding first analysis stage level to generate one or more full bands of modified inverse wavelet coefficients at said first synthesis stage level.

30. The apparatus of claim 28, further comprising:

a storage device for storing digital signal arrays in a computer readable memory, said digital signal arrays having at least one-dimension, wherein an analysis decomposition includes N number (N=2,3,4 . . . ) of recursively ascending analysis stage levels and wherein a synthesis reconstruction includes a corresponding N number (N=2,3,4 . . . ) of recursively descending synthesis stage levels, wherein the N number of stage levels is at least two stage levels, and wherein;

said wavelet transform means at said analysis decomposition;

performs said modified wavelet transformation at the first analysis stage level for said analysis decomposition on said digital signals to generate one or more sub-bands of modified wavelet coefficients at said first analysis stage level; and

sequentially performs one or more designated wavelet transformations at recursively ascending stage levels for analysis decomposition on said wavelet coefficients received from immediately preceding stage level to generate wavelet coefficients as a succession of sub-bands, and said inverse wavelet transform at said synthesis reconstruction;

sequentially performs one or more designated inverse wavelet transformations at each of the first through (N−

1) synthesis stage levels for synthesis reconstruction at the recursively descending synthesis stage levels on said coefficients received from immediately preceding synthesis stage level or corresponding analysis stage level to generate inverse wavelet coefficients as a succession of full bands; and

performs said modified inverse wavelet transformation in last synthesis stage level, Nth level, for synthesis reconstruction on coefficients received from immediately preceding synthesis stage level to generate one or more full bands of modified inverse wavelet coefficients at said last stage level, N^th level.

31. The apparatus of claims 29 or 30, further comprising elements for compressing and decompressing said digital signals wherein:

said elements for compressing includes;

a quantizer for quantizing at a selected quantization level said modified wavelet coefficients or said designated wavelet coefficients existing at the highest said analysis stage level; and

an encoder for entropy encoding said quantized coefficients to obtain the compressed data, and

said elements for decompressing includes;

a quantizer for dequantizing at a selected dequantization level said modified inverse wavelet coefficients at the highest synthesis stage level, Nth level; and

a decoder for entropy decoding said dequantized coefficients to obtain the decompressed data.

32. A computer usable medium having computer readable program code thereon for linear filtering digital signals using desired filter means of various shape and length to establish a desired filtered effect on said digital signals, whereby said computer usable medium for use in a computer is controlled by a control means for operating the computer, and a signal sensing means that receives said digital signals from a signal data source, wherein said computer usable medium comprises:

a wavelet transform means for wavelet transforming said digital signals with modified wavelet filter bank functions using said wavelet transform means as a computation engine, said digital signals being at least one-dimensional wherein;

said modified wavelet filter bank functions are formed in accordance with said filtering effect by convolving each of the filter bank functions of at least one stage level of said wavelet transform with said desired filter, thereby forming a modified wavelet transform.

33. The computer usable medium of claim 32, wherein said digital signals being stored in a computer readable memory, and

said wavelet transform means performs said modified wavelet transformation for analysis decomposition on said digital signal arrays in a first analysis stage level to generate one or more sub-bands of modified wavelet coefficients at said first stage level.

34. The computer usable medium of claim 33, wherein said wavelet transform means sequentially performs one or more designated wavelet transformations for analysis decomposition at recursively ascending analysis stage levels, wherein at each of said analysis stage levels said designated wavelet transformations are performed on said coefficients that are present at immediately preceding stage level to generate wavelet coefficients as a succession of sub-bands.

35. The computer usable medium of claims 33 or 34, further comprising means for compressing said digital signals as follows:

a quantizer means for quantizing at a selected quantization level of said modified wavelet coefficients or said designated wavelet coefficients existing at highest said analysis stage level; and

an encoder means for entropy encoding said quantized coefficients to obtain the compressed data.

36. A computer usable medium having computer readable program code thereon for linear filtering digital signals using desired filter means of various shape and length to establish a desired filtered effect on said digital signals, whereby said computer usable medium for use in a computer is controlled by a control means for operating the computer, and a signal sensing means that receives said digital signals from a signal data source, wherein said computer usable medium comprises:

an inverse wavelet transform means for inverse wavelet transforming said digital signals with modified inverse wavelet filter bank functions during an inverse wavelet reconstruction synthesis using said inverse wavelet transform as a computation engine, wherein;

said modified inverse wavelet filter bank functions are formed in accordance with said desired filtering effect, by convolving each of the filter bank functions of at least one stage level of said inverse wavelet transform with said desired filter, thereby forming a modified inverse wavelet transform.

