Noisy Image Reconstruction Via Fast Linearized Lagrangian Dual Alternating Direction Method of Multipliers

摘要

In this paper, an efficient noisy image reconstruction algorithm based on compressed sensing in the wavelet domain is proposed. The new algorithm is composed of three steps. Firstly, the noisy image is represented with its coefficients using the discrete wavelet transform. Secondly, the measurement is obtained by using a random Gaussian matrix. Finally, a fast linearized Lagrangian dual alternating direction method of multipliers is proposed to reconstruct the sparse coefficients, which will be converted by the inverse discrete wavelet transform to the reconstructed image. Our experimental results show that the proposed reconstruction algorithm yields a slightly higher peak signal to noise ratio reconstructed image as well as a much faster convergence rate as compared to some existing reconstruction algorithms.