Sparse Signal Separation in Redundant Dictionaries

We formulate a unified framework for the separation of signals that are sparse in "morphologically" different redundant dictionaries. This formulation incorporates the so-called "analysis" and "synthesis" approaches as special cases and contains novel hybrid setups. We find corresponding coherence-based recovery guarantees for an l1-norm based separation algorithm. Our results recover those reported in Studer and Baraniuk, ACHA, submitted, for the synthesis setting, provide new recovery guarantees for the analysis setting, and form a basis for comparing performance in the analysis and synthesis settings. As an aside our findings complement the D-RIP recovery results reported in Cand\`es et al., ACHA, 2011, for the "analysis" signal recovery problem: minimize_x ||{\Psi}x||_1 subject to ||y - Ax||_2 \leq {\epsilon}, by delivering corresponding coherence-based recovery results.Comment: Proc. of IEEE International Symposium on Information Theory (ISIT), Boston, MA, July 201

Inpainting of long audio segments with similarity graphs

We present a novel method for the compensation of long duration data loss in audio signals, in particular music. The concealment of such signal defects is based on a graph that encodes signal structure in terms of time-persistent spectral similarity. A suitable candidate segment for the substitution of the lost content is proposed by an intuitive optimization scheme and smoothly inserted into the gap, i.e. the lost or distorted signal region. Extensive listening tests show that the proposed algorithm provides highly promising results when applied to a variety of real-world music signals

Corrupted Sensing with Sub-Gaussian Measurements

This paper studies the problem of accurately recovering a structured signal from a small number of corrupted sub-Gaussian measurements. We consider three different procedures to reconstruct signal and corruption when different kinds of prior knowledge are available. In each case, we provide conditions for stable signal recovery from structured corruption with added unstructured noise. The key ingredient in our analysis is an extended matrix deviation inequality for isotropic sub-Gaussian matrices.Comment: To appear in Proceedings of IEEE International Symposium on Information Theory 201