Compressive sampling image recovery with structure features and approximate l₀ norm

This paper presents a new model named TVSl₀ for natural image recovery from compressive samples. The model combines total variation norm and approximate l₀ norm. Simulated Annealing is employed to achieve optimization. The model is based on the approximate l₀ norm, in which the approximate function is used to tackle the discontinuity of l₀, and the approximate TV norm reflects the image structure features, i.e. bounded variation in space domain. The simulation results show that the natural images could be recovered rapidly and accurately. Comparing with TV minimization model, TVSl₀ can provide the recovery images in the same quality, with smaller number of iteration and lower complexity.