Image compression via wavelets and row compression

This work exploits a stable row compression algorithm for decomposing a hierarchically or sequentially structured matrix to compress an n × n image represented by a wavelet transform. The multiresolution discrete wavelet transform is used to decompose an image. The row compression algorithm builds up a low rank approximation of the wavelet transform by applying orthogonal transformations and updating techniques. The cost is O(n2) operations.

[1]  Michel Barlaud,et al.  Image coding using wavelet transform , 1992, IEEE Trans. Image Process..

[2]  W. Hackbusch,et al.  An introduction to hierarchical matrices , 2001 .

[3]  L. Greengard,et al.  A Fast Adaptive Multipole Algorithm for Particle Simulations , 1988 .

[4]  Rafael C. González,et al.  Local Determination of a Moving Contrast Edge , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[5]  MICHAEL STEWART,et al.  Nested Product Decomposition of Quasiseparable Matrices , 2013, SIAM J. Matrix Anal. Appl..

[6]  Milan Sonka,et al.  Image Processing, Analysis and Machine Vision , 1993, Springer US.

[7]  Wolfgang Hackbusch,et al.  A Sparse Matrix Arithmetic Based on H-Matrices. Part I: Introduction to H-Matrices , 1999, Computing.

[8]  Milan Sonka,et al.  Image pre-processing , 1993 .

[9]  J. CARRIERt,et al.  A FAST ADAPTIVE MULTIPOLE ALGORITHM FOR PARTICLE SIMULATIONS * , 2022 .

[10]  Mary Hudachek-Buswell Row Compression and Nested Product Decomposition of a Hierarchical Representation of a Quasiseparable Matrix , 2014 .

[11]  R. Stephenson A and V , 1962, The British journal of ophthalmology.

[12]  Ronald A. DeVore,et al.  Image compression through wavelet transform coding , 1992, IEEE Trans. Inf. Theory.

[13]  W. Hackbusch,et al.  A short overview of ℋ︁2‐matrices , 2003 .

[14]  W. Hackbusch A Sparse Matrix Arithmetic Based on $\Cal H$-Matrices. Part I: Introduction to ${\Cal H}$-Matrices , 1999, Computing.

[15]  Thomas S. Huang,et al.  Image processing , 1971 .