Compressive sensing is an impressive approach for fast MRI. It aims at\nreconstructing MR image using only a few under-sampled data in k-space,\nenhancing the efficiency of the data acquisition. In this study, we propose to\nlearn priors based on undecimated wavelet transform and an iterative image\nreconstruction algorithm. At the stage of prior learning, transformed feature\nimages obtained by undecimated wavelet transform are stacked as an input of\ndenoising autoencoder network (DAE). The highly redundant and multi-scale input\nenables the correlation of feature images at different channels, which allows a\nrobust network-driven prior. At the iterative reconstruction, the transformed\nDAE prior is incorporated into the classical iterative procedure by the means\nof proximal gradient algorithm. Experimental comparisons on different sampling\ntrajectories and ratios validated the great potential of the presented\nalgorithm.\n