This work proposes, an image restoration technique with modified subbsnd-adaptive iterative shrinkage thresholding (MSIST) and (2-D) non-separable oversampled lapped transforms (NSOLTs). An NSOLT is a lattice-structure-based redundant transform which satisfies the symmetric, real-valued and compact-support property, and capable to have rational redundancy. MSIST is an image restoration algorithm which sets a threshold for each subband independently, and allows the subband adaptive processing. In this study, the performance of the proposed method for deblurring, super-resolution and image inpainting is evaluated. It is verified that NSOLT with MSIST yields superior restoration performance to undecimated Haar transform with MSIST and NSOLT with ISTA in both of PSNR and SSIM.