Compressive Sampling Recovery for Natural Images

Compressive sampling (CS) is a novel data collection and coding theory which allows us to recover sparse or compressible signals from a small set of measurements. This paper presents a new model for natural image recovery, in which the smooth l₀ norm and the approximate total-variation (TV) norm are adopted simultaneously. By using one-order gradient decrease, the speed of algorithm for this new model can be guaranteed. Experimental results demonstrate that the principle of the model is correct and the performance is as good as that based on TV model. The computing speed of the proposed method is two orders of magnitude faster than that of interior point method and two times faster than that of the Nesta optimization based on TV model.