An lp-based reconstruction algorithm for compressed sensing radar imaging

Radar scientists have recently explored the application of compressed sensing for generating high resolution range profiles (HRRPs) from a limited number of measurements. The last decade has witnessed a surge of algorithms for this purpose. Among these algorithms complex-valued approximate message passing (CAMP) has attracted attention for the following reasons: (i) it converges very fast, (ii) its mean-squared-error can be accurately predicted theoretically at every iteration, (iii) it is straightforward to control the false alarm rate and optimize for the best probability of detection. Despite its nice features, the recovery performance of CAMP is similar to ℓ1-minimization and hence is expected to be improved. The goal of this paper is to first show how the algorithm can be extended to solve non-convex optimization problems. Based on our framework we develop a new algorithm called adaptive ℓp-CAMP that not only has all the nice properties of CAMP, but also provably outperforms it. We explore the performance of our algorithm on a real radar data and show that our new algorithm generates SNRs that are up to 6dB better than those of the other existing algorithms including the original CAMP.