37. The computer usable medium of claim 36 wherein said digital signals being stored in a computer readable memory representing said digital signals and said digital signals being at least one-dimensional, said digital signals have been decomposed in a wavelet transform decomposition analysis having N number (N=1,2,3,4 . . . ) of recursively ascending analysis stage levels, said decomposed analysis digital signals are reconstructed in an inverse wavelet transform reconstruction synthesis having a corresponding and equal N number (N=1,2,3,4 . . . ) of recursively descending synthesis stage levels, and if the N number of stage levels is greater than one, said computer usable medium comprises:

said wavelet transform means that sequentially performs one or more designated inverse wavelet transformations for synthesis reconstruction at the recursively descending synthesis stage levels at each of the first through (N−

1) synthesis stage levels, wherein at each of said synthesis stage levels said designated inverse wavelet transformations are performed on said coefficients that are present at immediately preceding synthesis stage level or at corresponding analysis stage level to generate inverse wavelet coefficients as a succession of full bands.

38. The computer usable medium of claim 37, wherein said inverse wavelet transform means performs said modified inverse wavelet transformation in last synthesis stage level, Nth level, for synthesis reconstruction, wherein said modified inverse wavelet transformation is performed on coefficients that are present at immediately preceding synthesis stage level or at corresponding analysis stage level to generate one or more full bands of modified inverse wavelet coefficients at said last stage level, N^th level.

39. The computer usable medium of claims 37 or 38, further comprising means for decompressing said digital signals as follows:

a dequantizer means for dequantizing said modified inverse wavelet coefficients at the highest synthesis stage level, Nth level; and

a decoder means for entropy decoding said dequantized coefficients to obtain the decompressed data.

40. A computer usable medium having computer readable program code thereon for linear filtering digital signals using desired filter means of various shape and length to establish a desired filtered effect on said digital signals, whereby said computer usable medium for use in a computer is controlled by a control means for operating the computer, and whereby said computer usable medium is for use with a signal sensing means that receives said digital signals from a signal data source, wherein said computer usable medium comprises:

wavelet transform means and inverse wavelet transform means for wavelet transforming and inverse wavelet transforming, respectively, said digital signals in with respective modified wavelet filter bank functions and modified inverse wavelet filter bank functions, using said wavelet and inverse wavelet transforms as a computation engines, wherein;

said desired filter is split into a first part and a second part; and

said modified wavelet filter bank functions of said wavelet transform are formed in accordance with said desired filtering effect, by;

convolving the filter bank functions of at least one stage level of said wavelet transform with said first part of said desired filter, thereby forming a modified wavelet transform; and

said modified inverse wavelet filter bank functions of said inverse wavelet transform are formed in accordance with said desired filtering effect by;

convolving the filter bank functions of at least one stage level of said inverse wavelet transform with said second part of said desired filter, thereby forming a modified inverse wavelet transform.

41. The computer usable medium of claim 40, wherein said digital signals being stored in a computer readable memory representing said digital signals and said digital signals being at least one-dimensional, wherein an analysis decomposition and a corresponding synthesis reconstruction each includes only one stage level, whereby said stage level defines a first stage level, and wherein:

said wavelet transform means performs said modified wavelet transformation for said analysis decomposition on said digital signals in said first analysis stage level to generate one or more sub-bands of modified wavelet coefficients at said first analysis stage level; and

said inverse wavelet transform means performs said modified inverse wavelet transformation in said first synthesis stage level for synthesis reconstruction on coefficients received from corresponding first analysis stage level to generate one or more full bands of modified inverse wavelet coefficients at said first synthesis stage level.

42. The computer usable medium of claim 40, wherein said digital signals being stored in a computer readable memory representing said digital signals and said digital signals being at least one-dimensional, wherein an analysis decomposition includes N number (N=2,3,4 . . . ) of recursively ascending analysis stage levels and wherein a synthesis reconstruction includes a corresponding N number (N=2,3,4 . . . ) of recursively descending synthesis stage levels, wherein the N number of stage levels is at least two levels, said computer usable medium comprises:

said wavelet transform means at said analysis decomposition that;

performs said modified wavelet transformation of the first analysis stage level for said analysis decomposition on said digital signals to generate one or more sub-bands of modified wavelet coefficients at said first analysis stage level; and

sequentially performs one or more designated wavelet transformations at recursively ascending stage levels for analysis decomposition on said wavelet coefficients received from immediately preceding analysis stage level to generate wavelet coefficients as a succession of sub-bands, and

said inverse wavelet transform at said synthesis reconstruction that;

sequentially performs one or more designated inverse wavelet transformations at each of the first through (n−

1) synthesis stage levels for synthesis reconstruction at the recursively descending synthesis stage levels on said wavelet coefficients received from immediately preceding synthesis stage level or corresponding analysis stage level to generate inverse wavelet coefficients as a succession of sub-bands; and

performs said modified inverse wavelet transformation in last synthesis stage level, Nth level, for synthesis reconstruction on coefficients received from immediately preceding synthesis stage level to generate one or more full bands of modified inverse wavelet coefficients at said last stage level, N^th level.

