Processing or compressing n-dimensional signals with warped wavelet packets and bandelets
View Patent ↗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.
1. A method of processing n-dimensional digital signals, n being an integer at least equal to 1, comprising the steps of:
(a) receiving an n-dimensional digital input signal;
(b) computing an n-dimensional warped signal from said n-dimensional digital input signal, the n-dimensional warped signal including n-dimensional warped coefficients and n-dimensional signal warping grids; and
(c) 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;
wherein said signal warping grids are computed from a warping geometry defined by region parameters specifying a partition of a signal support into a plurality of regions and deformation parameters specifying 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;
wherein n=3, said n-dimensional digital input signal represents a video image sequence, and wherein the step of computing the n-dimensional warped signal comprises estimating motion vectors within said video image sequence, determining at least one of said n-dimensional geometrical deformation functions by applying a time displacement to a 2-dimensional geometrical deformation using said estimated motion vectors, and computing said n-dimensional warped signal from said warping geometry and said n-dimensional digital input signal.
2. A signal processing method according to claim 1 , further comprising the step of 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.
3. A signal processing method according to claim 2 , further comprising the steps of:
(a) quantizing said bandelet coefficients to produce quantized bandelet coefficients; and
(b) encoding said quantized bandelet coefficients and said region and deformation parameters into a multiplexed data stream suitable for storage in a storage medium or for transmission over a transmission medium, said multiplexed data stream being a compressed representation of said n-dimensional digital input signal from which the n-dimensional warped signal is computed.
4. A signal processing method according to claim 1 , wherein the step of computing an n-dimensional warped signal includes computing an n-dimensional warped signal from said n-dimensional digital input signal, the n-dimensional warped signal including n-dimensional warped coefficients and n-dimensional signal warping grids from which the n-dimensional digital input signal can be reconstructed without any residual.
5. A method of processing n-dimensional digital signals, n being an integer at least equal to 1, comprising the steps of:
receiving an n-dimensional digital input signal;
computing an n-dimensional warped signal from said n-dimensional digital input signal, the n-dimensional warped signal including n-dimensional warped coefficients and n-dimensional signal warping grids;
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;
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;
quantizing said bandelet coefficients to produce quantized bandelet coefficients; and
encoding said quantized bandelet coefficients and said region and deformation parameters into a multiplexed data stream suitable for storage in a storage medium or for transmission over a transmission medium, said multiplexed data stream being a compressed representation of said n-dimensional digital input signal from which the n-dimensional warped signal is computed;
wherein said signal warping grids are computed from a warping geometry defined by region parameters specifying a partition of a signal support into a plurality of regions and deformation parameters specifying 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;
wherein n=3 and said n-dimensional digital input signal represents a video image sequence, and wherein the step of computing the parameters defining the warping geometry comprises
estimating motion vectors within said video image sequence, and determining at least one of said n-dimensional geometrical deformation functions by applying a time displacement to a 2-dimensional geometrical deformation using said estimated motion vectors.