Maximum Block Improvement Method and Its Applications

We consider compressed sensing of piecewise constant signals, which have sparse gradients and arise frequently from problems of practical interests. We use total variation minimization to recover such signals from a small number of measurements. We establish the proof for the performance guarantee of total variation (TV) minimization in recovering one-dimensional signal with sparse gradient support. In particular, we have shown that the recoverable gradient sparsity can grow linearly with the signal dimension when TV minimization is used. (Joint work with Weiyu Xu from Department of Electrical and Computer Engineering, University of Iowa)