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Abstract: In recent work, we studied the problem of causally reconstructing timesequences of spatially sparse signals, with unknown and slow time-varyingsparsity patterns, from a limited number of linear -incoherent- measurements.We proposed a solution called Kalman Filtered Compressed Sensing KF-CS. Thekey idea is to run a reduced order KF only for the current signal-s estimatednonzero coefficients- set, while performing CS on the Kalman filtering error toestimate new additions, if any, to the set. KF may be replaced by Least SquaresLS estimation and we call the resulting algorithm LS-CS. In this work, a webound the error in performing CS on the LS error and b we obtain theconditions under which the KF-CS or LS-CS estimate converges to that of agenie-aided KF or LS, i.e. the KF or LS which knows the true nonzero sets.



Author: Namrata Vaswani

Source: https://arxiv.org/







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