Abstract: In this paper, we present an adaptive contourlet-wavelet iterative shrinkage thresholding algorithm (TcwIST) for re-mote sensing image restoration. This algorithm can be used to deal with various linear inverse problems (LIPs), including image deconvolution and reconstruction. This algorithm is a new version of the famous two-step iterative shrinkage/thresholding algo-rithm (TwIST). First, we use the split Bregman Rudin–Osher–Fatemi (ROF) model, based on a sparse dictionary, to decompose the image into cartoon and texture parts, which are represented by wavelet and contourlet, respectively. Second, we use an adaptive method to estimate the regularizition parameter and the shrinkage threshold. Finally, we use a linear search method to find a step length and a fast method to accelate convergence. Results show that our method can achieve an SNR improvement (ISNR) for image restoration and fast convergence speed.