Single-image Super-resolution Via Rank Minimization Theory

With the development of society,people are increasingly demanding high-quality images,and the cost of acquiring image have also received much attention.Therefore,low cost of image super-resolution restoration technology becomes a very popular research topic in the field of image processing.Super-resolution reconstruction mainly uses single picture or multiple low-resolution images to restore a high resolution image by recovering the loss of high frequency pixel.In recent years,there are many vector sparse methods that were used to study image super-resolution algorithm via compressed sensing theory.Inspired by that,this article presents a method based on the matrix rank minimization theory and block similarity property for image single super-resolution and establishes a noiseless low rank recovery model and noisy low rank recovery model.In noiseless low rank recovery model,firstly,for each of input low-resolution image patch,we find its similar image patch in the training image set.The training set does not use the extra,but only use input low-resolution images itself.Secondly,the corresponding high-resolution image blocks to these low resolution similar patches configure an approximate low rank matrix.Inexact Augmented Lagrange Multiplier is used to decompose the approximate low-rank matrix into the sum of sparse matrix and low-rank matrix.Finally,according to the rank structure of similar high resolution subspace,super-resolution image restoration is achieved.Numerical simulation experiment results show that the proposed noiseless single image super-resolution restoration model via the rank minimization theory is feasible.Noisy low rank recovery model is similar to the noiseless model mentioned above.The difference between two models is that noisy low rank recovery model decomposes the approximate low rank matrix into the sum of a sparse matrix,a low-rank matrix and a noise matrix.At last,the noise matrix is abandoned and the low rank matrix and sparse matrix are used to recovery high resolution image.The simulation results show that the proposed noisy low rank model has better results than noiseless low rank model for the image super resolution.