Compressed Sensing of Compressible Signals

We present a novel and general approach that elevates the scope of compressed sensing recovery algorithms far beyond simple structures such as sparsity. The proposed method, referred to as compressionbased gradient descent (C-GD), is capable of employing state-of-the-art compression algorithms to solve structured signal recovery problems. This enables CGD to take advantage of complex structures that are used by the state-of-the-art compression codes, such as JPEG2000 and MPEG4. Our simulation results show that, in many instances, C-GD achieves state-of-the-art signal recovery performance. Furthermore, our theoretical results justify the performance of C-GD observed in our simulations.