Image restoration with 2-D non-separable oversampled lapped transforms

This work proposes to apply a two-dimensional (2-D) non-separable oversampled lapped transform (NSOLT) to image restoration. NSOLT is a lattice-structure-based redundant transform which satisfies the symmetric, real-valued and compact-support property. The lattice structure is able to constitute a Parseval frame with rational redundancy and produce a dictionary with directional atoms. In this study, the performance for deblurring, super-resolution and inpainting is evaluated. The iterative-shrinkage/thresholding algorithm (ISTA) is adopted to show the significance of NSOLT in the image restoration applications. It is verified that the six-level NSOLT with redundancy less than two yields superior or comparable restoration performance to the two-level non-subsampled Haar transform of redundancy seven in both of PSNR and SSIM.