Processing or compressing n-dimensional signals with warped wavelet packets and bandelets

A digital signal restoration system, comprising:

• a geometrical segmentation and sampling section to receive an n-dimensional digital input signal, n being an integer at least equal to 1, and to provide 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;
• a signal warping unit to compute 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;
• a warped wavelet packet processor to compute 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≦d≦n;
• a bandeletisation unit to apply 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;
• a processor to apply a restoration process to said bandelet coefficients and said warping geometry and provide processed bandelet coefficients and processed warping geometry;
• a geometrical sampling and wavelet packet warping grid subsampling unit to compute processed wavelet packet warping grids from said processed warping geometry;
• an inverse bandeletisation unit to compute 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 warning grids;
• an inverse warped wavelet packet processor to compute 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≦d≦n;
• and
• an inverse warping unit to apply an inverse warping operation to said warped signal to produce a restored n-dimensional digital output signal.

A non-transitory computer readable medium storing computer readable instructions that, when executed by at least one processor of a computer system, instruct the at least one processor to perform a method of restoring n-dimensional digital signals, the method comprising:

• (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≦d≦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≦d≦n;
• and
• (j) applying an inverse warping operation to said warped signal to produce a restored n-dimensional digital output signal.