A high quality image reconstruction method based on nonconvex decoding

The article proposes a fast reconstruction algorithm for ℓ0⩽p⩽1 norm nonconvex model, called Gradient projection nonconvex sparse recovery (GPNSR), which makes a good performance in high-quality image reconstruction. We apply the GPNSR into canonical multiple description coding theory and propose a robust high-quality compressed sensing-based coding method. Combined with iterative weighted technique and fast gradient descent method, the proposed method implicitly implements matrix inverse operations to highly reduce the storage pressure. Also the weighted norm method is taken to optimize the descent steps, which highly increases convergent speed of the algorithm. Taking an image has sparse Fourier representations as an example, the paper presents the detailed image sparse coding and fast reconstruction procedure. By integrating the compressive sensing multi-description coding framework, the simulation demonstrates the superior reconstruction performance of the proposed algorithm. Most importantly, with p close to zero, the reconstruction performance of GPNSR can approximate that of ℓ0 norm optimization result.