A comparison of typical sparse optimization for 1D signal recovery

Recently, researchers have found that most high dimensional signal are of inherent low dimension and can be recovered from its low dimensional observations under the sparse assumption. Since various algorithms have been proposed to solve this problem including convex relaxation, ℓ₀ optimization and greedy heuristics. In the sense of sparse optimization, this paper makes a comparison of some typical algorithms for 1D signal recovery. Not only the algorithm procedures are reviewed but also some verification experiments are implemented to exploit their performance.