Compressed sensing theory samples and compresses the signals at the same time and uses the prior knowledge that signals can be represented sparsely in the transform domain to reconstruct the original signals with less measurements than Shannon-Nyquist theory. Recently

two-step Iterative Shrinkage/Threshold algorithm has been applied to compressed reconstruction as an optimization method to solve inverse problems for its tight connection with multi-scale geometry analysis

fewer parameters and simplicity. Using the hard and soft threshold operators in the time domain makes it hard to obtain sparse representation for two dimensional images. Consequently

the reconstruction precision of the algorithm is low. Based on the TwIST algorithm

an adaptive two-step Iterative Shrinkage/Threshold algorithm is presented. It makes use of the information obtained from current estimated values to calculate the step parameters and ensure the estimate value moving towards the optimum solution to improve its reconstruction precision. Regarding the poor ability to represent images sparsely

we use the Gaussian scale mixture model to model the curvelet neighborhood coefficients and enhance the ability of image sparse representation with the shift-invariance and directional-selectivity of the curvelet transform. Finally

the method is applied to image compression reconstruction and the experimental results show that it is better than both

the wavelet Gaussian scale mixture models and the curvelet hard threshold reconstruction methods in terms of subjective visual and peak signal noise ratio.