Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Surface compression with geometric bandelets
ACM SIGGRAPH 2005 Papers
IEEE Transactions on Information Theory
An EM algorithm for wavelet-based image restoration
IEEE Transactions on Image Processing
Sparse geometric image representations with bandelets
IEEE Transactions on Image Processing
Morphological Diversity and Sparsity for Multichannel Data Restoration
Journal of Mathematical Imaging and Vision
Exploiting structure in wavelet-based Bayesian compressive sensing
IEEE Transactions on Signal Processing
Image representation by compressive sensing for visual sensor networks
Journal of Visual Communication and Image Representation
Image restoration using a sparse quadtree decomposition representation
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
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This paper proposes an extension of compressed sensing that allows to express the sparsity prior in a dictionary of bases. This enables the use of the random sampling strategy of compressed sensing together with an adaptive recovery process that adapts the basis to the structure of the sensed signal. A fast greedy scheme is used during reconstruction to estimate the best basis using an iterative refinement. Numerical experiments on sounds and geometrical images show that adaptivity is indeed crucial to capture the structures of complex natural signals.