Sparse Approximate Solutions to Linear Systems
SIAM Journal on Computing
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
Convex Optimization
Compressive Sensing for Background Subtraction
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part II
RLS-weighted Lasso for adaptive estimation of sparse signals
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Compressive sensing reconstruction with prior information by iteratively reweighted least-squares
IEEE Transactions on Signal Processing
A multiscale framework for compressive sensing of video
PCS'09 Proceedings of the 27th conference on Picture Coding Symposium
Weighted l1 minimization for sparse recovery with prior information
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Modified-CS: modifying compressive sensing for problems with partially known support
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
Modified compressive sensing for real-time dynamic MR imaging
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
LS-CS-residual (LS-CS): compressive sensing on least squares residual
IEEE Transactions on Signal Processing
Sparse Bayesian learning for basis selection
IEEE Transactions on Signal Processing
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Just relax: convex programming methods for identifying sparse signals in noise
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
LS-CS-residual (LS-CS): compressive sensing on least squares residual
IEEE Transactions on Signal Processing
Block-Based Compressed Sensing of Images and Video
Foundations and Trends in Signal Processing
On the reconstruction of sequences of sparse signals - The Weighted-CS
Journal of Visual Communication and Image Representation
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We study the problem of reconstructing a sparse signal from a limited number of its linear projections when a part of its support is known, although the known part may contain some errors. The "known" part of the support, denoted T, may be available from prior knowledge. Alternatively, in a problem of recursively reconstructing time sequences of sparse spatial signals, one may use the support estimate from the previous time instant as the "known" part. The idea of our proposed solution (modified.CS) is to solve a convex relaxation of the following problem: find the signal that satisfies the data constraint and is sparsest outside of T. We obtain sufficient conditions for exact reconstruction using modified-CS. These are much weaker than those needed for compressive sensing (CS) when the sizes of the unknown part of the support and of errors in the known part are small compared to the support size. An important extension called regularized modified-CS (RegModCS) is developed which also uses prior signal estimate knowledge. Simulation comparisons for both sparse and compressible signals are shown.