Recovery of a compressed sensing CT image using a smooth re-weighted function- regularized least-squares algorithm

It is challenging to recover the required compressed CT (Computed Tomography, CT) image, which is got by transferred through the internet or is stored in a signal library after being compressed. We present a recovery method for compressed sensing CT images. At present, minimizing 0-norm, 1-norm and p-norm is used to recover compressed sensing signals. However, sometimes 0-norm is an NP problem, 1-norm has no solution in theory and p-norm is not a convex function. We introduce a recovery method of compressed sensing signal based on regularized smooth convex optimization. In order to avoid solving the non-convex optimization problems and no solution condition, a convex function is designed as the objective function of optimization to fit 0-norm of signal and a fast iterative shrinkage-thresholding algorithm is proposed to find solution with the convergence speed is quadratic convergence. Experimental results show that our method has a sound recovery effect and is well suitable for processing big data of compressed CT images.