Recovering overcomplete sparse representations from structured sensing
In many signal processing applications, one wishes to acquire images that are approximately sparse in transform domains such as wavelets using frequency domain samples. Often the quality of the sparsity based model significantly improves when one considers redundant representation systems such as wavelet frames. To date, compressed sensing with redundant representation systems has, however, only been studied for measurement systems that have certain concentration properties, which is not the case for frequency domain samples. In this talk, we close this gap, providing more general reconstruction guarantees for signals that are sparse with respect to redundant systems. This is joint work with Felix Krahmer and Rachel Ward.