System and method for performing wavelet and inverse wavelet transformations of digital data using semi-orthogonal wavelets

• US 6,275,619 B1
• Filed: 06/15/2000
• Issued: 08/14/2001
• Est. Priority Date: 08/29/1997
• Status: Expired due to Term

• Current Assignee: Qualcomm, Inc.
• Original Assignee: TeraLogic, Inc. (Qualcomm, Inc.)
• Inventors: Chui, Charles K.
• Primary Examiner(s): Chang, Jon
• Assistant Examiner(s): Wu, Jingge
• Application Number:
  US09/595,341
• Time in Patent Office: 425 Days
• Field of Search: 382/232, 382/233, 382/234, 382/248, 382/249, 375/240.18, 375/240.19
• US Class Current: 382/248
• CPC Class Codes: G06F 17/148 Wavelet transforms

Abstract

A wavelet transform system and an inverse wavelet transform system are disclosed that respectively implement a wavelet transform and an inverse wavelet transform. Semi-orthogonal standard wavelets are used as the basic wavelets in the wavelet transform and the inverse wavelet transform. As a result, two finite sequences of decomposition coefficients are used for decomposition in the wavelet transform. Furthermore, two finite sequences of reconstruction coefficients that are derived from the two finite sequences of decomposition coefficients are used for reconstruction in the inverse wavelet transform. The finite sequences of decomposition and reconstruction coefficients are not infinite sequences of coefficients that have been truncated. Furthermore, in one embodiment, downsampling is not used in the wavelet transform and upsampling is not used in the inverse wavelet transform.

Claims

1. A decomposition filter stage for decomposing a set of input coefficients into a first set of output coefficients and a second set of output coefficients by applying a first sequence of decomposition coefficients and a second sequence of decomposition coefficients to the set of input coefficients, the decomposition filter stage comprising:

a deinterleaver that deinterleaves the set of input coefficients into a first subset of the set of input coefficients and a second subset of the set of input coefficients;

a first filter that applies a first subsequence of the first sequence of coefficients to the first subset of the set of input coefficients to generate a first set of intermediate coefficients;

a second filter that applies a first subsequence of the second sequence of coefficients to the second subset of the set of input coefficients to generate a second set of intermediate coefficients;

a first summer that sums the first and second sets of intermediate coefficients to generate the first set of output coefficients;

a third filter that applies a second subsequence of the first sequence of coefficients to the first subset of the set of input coefficients to generate a third set of intermediate coefficients;

a fourth filter that applies a second subsequence of the second sequence of coefficients to the second subset of the set of input coefficients to generate a fourth set of intermediate coefficients; and

a second summer that sums the third and fourth sets of intermediate coefficients to generate the second set of output coefficients.

2. The decomposition filter stage of claim 1 wherein the first, second, third, and fourth filters comprise FIR filters that respectively apply the first subsequence of the first sequence of coefficients, the first subsequence of the second sequence of coefficients, the second subsequence of the first sequence of coefficients, and the second subsequence of the second sequence of coefficients in respective moving average operations.

3. The decomposition filter stage of claim 2 wherein:

the first and second subsets of the set of input coefficients respectively comprises those of the input coefficients in the set of input coefficients with even and odd indexes;

the first and second subsequences of the first sequence of coefficients respectively comprises those of the coefficients in the first sequence of coefficients with even and odd indexes; and

the first and second subsequences of the second sequence of coefficients respectively comprises those of the coefficients in the second sequence of coefficients with odd and even indexes.

4. A method of decomposing a set of input coefficients into a first set of output coefficients and a second set of output coefficients by applying a first sequence of decomposition coefficients and a second sequence of decomposition coefficients to the set of input coefficients, the method comprising the steps of:

deinterleaving the set of input coefficients into a first subset of the set of input coefficients and a second subset of the set of input coefficients;

applying a first subsequence of the first sequence of coefficients to the first subset of the set of input coefficients to generate a first set of intermediate coefficients;

applying a first subsequence of the second sequence of coefficients to the second subset of the set of input coefficients to generate a second set of intermediate coefficients;

summing the first and second sets of intermediate coefficients to generate the first set of output coefficients;

applying a second subsequence of the first sequence of coefficients to the first subset of the set of input coefficients to generate a third set of intermediate coefficients;

applying a second subsequence of the second sequence of coefficients to the second subset of the set of input coefficients to generate a fourth set of intermediate coefficients; and

summing the third and fourth sets of intermediate coefficients to generate the second set of output coefficients.