43. The apparatus of claims 41 or 42, further comprising means for compressing and decompressing said digital signals wherein:

said means for compressing includes;

a quantizer means for quantizing at a selected quantization level said modified wavelet coefficients or said designated wavelet coefficients existing at the highest said analysis stage level; and

an encoder means for entropy encoding said quantized coefficients to obtain the compressed data, and

said means for decompressing includes;

a quantizer means for dequantizing at a selected dequantization level said modified inverse wavelet coefficients at the highest synthesis stage level, Nth level; and

a decoder means for entropy decoding said dequantized coefficients to obtain the decompressed data.

44. A method for electronically sending digital signals over a communication network from a source acquisition system for use at a remote destination rendering system, said method comprising the steps of:

establishing an electronics communications link between said source acquisition system and said remote destination rendering system over said network; and

operating said source acquisition system to transmit said digital signals over said network for use in a rendering device or output device at said remote destination rendering system, said method further comprising the steps of;

linear filtering at said source acquisition system said digital signals using a desired filter of various shape and length to establish a desired filtered effect, said linear filtering comprising the steps of;

wavelet transforming said digital signals with modified wavelet filter bank functions during a wavelet decomposition analysis using said wavelet transform as a computation engine; and

forming said modified wavelet filter bank functions of said wavelet transform in accordance with said desired filtering effect, wherein said modification is effected by convolving the filter bank functions of at least one stage level of said wavelet transform with said desired filter, thereby forming a modified wavelet transform.

45. A method for electronically rendering digital signals at a destination rendering system, said signals being transmitted over a communication network that originates from a source acquisition system, said method comprising the steps of:

establishing an electronic communications link between said source acquisition system and said destination rendering system over said network; and

operating said destination rendering system to receive said digital signals over said network for use in a rendering device or output device at said destination rendering system, said method further comprising the steps of;

linear filtering at said destination rendering system said digital signals transmitted from said source acquisition system using a desired filter of various shape and length to establish a desired filtered effect, said linear filtering comprising the steps of;

inverse wavelet transforming said digital signals with modified inverse wavelet filter bank functions during an inverse wavelet reconstruction analysis using said inverse wavelet transform as a computation engine; and

forming said modified inverse wavelet filter bank functions of said inverse wavelet transform in accordance with said desired filtering effect, wherein said modification is effected by convolving each of the filter bank functions of at least one stage level of said inverse wavelet transform with said desired filter, thereby forming a modified inverse wavelet transform.

46. A method for electronically acquiring digital signals over a communication network from a source acquisition system by means of a remote destination rendering system, said method comprising the steps of:

establishing an electronic communications link between said source acquisition system and said remote destination rendering system over said network; and

operating said source acquisition system to transmit said digital signals over said network for use in a rendering device or output device at said remote destination rendering system, and

operating said remote destination rendering system to receive said digital signals transmitted from said source acquisition system for use in said rendering device or output device, and said method further comprising the steps of;

a) splitting a desired filter of various shape and length into a first part and second part;

b) linear filtering at said source acquisition system said digital signals using said first part of said desired filter to establish a desired filtered effect, wherein said linear filtering comprises the steps of;

wavelet transforming said digital signals with modified wavelet filter bank functions during a wavelet decomposition analysis using said wavelet transform as a computation engine; and

forming said modified wavelet filter bank functions from the filter bank functions of said wavelet transform in accordance with said desired filtering effect, wherein said modification is effected by convolving each of the filter bank functions of at least one stage level of said wavelet transform with said first part desired filter, thereby forming a modified wavelet transform; and

c) linear filtering at said remote destination rendering system said digital signals transmitted from said source acquisition system using said second part of said desired filter to establish a desired filtered effect, said linear filtering comprising the steps of;

inverse wavelet transforming said digital signals with modified inverse wavelet filter bank functions during a wavelet reconstruction analysis using said inverse wavelet transform as a computation engine; and

forming said modified inverse wavelet filter bank functions from the filter bank functions of said inverse wavelet transform in accordance with said desired filtering effect, wherein said inverse wavelet modification is effected by convolving each of the filter bank functions of at least one stage level of said inverse wavelet transform with said second part desired filter, thereby forming a modified inverse wavelet transform.