Single Image Super-Resolution Method Using Transform-Invariant Directional Total Variation with S1/2+L1/2-norm

摘要

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.

主权项

1. A method for generating a high-resolution image from a low-resolution blurred image by one or more processors, the method comprising:
determining an affine transform for transforming a first image into a second image that is aligned horizontally and vertically with the first image, the affine transform being determined from the low-resolution blurred image such that a weighted sum of a Schattenp=1/2-norm (S1/2-norm) of a low-rank component and a L1/2-norm of a sparse component is substantially minimized; wherein the low-rank component and the spare component are obtained by applying a candidate affine transform to the low-resolution blurred image to yield a third image and then decomposing the third image into the low-rank component for representing an edge structure of the third image, and the spare component for representing noise or blur information thereof; wherein the determining of the affine transform comprises iteratively refining the candidate affine transform so as to successively reduce the weighted sum, wherein the weighted sum is given by
∥A∥S1/21/2+λ∥E∥1/21/2 where:
A and E are the low-rank component and the sparse component, respectively,∥A∥S1/21/2 is the S1/2-norm of A,∥E∥1/21/2 is the L1/2-norm of E, andλ is a pre-determined parameter for balancing a contribution of the L1/2-norm with the weighted sum; wherein the candidate affine transform is iteratively refined according to {Ak+1=argminA12A-(Ioτ-Ek+1μYk)F2+AS1/21/2Ek+1=argminE12λE-(Ioτ-Ak+1+1μYk)F2+ElaaYk+1=Yk+μ(Ioτ-Ak+1-Ek+1) where:
Ioτ=Ak+Ek,Ak is the low-rank component obtained in a kth iteration, and Ak+1 is the low-rank component obtained in a (k+1)th iteration, an iteration immediately after the kth iteration,Ek is the spare component obtained in the kth iteration, and Ek+1 is the spare component obtained in the (k+1)th iteration,Yk is an augmented Lagrangian multiplier obtained in the kth iteration, and
Yk+1 is an augmented Lagrangian multiplier obtained in the (k+1)th iteration,μ is a nonnegative parameter,∥A∥S1/21/2 denotes a S1/2-norm, and∥E∥lαα denotes a L1/2-norm; wherein the candidate affine transform is iteratively refined untilIoτ-Ak+1-Ek+1FIoτF<ɛis satisfied, where ε is a pre-determined threshold;
wherein the iterative refinement of the candidate affine transform is computed by an iterative process comprising: Step 1: performing an initialization comprising:
K=0;A0=0;Y0=0;E0=0;Δτ0>0;μ0>0;ρ>1; Step 2: determining:Ioτ-Ek+μ-1Yk=UrSrVrTAk+1=UrH2μ(Sr)VrT; Step 3: determining:Ek+1=H2λμ(Ioτ-Ak+1+μ-1Yk) Step 4: determining:
Δτk+1(∀I)+(Ak+1+Ek+1−Ioτ−μ−1Yk) Step 5: determining:
Yk+1=Ykμ(Ioτ−Ak+1−μ−1Yk+1) Step 6: determining:
μk+1=ρμk Step 7: ifIoτ-Ak+1-Ek+1FIoτF<ɛfor the pre-determined threshold, repeat Step 2;
otherwise set values for A, E and τ; and generating the high-resolution image by a transform-invariant directional total variation (TI-DTV) regularization method, wherein the regularization method comprises computing a directional total variation (DTV) of a transformed image obtained by applying the determined affine transform to a candidate high-resolution image.