Time invariant error bounds for modified-CS based sparse signal sequence recovery

In this work, we obtain performance guarantees for modified-CS and for its improved version, modified-CS-Add-LS-Del, for recursive reconstruction of sparse signal sequences from noisy measurements. Under mild assumptions, and for a realistic signal change model, we show that the support recovery error of both algorithms is bounded by a time-invariant and small value at all times. The same is also true for the reconstruction error. Under a slow support change assumption, our results hold under weaker assumptions on the number of measurements than what simple compressive sensing (basis pursuit denoising) needs. Also, the result for modified-CS-add-LS-del holds under weaker assumptions on the signal magnitude increase rate than the result for modified-CS. Similar results were obtained in an earlier work, however the signal change model assumed there was very simple and not practically valid.