The problem of computing sparse (mostly zero) solutions to underdetermined linear systems of equations has received much attention recently, due to its applications to compressed sensing. Under mild assumptions, the sparsest solution has minimum-L1norm, and can be computed using linear programming. We present a non-iterative algorithm for this problem that requires only that each row of the sys...

With the advent of big data, there is a growing demand for smart algorithms that can extract relevant information from high-dimensional large data sets, potentially corrupted by faulty measurements (outliers). In this context, we present a novel line of research that utilizes the robust nature of L1norm subspaces for data dimensionality reduction and outlier processing. Specifically, (i) we use...

Completing a matrix from a small subset of its entries, i.e., matrix completion, is a challenging problem arising from many real-world applications, such as machine learning and computer vision. One popular approach to solving the matrix completion problem is based on low-rank decomposition/factorization. Low-rank matrix decomposition-based methods often require a pre-specified rank, which is d...

We present an optimization framework for expressing image processing applications that can account for certain perceptual biases of the human vision system (HVS). Perception literature is ripe with studies demonstrating the HVS to be more sensitive to pixel gradients than absolute pixel values, which has led to some important work in gradient domain image filtering. Inspired by this work, our o...

By coding a query sample as a sparse linear combination of all training samples and then classifying it by evaluating which class leads to the minimal coding residual, sparse representation based classification (SRC) leads to interesting results for robust face recognition. It is widely believed that the l1norm sparsity constraint on coding coefficients plays a key role in the success of SRC, w...

The purpose of present study is to investigate a nonparametric model that improves accuracy of option prices found by previous models. In this study option prices are calculated using multiple kernel Support Vector Regression with different norm values and their results are compared. L1norm multiple kernel learning Support Vector Regression (MKLSVR) has been successfully applied to option price...

An efficient simplification procedure of the optical flow (OF) algorithm as well as its hardware implementation using the field programmable gate array (FPGA) technology is presented. The modified algorithm is based on block matching of subsets of successive frames, and exploits onedimensional representation of subsets as well as the adaptive adjustments of their sizes. Also, an l1norm-based co...

It is a challenging problem to detect partially occluded pedestrians due to the diversity of occlusion patterns. Although training occlusionspecific detectors can help handle various partial occlusions, it is a nontrivial problem to integrate these detectors properly. A direct combination of all occlusion-specific detectors can be affected by unreliable detectors and usually does not favor heav...

INTRODUCTION: Compressed Sensing (CS) ([1], [2], [3], [4]) allows reconstructing a signal, if it can be represented sparsely in a suitable basis [4], from only a portion of its Fourier coefficients. It was first used by Lustig et al. [5] in MRI, and it has become popular for speeding up the acquisition process. Initially, CS was introduced as an l0-norm minimization [1] which is in practice uns...

This report presents an algorithm for the solution of multiple kernel learning (MKL) problems with elastic-net constraints on the kernel weights. Please see Sun et al. (2013) and Yang et al. (2011) for a review on multiple kernel learning and its extensions. In particular Yang et al. (2011) introduced the generalized multiple kernel learning (GMKL) model where the kernel weights are subject to ...