Since the rapidly increasing data scale imposes a great computational challenge to the problem of Sparse Subspace Clustering (SSC), the existing optimization algorithms e.g. ADMM (Alternating Direction Method of Multipliers) for SSC are implemented in a sequential way which is unable to make use of multi-core processors to improve computational efficiency. To address this issue, a parallel SSC based on coordinate descent was proposed,inspired by a simple observation that the SSC can be formulated as a sequence of sample based sparse self-expression sub-problems. The proposed algorithm solves individual sub-problems by using a coordinate descent algorithm with fewer parameters and fast convergence. Based on the fact that the self-expression sub-problems are independent, a strategy was adopted to solve these sub-problems simultaneously on different processor cores, which brings the benefits of low computer resource consumption and fast running speed, it means that that the proposed algorithm is suitable for large scale clustering. Experiments on simulated data and Hopkins-155 motion segmentation dataset demonstrate that the proposed parallel SSC method on multi-core processors significantly improves the computational efficiency and ensures the accuracy when compared with ADMM.

The classic super-resolution algorithm via sparse coding has high computational cost during the reconstruction phase. In view of the disadvantages, a predictive sparse coding-based single image super-resolution method was proposed. In the training phase, the proposed method imposed a code prediction error term to the traditional sparse coding error function, and used an alternating minimization procedure to minimize the resultant objective function. In the testing phase, the reconstruction coefficient could be estimated by simply multiplying the low-dimensional image patch with the low-dimensional dictionary, without any need to solve sparse regression problems. The experimental results demonstrate that, compared with the classic single image super-resolution algorithm via sparse coding, the proposed method is able to significantly reduce the reconstruction time while maintaining super-resolution visual effect.