Analyzing Least Squares and Kalman Filtered Compressed Sensing
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Real-time dynamic MR image reconstruction using Kalman Filtered Compressed Sensing
ICASSP '09 Proceedings of the 2009 IEEE International Conference on Acoustics, Speech and Signal Processing
Decoding by linear programming
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Signal Reconstruction From Noisy Random Projections
IEEE Transactions on Information Theory
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
Modified-CS: modifying compressive sensing for problems with partially known support
IEEE Transactions on Signal Processing
Compressive acquisition of dynamic scenes
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part I
Compressive sensing based sub-mm accuracy UWB positioning systems: A space-time approach
Digital Signal Processing
On the Performance of Compressed Sensing with Partially Correct Support
Wireless Personal Communications: An International Journal
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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. This 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 of the support. The idea of our solution (modified-CS) is to solve a convex relaxation of the following problem: find the signal that satisfies the data constraint and whose support contains the smallest number of new additions to the known support. We obtain sufficient conditions for exact reconstruction using modified-CS. These turn out to be much weaker than those needed for CS, particularly when the known part of the support is large compared to the unknown part.