US 7,508,991 B2 · Method of generating a sequence of matrix factors for a transformation matrix

Abstract

A method of generating a sequence of matrix factors for a transformation matrix having a plurality of rows and columns using a computer, wherein the transformation matrix stores data values representing a wavelet transform. In a first aspect, at least one plurality of row reduction operations are applied to the transformation matrix. The sequence of matrix factors is generated from the reduced transformation matrix and the row reduction operations. A scaling factor may be removed from the transformation matrix before applying the row reduction operations, wherein the scaled transformation matrix has a determinant with a coefficient equal to 1 or −1. In yet another aspect, the transformation matrix may have a nonzero monomial determinant and the sequence of matrix factors further includes a scaling matrix. The method may include further alternative features described herein.

Claims26

Dependent claims

A method of processing a digital signal representing an image to obtain an approximation of a transformed image signal obtained by applying a wavelet transform to the digital signal, the method comprising:

using a computer to perform the following:
applying at least one plurality of row reduction operations to a wavelet transformation matrix to produce a reduced transformation matrix, the wavelet transformation matrix storing data values representing the wavelet transform;
generating a sequence of matrix factors from the reduced transformation matrix;
generating a modified transformation matrix using the sequence of matrix factors, wherein the modified transformation matrix approximates the wavelet transformation matrix;
and
applying the modified transformation matrix to the digital signal representing the image to obtain the approximation of the transformed image signal.

3 more elements

A computer readable medium having computer executable instructions stored thereon for processing a digital signal representing an image, wherein said processing obtains an approximation of a transformed image signal obtained by applying a wavelet transform to the digital signal, wherein the instructions, when executed, cause a computer to:

apply at least one plurality of row reduction operations to a wavelet transformation matrix to produce a reduced transformation matrix, wherein the wavelet transformation matrix stores data values representing the wavelet transform;
generate a sequence of matrix factors from the reduced transformation matrix;
generate a modified transformation matrix using the sequence of matrix factors, wherein the modified transformation matrix approximates the wavelet transformation matrix;
and
apply the modified transformation matrix to the digital signal representing the image to obtain the approximation of the transformed image signal.

2 more elements

Dependencies are inferred from the claim text.

Method of generating a sequence of matrix factors for a transformation matrix

Life of this patent

Method of generating a sequence of matrix factors for a transformation matrix

Life of this patent

Abstract

Claims26