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
| Hi-index | 0.00 |
In recent work, we studied the problem of causally reconstructing time sequences of spatially sparse signals, with unknown and slow time-varying sparsity patterns, from a limited number of linear “incoherent” measurements. We proposed a solution called Kalman Filtered Compressed Sensing (KF-CS). The key idea is to run a reduced order KF only for the current signal's estimated nonzero coefficients' set, while performing CS on the Kalman filtering error to estimate new additions, if any, to the set. KF may be replaced by Least Squares (LS) estimation and we call the resulting algorithm LS-CS. In this work, (a) we bound the error in performing CS on the LS error and (b) we obtain the conditions under which the KF-CS (or LS-CS) estimate converges to that of a genie-aided KF (or LS), i.e. the KF (or LS) which knows the true nonzero sets.