Abstract: A method for determining a background component and a dynamic component of an image frame from an under-sampled data sequence obtained in a dynamic MRI application is provided. The two components are determined by optimizing a low-rank component and a sparse component of the image frame in a sense of minimizing a weighted sum of terms. The terms include a Schattenp=1/2 (S1/2-norm) of the low-rank component, an L1/2-norm of the sparse component additionally sparsified by a sparsifying transform, and an L2-norm of a difference between the sensed data sequence and a reconstructed data sequence. The reconstructed one is obtained by sub-sampling the image frame according to an encoding or acquiring operation. The background and dynamic components are the low-rank and sparse components, respectively. Experimental results demonstrate that the method outperforms an existing technique that minimizes a nuclear-norm of the low-rank component and an L1-norm of the sparse component.

Abstract: A super-resolution method for generating a high-resolution (HR) image from a low-resolution (LR) blurred image is provided. The method is based on a transform-invariant directional total variation (TI-DTV) approach with Schattenp=1/2 (S1/2-norm) and L1/2-norm penalties. The S1/2-norm and the L1/2-norm are used to induce a lower-rank component and a sparse component of the LR blurred image so as to determine an affine transform to be adopted in the TI-DTV approach. In particular, the affine transform is determined such that a weighted sum of the S1/2-norm and the L1/2-norm is substantially minimized. Based on the alternating direction method of multipliers (ADMM), an iterative algorithm is developed to determine the affine transform. The determined affine transform is used to transform a candidate HR image to a transformed image used in computing a directional total variation (DTV), which is involved in determining the HR image.

Abstract: A super-resolution method for generating a high-resolution (HR) image from a low-resolution (LR) blurred image is provided. The method is based on a transform-invariant directional total variation (TI-DTV) approach with Schattenp=1/2 (S1/2-norm) and L1/2-norm penalties. The S1/2-norm and the L1/2-norm are used to induce a lower-rank component and a sparse component of the LR blurred image so as to determine an affine transform to be adopted in the TI-DTV approach. In particular, the affine transform is determined such that a weighted sum of the S1/2-norm and the L1/2-norm is substantially minimized. Based on the alternating direction method of multipliers (ADMM), an iterative algorithm is developed to determine the affine transform. The determined affine transform is used to transform a candidate HR image to a transformed image used in computing a directional total variation (DTV), which is involved in determining the HR image.