Sparse Representation In The Application Of Single Image Super-resolution Reconstruction Research

With the development of the Internet, communication and digital technology, the high resolution image which can provide more detailed information is gradually becoming a widespread demand. Image Super-resolution (SR) reconstruction is a post-processing method used to enhance image resolution. Without using the high-cost chips and imaging sensors, it has been widely used in many fields. The simplest implementation of SR is the interpolation based methods, such as Bicubic, which usually gets blur. The learning based methods can achieve better results than the conventional ones, by reason of bringing the high frequency information from the training data. Recently, sparse representation has received a lot of attention in image processing in recent years, partly due to the fact that images are sparse or compressible in some dictionaries.In this thesis, we study the single image super-resolution reconstruction via sparse representation. According to the theory of sparse representation and the inverse problem of the single image SR reconstruction, the scheme employed in this thesis is as follows. First, the sparse representation from low-resolution input patches is sought by sparse representation algorithms. Then the corresponding high-resolution outputs are generated from them. And finally, the whole high-resolution image from patches is reconstructed.We emphasize the algorithms which are used to compute the sparse representation coefficients. The sparse representation algorithms have important impact on the reconstruction results. In this thesis, we analyse the typical sparse representation algorithms in detail, such as Matching Pursuit (MP), Orthogonal Matching Pursuit (OMP), Basis Pursuit (BP) and Least Angle Regression (LARS).On account of the inaccuracy of the solution from the general sparse representation algorithms, we propose an interior point method in the image reconstruction scheme, and adopt the preconditioned conjugate gradients to improve the performance. Based on the primal-dual interior point method, this method uses the preconditioned conjugate gradients to compute the search direction. Simulation results show that our method has better visual results than the Bicubic based on the interpolation, the NE method based on the learning and others sparse representation algorithms. And it can achieve better results in qualitative evaluations. The Root-Mean-Square-Error (RMSE) reduction of1.1is achieved over Bicubic,0.74is achieved over LARS, and1.75,1.53and0.12is achieved over MP, OMP and BP, respectively.