Subspace tracking from missing and corrupted data using NORST and its heuristic extensions

We study the problem of subspace tracking (ST) in the presence of missing and corrupted data. We are able to show that, under assumptions on only the algorithm inputs (input data and/or initialization), the output subspace estimates are close to the true data subspaces at all times. The guarantees hold under mild and easily interpretable assumptions and handle time-varying subspaces. We also show that our algorithm and its extensions are fast and have competitive experimental performance when compared with existing methods. Finally, this solution can be interpreted as a provably correct mini-batch and memory-efficient solution to low rank Matrix Completion (MC)

Time Invariant Error Bounds for Modified-CS based Sparse Signal Sequence Recovery

PAPER AWARD”. 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. I