Relevance Singular Vector Machine for low-rank matrix sensing

In this paper we develop a new Bayesian inference method for low rank matrix reconstruction. We call the new method the Relevance Singular Vector Machine (RSVM) where appropriate priors are defined on the singular vectors of the underlying matrix to promote low rank. To accelerate computations, a numerically efficient approximation is developed. The proposed algorithms are applied to matrix completion and matrix reconstruction problems and their performance is studied numerically.Comment: International Conference on Signal Processing and Communications (SPCOM), 5 page

Iteratively Reweighted Least Squares Algorithms for L1-Norm Principal Component Analysis

Principal component analysis (PCA) is often used to reduce the dimension of data by selecting a few orthonormal vectors that explain most of the variance structure of the data. L1 PCA uses the L1 norm to measure error, whereas the conventional PCA uses the L2 norm. For the L1 PCA problem minimizing the fitting error of the reconstructed data, we propose an exact reweighted and an approximate algorithm based on iteratively reweighted least squares. We provide convergence analyses, and compare their performance against benchmark algorithms in the literature. The computational experiment shows that the proposed algorithms consistently perform best

"Plug-and-Play" Edge-Preserving Regularization

In many inverse problems it is essential to use regularization methods that preserve edges in the reconstructions, and many reconstruction models have been developed for this task, such as the Total Variation (TV) approach. The associated algorithms are complex and require a good knowledge of large-scale optimization algorithms, and they involve certain tolerances that the user must choose. We present a simpler approach that relies only on standard computational building blocks in matrix computations, such as orthogonal transformations, preconditioned iterative solvers, Kronecker products, and the discrete cosine transform -- hence the term "plug-and-play." We do not attempt to improve on TV reconstructions, but rather provide an easy-to-use approach to computing reconstructions with similar properties.Comment: 14 pages, 7 figures, 3 table