Compressive sensing predicts that sufficiently sparse vectors can be recovered from highly incomplete information using efficient recovery methods such as `1-minimization. Random matrices have become a popular choice for the measurement matrix. Indeed, near-optimal uniform recovery results have been shown for such matrices. In this note we focus on nonuniform recovery using subgaussian random m...

The Σ-method for structural analysis of a differential-algebraic equation (DAE) system produces offset vectors from which the sparsity pattern of a system Jacobian is derived. This pattern implies a block-triangular form (BTF) of the DAE that can be exploited to speed up numerical solution. The paper compares this fine BTF with the usually coarser BTF derived from the sparsity pattern of the si...

In this paper, we propose a greedy sparse recovery algorithm for target localization with RF sensor networks. The target spatial domain is discretized by grid pixels. When the network area consists only of several targets, the target localization is a sparsity-seeking problem such that the Compressed Sensing (CS) framework can be applied. We cast the target localization as a CS problem and solv...

Many wireless channel behavior exhibits approximate sparse modeling in time domain, therefore compressive sensing (CS) approaches are applied for more accurate wireless channel estimation than traditional least squares approach. However, the CS approach is not applied for multicarrier data information recovery because the transmitted symbol can be sparse neither in time domain nor in frequency ...

We propose a new approach, two-dimensional binary fused compressive sensing (2DBFCS) to recover 2D sparse piece-wise signals from 1-bit measurements, exploiting group sparsity in 2D 1-bit compressive sensing. The proposed method is a modified 2D version of the previous binary iterative hard thresholding (2DBIHT) algorithm, where, the objective function consists of a 2D one-sided l1 (or l2) func...

Sparsity-driven image recovery methods assume that images of interest can be sparsely approximated under some suitable system. As discontinuities of 2D images often show geometrical regularities along image edges with different orientations, an effective sparsifying system should have high orientation selectivity. There have been enduring efforts on constructing discrete frames and tight frames...

Compressed Sensing (CS) is an appealing framework for applications such as Magnetic Resonance Imaging (MRI). However, up-to-date, the sensing schemes suggested by CS theories are made of random isolated measurements, which are usually incompatible with the physics of acquisition. To reflect the physical constraints of the imaging device, we introduce the notion of blocks of measurements: the se...

Compressed Sensing is about recovering an unknown vector of dimension n from m n linear measurements. This task becomes possible, for instance, when few entries of the vector have large magnitude and, hence, the vector is essentially of low intrinsic dimension. If one wishes to recover an n1 × n2 matrix instead, low-rankness can be added as sparsity structure of low intrinsic dimensionality. Fo...

The non-negative solution to an underdetermined linear system can be uniquely recovered sometimes, even without imposing any additional sparsity constraints. In this paper, we derive conditions under which a unique non-negative solution for such a system can exist, based on the theory of polytopes. Furthermore, we develop the paradigm of combined sparse representations, where only a part of the...

In order to get better reconstruction quality from compressive sensing of images, exploitation of the dependency or correlation patterns among the transform coefficients has been popularly employed. Nevertheless, both recovery quality and recovery speed are not compromised well. In this paper, we study a new image sensing technique, called turbo fast compression image sensing, with computationa...