A Multi-Scale Compressed Sensing Algorithm Based on Variational Mode

The compressed sensing algorithm based on the hybrid sparse base (TFWBST+wave atom) usually uses two kinds of image sparse transformations to realize the sparse representation of structure and texture respectively. However, due to the lack of constraints on image texture and structure and the lack of orthogonality of the two sparse bases, the sparse coefficient of structure and the sparse coefficient of texture after transformation are often not good enough to reflect their respective components, that is, the texture coefficient often loses the detail information of texture. To overcome this phenomenon, this paper combines the compressed sensing algorithm based on hybrid base with the layered variational image decomposition method to form the variational multi-scale compressed sensing, which is to establish the CS image reconstruction model with minimal energy functional. The layered variational image decomposition decomposes image into different feature components by minimizing energy functional. The reconstruction of each layer by compressed sensing algorithm is very suitable for texture and detail reconstruction. In this model, TFWBST transform and wave atom are combined as a joint sparse dictionary, and the image decomposition is carried out under the (BV, G, E) variational framework, which is introduced into multi-scale compressed sensing technology to reconstruct the original image. In this new functional, TFWBST transform and wave atom are used to represent structure and texture respectively, and multiscale (BV, G, E) decomposition which can decompose an image into a sequence of image structure, texture and noise is added for restricting image parts. Experiments show that the new model is very robust for noise, and that can keep edges and textures stably than other multi-scale restoration and reconstruction of images.