Related papers: Deriving RIP sensing matrices for sparsifying dict…
The restricted isometry property (RIP) for design matrices gives guarantees for optimal recovery in sparse linear models. It is of high interest in compressed sensing and statistical learning. This property is particularly important for…
This paper observes the application of the Compressive Sensing in reconstruction of the under-sampled iris images. Iris recognition represents form of biometric identification whose usage in real applications is growing. Compressive Sensing…
In compressed sensing, the restricted isometry property (RIP) on $M \times N$ sensing matrices (where $M < N$) guarantees efficient reconstruction of sparse vectors. A matrix has the $(s,\delta)$-$\mathsf{RIP}$ property if behaves as a…
Matrices satisfying the Restricted Isometry Property (RIP) play an important role in the areas of compressed sensing and statistical learning. RIP matrices with optimal parameters are mainly obtained via probabilistic arguments, as explicit…
The choice of the sensing matrix is crucial in compressed sensing. Random Gaussian sensing matrices satisfy the restricted isometry property, which is crucial for solving the sparse recovery problem using convex optimization techniques.…
Compressive sensing (CS) is well-known for its unique functionalities of sensing, compressing, and security (i.e. CS measurements are equally important). However, there is a tradeoff. Improving sensing and compressing efficiency with prior…
Compressive Sensing (CS) exploits the surprising fact that the information contained in a sparse signal can be preserved in a small number of compressive, often random linear measurements of that signal. Strong theoretical guarantees have…
This paper addresses the problem of simultaneous signal recovery and dictionary learning based on compressive measurements. Multiple signals are analyzed jointly, with multiple sensing matrices, under the assumption that the unknown signals…
Compressed sensing (CS) enables people to acquire the compressed measurements directly and recover sparse or compressible signals faithfully even when the sampling rate is much lower than the Nyquist rate. However, the pure random sensing…
In compressed sensing (CS) framework, a signal is sampled below Nyquist rate, and the acquired compressed samples are generally random in nature. However, for efficient estimation of the actual signal, the sensing matrix must preserve the…
Compressive sensing aims to recover a high-dimensional sparse signal from a relatively small number of measurements. In this paper, a novel design of the measurement matrix is proposed. The design is inspired by the construction of…
This paper deals with the design of a sensing matrix along with a sparse recovery algorithm by utilizing the probability-based prior information for compressed sensing system. With the knowledge of the probability for each atom of the…
This paper establishes a sharp condition on the restricted isometry property (RIP) for both the sparse signal recovery and low-rank matrix recovery. It is shown that if the measurement matrix $A$ satisfies the RIP condition…
Compressive Sensing (CS) theory shows that a signal can be decoded from many fewer measurements than suggested by the Nyquist sampling theory, when the signal is sparse in some domain. Most of conventional CS recovery approaches, however,…
Non-convex constraints have recently proven a valuable tool in many optimisation problems. In particular sparsity constraints have had a significant impact on sampling theory, where they are used in Compressed Sensing and allow structured…
Recovery of the initial state of a high-dimensional system can require a large number of measurements. In this paper, we explain how this burden can be significantly reduced when randomized measurement operators are employed. Our work…
Many emerging applications involve sparse signals, and their processing is a subject of active research. We desire a large class of sensing matrices which allow the user to discern important properties of the measured sparse signal. Of…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
Compressed sensing (CS) shows that a signal having a sparse or compressible representation can be recovered from a small set of linear measurements. In classical CS theory, the sampling matrix and representation matrix are assumed to be…
We consider the compressive sensing of a sparse or compressible signal ${\bf x} \in {\mathbb R}^M$. We explicitly construct a class of measurement matrices, referred to as the low density frames, and develop decoding algorithms that produce…