US 2010/0135400 A1 · Processing Or Compressing N-dimensional Signals With Warped Wavelet Packets And Bandelets

Abstract

A method and apparatus for processing or compressing an n-dimensional digital signal by constructing a sparse representation which takes advantage of the signal geometrical regularity. The invention comprises a warped wavelet packet transform which performs a cascade of warped subband filtering along warping grids of sampling points adapted to the signal geometry. It also comprises a bandeletisation which decorrelates the warped wavelet packet coefficients to produce a sparse representation. An inverse warped wavelet packet transform and an inverse bandeletisation reconstruct a signal from its bandelet representation. The invention comprises a compression system which quantizes and codes the bandelet representation, a decompression system, a restoration system which enhances a signal by filtering its bandelet representation, and a feature vector extraction system for pattern recognition applications of a bandelet representation.

Claims9

Dependent claims

1-58. (canceled)

A signal restoration method, comprising the steps of:

(a) receiving an n-dimensional digital input signal, n being an integer at least equal to 1;
(b) providing region and deformation parameters defining a warping geometry, wherein the region parameters specify a partition of an n-dimensional signal support into a plurality of regions and the deformation parameters specify geometrical deformation functions respectively associated with said regions, whereby the geometrical deformation function associated with one of the regions provides positions of sampling points within said one of the regions;
(c) computing an n-dimensional warped signal including n-dimensional warped coefficients and n-dimensional signal warping grids from said warping geometry and the received n-dimensional digital input signal;
(d) computing warped wavelet packet coefficients and wavelet packet warping grids by applying an n-dimensional warped wavelet packet transform to said warped signal, with a binary tree where each node performs a one-dimensional warped subband processing along a respective dimension d, with 1.ltoreq.d.ltoreq.n;
(e) applying a bandeletisation to said warped wavelet packet coefficients and wavelet packet warping grids, wherein said bandeletisation comprises computing bandelet coefficients by applying invertible one-dimensional decorrelation operators to said warped wavelet packet coefficients along selected directions of said wavelet packet warping grids;
(f) applying a restoration process to said bandelet coefficients and said warping geometry to provide processed bandelet coefficients and processed warping geometry;
(g) computing processed wavelet packet warping grids from said processed warping geometry;
(h) computing processed warped wavelet packet coefficients by applying an inverse bandeletisation to said processed bandelet coefficients, wherein said inverse bandeletisation comprises computing processed warped wavelet packet coefficients by applying inverse one-dimensional decorrelation operators to said processed bandelet coefficients, along selected directions of said processed wavelet packet warping grids;
(i) computing a processed warped signal including n-dimensional processed warped coefficients and n-dimensional processed signal warping grids based on said processed warped wavelet packet coefficients and processed wavelet packet warping grids, with a binary tree where each node performs a one-dimensional inverse warped subband processing along a particular dimension d, with 1.ltoreq.d.ltoreq.n;
and j) applying an inverse warping operation to said warped signal to produce a restored n-dimensional digital output signal.

7 more elements

A digital signal restoration system, comprising:

(a) means for receiving an n-dimensional digital input signal, n being an integer at least equal to 1, (b) means for providing region and deformation parameters defining a warping geometry, wherein the region parameters specify a partition of an n-dimensional signal support into a plurality of regions and the deformation parameters specify geometrical deformation functions respectively associated with said regions, whereby the geometrical deformation function associated with one of the regions provides positions of sampling points within said one of the regions;
(c) means for computing an n-dimensional warned signal including n-dimensional warped coefficients and n-dimensional signal warping grids from said warping geometry and the received n-dimensional digital input signal;
(d) means for computing warped wavelet packet coefficients and wavelet packet warping grids by applying an n-dimensional warped wavelet packet transform to said warped signal, with a binary tree where each node performs a one-dimensional warped subband processing along a respective dimension d, with 1.ltoreq.d.ltoreq.n;
(e) means for applying a bandeletisation to said warped wavelet packet coefficients and wavelet packet warping grids, wherein said bandeletisation comprises computing bandelet coefficients by applying invertible one-dimensional decorrelation operators to said warped wavelet packet coefficients along selected directions of said wavelet packet warping grids:
(f) means for applying a restoration process to said bandelet coefficients and said warping geometry to provide processed bandelet coefficients and processed warping geometry, (e) means for computing processed wavelet packet warping grids from said processed warping geometry;
(h) means for computing processed warped wavelet packet coefficients by applying an inverse bandeletisation to said processed bandelet coefficients, wherein said inverse bandeletisation comprises computing processed warped wavelet packet coefficients by applying inverse one-dimensional decor-relation operators to said processed bandelet coefficients, along selected directions of said processed wavelet packet warning grids;
(i) means for computing a processed warped signal including n-dimensional processed warped coefficients and n-dimensional processed signal warping grids based on said processed warped wavelet packet coefficients and processed wavelet packet warping grids, with a binary tree where each node performs a one-dimensional inverse warped subband processing along a particular dimension d, with 1.ltoreq.d.ltoreq.n;
and (j) means for applying an inverse warping operation to said warped signal to produce a restored n-dimensional digital output signal.

5 more elements

A computer program product for restoring n-dimensional digital signals in a computer system, comprising:

(a) code instructions for receiving an n-dimensional digital input signal, n being an integer at least equal to 1;
(b) code instructions for providing region and deformation parameters defining a warping geometry, wherein the region parameters specify a partition of an n-dimensional signal support into a plurality of regions and the deformation parameters specify geometrical deformation functions respectively associated with said regions, whereby the geometrical deformation function associated with one of the regions provides positions of sampling points within said one of the regions;
(c) code instructions for computing an n-dimensional warped signal including n-dimensional warped coefficients and n-dimensional signal warping grids from said warping geometry and the received n-dimensional digital input signal;
(d) code instructions for computing warped wavelet packet coefficients and wavelet packet warping grids by applying an n-dimensional warped wavelet packet transform to said warped signal, with a binary tree where each node performs a one-dimensional warped subband processing along a respective dimension d, with 1.ltoreq.d.ltoreq.n;
(e) code instructions for applying a bandeletisation to said warped wavelet packet coefficients and wavelet packet warping grids, wherein said bandeletisation comprises computing bandelet coefficients by applying invertible one-dimensional decorrelation operators to said warped wavelet packet coefficients along selected directions of said wavelet packet warping grids;
(f) code instructions for applying a restoration process to said bandelet coefficients and said warping geometry to provide processed bandelet coefficients and processed warping geometry;
(g) code instructions for computing processed wavelet packet warping grids from said processed warping geometry;
(h) code instructions for computing processed warped wavelet packet coefficients by applying an inverse bandeletisation to said processed bandelet coefficients, wherein said inverse bandeletisation comprises computing processed warped wavelet packet coefficients by applying inverse one-dimensional decor-relation operators to said processed bandelet coefficients, along selected directions of said processed wavelet packet warping grids;
(i) code instructions for computing a processed warped signal including n-dimensional processed warped coefficients and n-dimensional processed signal warping grids based on said processed warped wavelet packet coefficients and processed wavelet packet warping grids, with a binary tree where each node performs a one-dimensional inverse warped subband processing along a particular dimension d, with 1.ltoreq.d.ltoreq.n;
and (j) code instructions for applying an inverse warping operation to said warped signal to produce a restored n-dimensional digital output signal.

7 more elements

Dependencies are inferred from the claim text.

Processing Or Compressing N-dimensional Signals With Warped Wavelet Packets And Bandelets

Life of this patent

Processing Or Compressing N-dimensional Signals With Warped Wavelet Packets And Bandelets

Life of this patent

Abstract

Claims9