Sparsity-based Algorithm Research Articles

A low-complexity multi-target tracking algorithm in urban environments using sparse modeling

We propose a novel sparsity-based algorithm for multiple-target tracking in a time-varying multipath environment. We develop a sparse measurement model for the received signal, by considering a finite dimensional representation of the time-varying system function which characterizes the transmission channel. The measurement model allows us to exploit the joint delay–Doppler diversity offered by the environment. We reformulate the problem of multiple-target tracking as a block support recovery problem and we derive an upper bound on the overall error probability of wrongly identifying the support of the sparse signal. Using this bound, we prove that spread-spectrum waveforms are ideal candidates for signaling. We also prove that under spread-spectrum signaling, the dictionary of the sparse measurement model exhibits a special structure. We exploit this structure to develop a computationally inexpensive support recovery algorithm by projecting the received signal on to the row space of the dictionary. Numerical simulations show that tracking using proposed algorithm for support recovery performs better when compared to tracking using other sparse reconstruction algorithms and tracking using a particle filter. The proposed algorithm takes significantly less time when compared to the time taken by other methods.

Hyperspectral Image Classification Using Dictionary-Based Sparse Representation

A new sparsity-based algorithm for the classification of hyperspectral imagery is proposed in this paper. The proposed algorithm relies on the observation that a hyperspectral pixel can be sparsely represented by a linear combination of a few training samples from a structured dictionary. The sparse representation of an unknown pixel is expressed as a sparse vector whose nonzero entries correspond to the weights of the selected training samples. The sparse vector is recovered by solving a sparsity-constrained optimization problem, and it can directly determine the class label of the test sample. Two different approaches are proposed to incorporate the contextual information into the sparse recovery optimization problem in order to improve the classification performance. In the first approach, an explicit smoothing constraint is imposed on the problem formulation by forcing the vector Laplacian of the reconstructed image to become zero. In this approach, the reconstructed pixel of interest has similar spectral characteristics to its four nearest neighbors. The second approach is via a joint sparsity model where hyperspectral pixels in a small neighborhood around the test pixel are simultaneously represented by linear combinations of a few common training samples, which are weighted with a different set of coefficients for each pixel. The proposed sparsity-based algorithm is applied to several real hyperspectral images for classification. Experimental results show that our algorithm outperforms the classical supervised classifier support vector machines in most cases.

Sparse Representation for Target Detection in Hyperspectral Imagery

In this paper, we propose a new sparsity-based algorithm for automatic target detection in hyperspectral imagery (HSI). This algorithm is based on the concept that a pixel in HSI lies in a low-dimensional subspace and thus can be represented as a sparse linear combination of the training samples. The sparse representation (a sparse vector corresponding to the linear combination of a few selected training samples) of a test sample can be recovered by solving an l0-norm minimization problem. With the recent development of the compressed sensing theory, such minimization problem can be recast as a standard linear programming problem or efficiently approximated by greedy pursuit algorithms. Once the sparse vector is obtained, the class of the test sample can be determined by the characteristics of the sparse vector on reconstruction. In addition to the constraints on sparsity and reconstruction accuracy, we also exploit the fact that in HSI the neighboring pixels have a similar spectral characteristic (smoothness). In our proposed algorithm, a smoothness constraint is also imposed by forcing the vector Laplacian at each reconstructed pixel to be minimum all the time within the minimization process. The proposed sparsity-based algorithm is applied to several hyperspectral imagery to detect targets of interest. Simulation results show that our algorithm outperforms the classical hyperspectral target detection algorithms, such as the popular spectral matched filters, matched subspace detectors, adaptive subspace detectors, as well as binary classifiers such as support vector machines.

Levelwise algorithms for vector processing of sparse power system matrices

Algorithms exploiting factorization path graph levels have been proposed in order to obtain a fine grain scheduling of sparse matrix operations suitable for vector/parallel processing. This paper deals with the problem of how to make levelwise algorithms more computationally efficient on vector processors. Existing implementations of (static) levelwise algorithms are reconsidered, showing that the recursive nature of the update operations is the bottleneck of the computation. A novel dynamic levelwise algorithm that is capable of overcoming the recurrence problem is proposed. It is based on reforming the level sets each time a new batch of vectorizable operations is scheduled. Test cases consist in the factorization and F/B substitution using sparse power system matrices with dimensions of up to 12000. The tests are carried out on a CRAY Y-MP C94/2128 vector computer. Speed-ups of about one order of magnitude have been achieved by the dynamic levelwise algorithm compared to a standard sparsity-based algorithm.