Accelerated augmented Lagrangian method for image reconstruction

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