Codes and Expansions (CodEx) Seminar

Vicky Kouni (University of Athens)
Analysis Compressed Sensing: from Model-Based Methods to Deep Unfolding Networks

In this talk, we examine Compressed Sensing from a model-based (Part I) and a data-driven (Part II) point of view. In Part I, we solve analysis-sparsity-based Compressed Sensing (analysis CS), employing spark deficient Gabor frames, and compare numerically our method with state-of-the-art Gabor transforms. Our results confirm that the high redundancy provided by spark deficient Gabor frames improves the performance and reconstruction quality of the CS algorithm. In Part II, we propose a new deep unfolding network coined Decoding Network (DECONET), which jointly learns a decoder for CS and a redundant sparsifying analysis operator. We deliver meaningful — in terms of sparsifier’s redundancy and number of layers — generalization error bounds for DECONET, using a chaining technique. Finally, we assess the validity of our theoretical results and compare DECONET to state-of-the-art unfolding networks, on real-world image datasets. Experimental results indicate that our proposed network outperforms the baselines, consistently for all datasets, and its behaviour complies with our theoretical findings.