LASSO approximation and application to image super-resolution with CUDA acceleration

Sparse learning based methods are effective for image restoration applications since they make use of texture priors learned by pre-trained over-complete dictionaries. However, sparse learning based methods are extremely slow due to complexity of sparse decomposition and a large number of image patches to process. In this paper, we introduce a fast approximation for LASSO (Least Absolute Shrinkage and Selection Operator) and apply the approach to single image super-resolution with CUDA acceleration. Our approach utilizes linear combinations of pre-computed sparse codes of standard orthogonal bases to estimate the sparse code of input signal. Error analysis is performed to find the feasible conditions of our approach and upper-bound of the estimation error. The simplicity of our approach makes it easy to be implemented on GPU. As for super-resolution application, we apply our approach to improve one of the best super-resolution methods by Yang et. al. The super-resolution results are comparable with that of the state-of-the-art methods while the speed can be increased to 620%.