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In this work, we obtain sufficient conditions for the "stability" of ourrecently proposed algorithms, Least Squares Compressive Sensing residual(LS-CS) and modified-CS, for recursively reconstructing sparse signal sequencesfrom noisy measurements. By "stability" we mean that the number of misses fromthe current support estimate and the number of extras in it remain bounded by atime-invariant value at all times. We show that, for a signal model with fixedsignal power and support set size; support set changes allowed at every time;and gradual coefficient magnitude increase/decrease, "stability" holds undermild assumptions -- bounded noise, high enough minimum nonzero coefficientmagnitude increase rate, and large enough number of measurements at every time.A direct corollary is that the reconstruction error is also bounded by atime-invariant value at all times. If the support set of the sparse signalsequence changes slowly over time, our results hold under weaker assumptionsthan what simple compressive sensing (CS) needs for the same error bound. Also,our support error bounds are small compared to the support size. Our discussionis backed up by Monte Carlo simulation based comparisons.

Stability of Modified-CS and LS-CS for Recursive Reconstruction of Sparse Signal Sequences