Anomaly detection is an important task for hyperspectral data exploitation. A standard approach for anomaly detection in the literature is the method developed by Reed and Xiaoli, also called RX algorithm. A variation of this algorithm consists of applying the same concept to a local sliding window centered around each image pixel. The computational cost is very high for RX algorithm and it strongly increases for its local versions. However, current advances in high performance computing help to reduce the run-time of these algorithms. So, for the standard RX, it is possible to achieve a processing time similar to the data acquisition time and to increase the practical interest for its local versions. In this paper, we discuss several optimizations which exploit different forms of acceleration for these algorithms. First, we explain how the calculation of the correlation matrix and its inverse can be accelerated through optimization techniques based on the properties of these particular matrices and the efficient use of linear algebra libraries. Second, we describe parallel implementations of the RX algorithm, optimized for multicore platforms. These are well-known, inexpensive and widely available high performance computing platforms. The ability to detect anomalies of the global and local versions of RX is explored using a wide set of experiments, using both synthetic and real data, which are used for comparing the optimized versions of the global and local RX algorithms in terms of anomaly detection accuracy and computational efficiency. The synthetic images have been generated under different noise conditions and anomalous features. The two real scenes used in the experiments are a hyperspectral data set collected by NASA's Airborne Visible Infra-Red Imaging Spectrometer (AVIRIS) system over the World Trade Center (WTC) in New York, five days after the terrorist attacks, and another data set collected by the HYperspectral Digital Image Collection Experiment (HYDICE). Experimental results indicate that the proposed optimizations can significantly improve the performance of the considered algorithms without reducing their anomaly detection accuracy.

Sparse matrices are involved in linear systems, eigensystems and partial differential equations from a wide spectrum of scientific and engineering disciplines. Hence, sparse matrix vector product (SpMV) is considered as key operation in engineering and scientific computing. For these applications the optimization of the sparse matrix vector product (SpMV) is very relevant. However, the irregular computation involved in SpMV prevents the optimum exploitation of computational architectures when the sparse matrices are very large. Graphics Processing Units (GPUs) have recently emerged as platforms that yield outstanding acceleration factors. SpMV implementations for GPUs have already appeared on the scene. This work proposes and evaluates new implementations of SpMV for GPUs called ELLR-T. They are based on the format ELLPACK-R, which allows storage of the sparse matrix in a regular manner. A comparative evaluation against a variety of storage formats previously proposed has been carried out based on a representative set of test matrices. The results show that: (1) the SpMV is highly accelerated with GPUs; (2) the performance strongly depends on the specific pattern of the matrix; and (3) the implementations ELLR-T achieve higher overall performance. Consequently, the new implementations of SpMV, ELLR-T, described in this paper can help to exploit the GPUs, because, they achieve high performance and they can be easily joined in the engineering and scientific computing.

Sparse matrix matrix (SpMM) multiplication is involved in a wide range of scientific and technical applications. The computational requirements for this kind of operation are enormous, especially for large matrices. This paper analyzes and evaluates a method to efficiently compute the SpMM product in a computing environment that includes graphics processing units (GPUs). Some libraries to compute this matricial operation can be found in the literature. However, our strategy (FastSpMM) outperforms the existing approaches because it combines the use of the ELLPACK-R storage format with the exploitation of the high ratio computation/memory access of the SpMM operation and the overlapping of CPU–GPU communications/computations by Compute Unified Device Architecture streaming computation. In this work, FastSpMM is described and its performance evaluated with regard to the CUSPARSE library (supplied by NVIDIA), which also includes routines to compute SpMM on GPUs. Experimental evaluations based on a representative set of test matrices show that, in terms of performance, FastSpMM outperforms the CUSPARSE routine as well as the implementation of the SpMM as a set of sparse matrix vector products.