5. The method of claim 4 wherein the first, second, third, and fourth applying steps respectively include applying the first subsequence of the first sequence of coefficients, the first subsequence of the second sequence of coefficients, the second subsequence of the first sequence of coefficients, and the second subsequence of the second sequence of coefficients in respective moving average operations.

6. The method of claim 5 wherein:

the first and second subsets of the set of input coefficients respectively comprises those of the input coefficients in the set of input coefficients with even and odd indexes;

the first and second subsequences of the first sequence of coefficients respectively comprises those of the coefficients in the first sequence of coefficients with even and odd indexes; and

the first and second subsequences of the second sequence of coefficients respectively comprises those of the coefficients in the second sequence of coefficients with odd and even indexes.

7. A reconstruction filter stage for reconstructing a first set of input coefficients and a second set of input coefficients into a set of output coefficients by applying a first sequence of coefficients and a second sequence of coefficients to the first and second sets of input coefficients, the reconstruction filter stage comprising:

a first filter that applies a first subsequence of the first sequence of coefficients to the first set of input coefficients to generate a first set of intermediate coefficients;

a second filter that applies a first subsequence of the second sequence of coefficients to the second set of input coefficients to generate a second set of intermediate coefficients;

a first summer that sums the first and second sets of intermediate coefficients to generate a first subset of the set of output coefficients;

a third filter that applies a second subsequence of the first sequence of coefficients to the first set of input coefficients to generate a third set of intermediate coefficients;

a fourth filter that applies a second subsequence of the second sequence of coefficients to the second set of input coefficients to generate a fourth set of intermediate coefficients;

a second summer that sums the third and fourth sets of intermediate coefficients to generate a second subset of the set of output coefficients; and

an interleaver that interleaves the first and second subsets of the set of output coefficients to generate the set of output coefficients.

8. The reconstruction filter stage of claim 7 wherein the first, second, third, and fourth filters comprise FIR filters that respectively apply the first subsequence of the first sequence of coefficients, the first subsequence of the second sequence of coefficients, the second subsequence of the first sequence of coefficients, and the second subsequence of the second sequence of coefficients in respective moving average operations.

9. The reconstruction filter stage of claim 8 wherein:

the first and second subsets of the set of input coefficients respectively comprises those of the input coefficients in the set of input coefficients with even and odd indexes;

the first and second subsequences of the first sequence of coefficients respectively comprises those of the coefficients in the first sequence of coefficients with even and odd indexes; and

the first and second subsequences of the second sequence of coefficients respectively comprises those of the coefficients in the second sequence of coefficients with odd and even indexes.

10. A method of reconstructing a first set of input coefficients and a second set of input coefficients into a set of output coefficients by applying a first sequence of coefficients and a second sequence of coefficients to the first and second sets of input coefficients, the method comprising the steps of:

applying a first subsequence of the first sequence of coefficients to the first set of input coefficients to generate a first set of intermediate coefficients;

applying a first subsequence of the second sequence of coefficients to the second set of input coefficients to generate a second set of intermediate coefficients;

summing the first and second sets of intermediate coefficients to generate a first subset of the set of output coefficients;

applying a second subsequence of the first sequence of coefficients to the first set of input coefficients to generate a third set of intermediate coefficients;

applying a second subsequence of the second sequence of coefficients to the second set of input coefficients to generate a fourth set of intermediate coefficients;

summing the third and fourth sets of intermediate coefficients to generate a second subset of the set of output coefficients; and

interleaving the first and second subsets of the set of output coefficients to generate the set of output coefficients.

11. The method of claim 10 wherein the first, second, third, and fourth applying steps respectively include applying the first subsequence of the first sequence of coefficients, the first subsequence of the second sequence of coefficients, the second subsequence of the first sequence of coefficients, and the second subsequence of the second sequence of coefficients in respective moving average operations.

12. The method of claim 11 wherein:

the first and second subsets of the set of input coefficients respectively comprises those of the input coefficients in the set of input coefficients with even and odd indexes;

the first and second subsequences of the first sequence of coefficients respectively comprises those of the coefficients in the first sequence of coefficients with even and odd indexes; and

the first and second subsequences of the second sequence of coefficients respectively comprises those of the coefficients in the second sequence of coefficients with odd and even indexes.