We consider the problem of sparse signal recovery from a small number of random projections (measurements). This is a well known NP-hard to solve combinatorial optimization problem. A frequently used approach is based on greedy iterative procedures,
such as the Matching Pursuit (MP) algorithm. Here, we discuss a fast GPU implementation of the MP algorithm, based on the recently released NVIDIA CUDA API and CUBLAS library. The results show that the GPU version is substantially faster (up to 31 times) than the highly optimized CPU version based on CBLAS (GNU Scientific Library).
Principal component analysis (PCA) is a key statistical technique for multivariate data analysis. For large data sets the common approach to PCA computation is based on the standard NIPALS-PCA algorithm, which unfortunately suffers from loss of ortho
gonality, and therefore its applicability is usually limited to the estimation of the first few components. Here we present an algorithm based on Gram-Schmidt orthogonalization (called GS-PCA), which eliminates this shortcoming of NIPALS-PCA. Also, we discuss the GPU (Graphics Processing Unit) parallel implementation of both NIPALS-PCA and GS-PCA algorithms. The numerical results show that the GPU parallel optimize
