We study the matrix completion problem: an underlying $$m \times n$$ P is low rank, with incoherent singular vectors, and a random A equal to on (uniformly) subset of entries size dn. All other are zero. The goal retrieve information from observation A. Let $$A_1$$ be where each entry multiplied by independent $$\{0,1\}$$ -Bernoulli variable parameter 1/2. This paper about when, how why non-Her...

Simultaneous sparse coding (SSC) has shown great potential in image denoising, because it exploits dependencies of patches in nature images. However, imposing joint sparsity might neglect the sight difference between patches. In this paper, we propose an image denoising algorithm based on robust simultaneous sparse coding (RSSC). In our algorithm, the sparse coefficient matrix is decomposed int...

Computing the null space of a sparse matrix, sometimes a rectangular sparse matrix, is an important part of some computations, such as embeddings and parametrization of meshes. We propose an efficient and reliable method to compute an orthonormal basis of the null space of a sparse square or rectangular matrix (usually with more rows than columns). The main computational component in our method...

In this paper, we present a new graph model of sparse matrix decomposition for parallel sparse matrix–vector multiplication. Our model differs from previous graph-based approaches in two main respects. Firstly, our model is based on edge colouring rather than vertex partitioning. Secondly, our model is able to correctly quantify and minimise the total communication volume of the parallel sparse...

In this paper we investigate a method to improve the performance of sparse LU matrix factorization used to solve unsymmetric linear systems, which appear in many mathematical models. We introduced and used the concept of the supernode for unsymmetric matrices in order to use dense matrix operations to perform the LU factorization for sparse matrices. We describe an algorithm that uses supernode...

A sparse decomposition approach of observed data matrix is presented in this paper and the approach is then used in blind source separation with less sensors than sources. First, sparse representation (factorization) of a data matrix is discussed. For a given basis matrix, there exist infinite coefficient matrices (solutions) generally such that the data matrix can be represented by the product...

Traditional Compressive Sensing (CS) recovery techniques resorts a dictionary matrix to recover a signal. The success of recovery heavily relies on finding a dictionary matrix in which the signal representation is sparse. Achieving a sparse representation does not only depend on the dictionary matrix, but also depends on the data. It is a challenging issue to find an optimal dictionary to recov...