Carlo Tomasi Any m n matrix of rank r transforms the unit sphere in Rn into an r-dimensional hyperellipsoid in Rm. For instance, the rank-2 matrix A = 1 p2 264 p3 p3 3 3 1 1 375 (1) transforms the unit circle on the plane into an ellipse embedded in three-dimensional space. Figure 1 shows the map y = Ax : Two diametrically opposite points on the unit circle are mapped into the two endpoints of ...

Despite the success of magnetic resonance imaging techniques in many applications, acquisition noise is still a limiting factor for the quality and hence the usefulness of the techniques. In this paper, a new algorithm for denoising magnetic resonance images based on higher order singular value decomposition is proposed. The proposed algorithm first forms a single tensor from the noisy data. Ne...

The affine rank minimization problem is to minimize the rank of a matrix under linear constraints. It has many applications in various areas such as statistics, control, system identification and machine learning. Unlike the literatures which use the nuclear norm or the general Schatten q (0 < q < 1) quasi-norm to approximate the rank of a matrix, in this paper we use the Schatten 1/2 quasi-nor...

The speech enhancement techniques are often employed to improve the quality and intelligibility of the noisy speech signals. This paper discusses a novel technique for speech enhancement which is based on Singular Value Decomposition. This implementation utilizes a Genetic Algorithm based optimization method for reducing the effects of environmental noises from the singular vectors as well as t...

in the process of structural analysis we often come to structures that can be analyzed with simpler methods than the standard approaches. for these structures, known as regular structures, the matrices involved are in canonical forms and their eigen-solution can be performed in a simple manner. however, by adding or removing some elements or nodes, such methods cannot be utilized. here, an effi...

Singular Value Thresholding Algorithms for Low-rank Matrix Completion Jianfeng Cai, University of California at Los Angles, USA Low-rank matrix completion refers to recovering a low-rank matrix from a sampling of its entries. It routinely comes up whenever one collects partially filled out surveys, and one would like to infer the many missing entries. Matrix completion is a natural extension of...

Abstract. In this paper we consider the trace regression model. Assume that we observe a small set of entries or linear combinations of entries of an unknown matrix A0 corrupted by noise. We propose a new rank penalized estimator of A0. For this estimator we establish general oracle inequality for the prediction error both in probability and in expectation. We also prove upper bounds for the ra...

The speech enhancement techniques are often employed to improve the quality and intelligibility of the noisy speech signals. This paper discusses a novel technique for speech enhancement which is based on Singular Value Decomposition. This implementation utilizes a Genetic Algorithm based optimization method for reducing the effects of environmental noises from the singular vectors as well as t...

In this paper, we propose a modified speech enhancement system using wavelet packets thresholding algorithm. First, we describe the basic algorithms of wavelet-based speech enhancement systems and we explain a previous introduced algorithm for improvement of the basic algorithm. Then we discuss on some factors affecting the performance of this system, including the thresholding function and the...

PURPOSE A calibrationless parallel imaging reconstruction method, termed simultaneous autocalibrating and k-space estimation (SAKE), is presented. It is a data-driven, coil-by-coil reconstruction method that does not require a separate calibration step for estimating coil sensitivity information. METHODS In SAKE, an undersampled, multichannel dataset is structured into a single data matrix. T...