Related papers: Frame Coherence and Sparse Signal Processing

Approximate message passing is an iterative algorithm for compressed sensing and related applications. A solid theory about the performance and convergence of the algorithm exists for measurement matrices having iid entries of zero mean.…

The construction of highly incoherent frames, sequences of vectors placed on the unit hyper sphere of a finite dimensional Hilbert space with low correlation between them, has proven very difficult. Algorithms proposed in the past have…

Signal processing is rich in inherently continuous and often nonlinear applications, such as spectral estimation, optical imaging, and super-resolution microscopy, in which sparsity plays a key role in obtaining state-of-the-art results.…

The present paper provides a comprehensive study of de-noising properties of frames and, in particular, tight frames, which constitute one of the most popular tools in contemporary signal processing. The objective of the paper is to bridge…

We propose a novel regularization method for compressive imaging in the context of the compressed sensing (CS) theory with coherent and redundant dictionaries. Natural images are often complicated and several types of structures can be…

Compressed sensing deals with the reconstruction of sparse signals using a small number of linear measurements. One of the main challenges in compressed sensing is to find the support of a sparse signal. In the literature, several bounds on…

Detecting or classifying already known sparse signals contaminated by Gaussian noise from compressive measurements is different from reconstructing sparse signals, as its objective is to minimize the error probability which describes…

In this paper, we propose a sparse signal estimation algorithm that is suitable for many wireless communication systems, especially for the future millimeter wave and underwater communication systems. This algorithm is not only…

We consider compressed sensing of block-sparse signals, i.e., sparse signals that have nonzero coefficients occuring in clusters. Based on an uncertainty relation for block-sparse signals, we define a block-coherence measure and we show…

Many signal processing and machine learning applications are built from evaluating a kernel on pairs of signals, e.g. to assess the similarity of an incoming query to a database of known signals. This nonlinear evaluation can be simplified…

In this paper we consider estimation of sparse covariance matrices and propose a thresholding procedure which is adaptive to the variability of individual entries. The estimators are fully data driven and enjoy excellent performance both…

Scaling frame vectors is a simple and noninvasive way to construct tight frames. However, not all frames can be modifed to tight frames in this fashion, so in this case we explore the problem of finding the best conditioned frame by…

A field known as Compressive Sensing (CS) has recently emerged to help address the growing challenges of capturing and processing high-dimensional signals and data sets. CS exploits the surprising fact that the information contained in a…

We introduce a learning-based algorithm to obtain a measurement matrix for compressive sensing related recovery problems. The focus lies on matrices with a constant modulus constraint which typically represent a network of analog phase…

In this paper three different scenarios in wide band spectrum sensing have been studied. While the signal and noise statistics are supposed to be unspecified, random matrixes have been utilized in order to estimate the noise variance. These…

Phase retrieval (PR) is a popular research topic in signal processing and machine learning. However, its performance degrades significantly when the measurements are corrupted by noise or outliers. To address this limitation, we propose a…

We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…

Recent work has demonstrated that using a carefully designed sensing matrix rather than a random one, can improve the performance of compressed sensing. In particular, a well-designed sensing matrix can reduce the coherence between the…

Spectrum sensing is an important process in cognitive radio. A number of sensing techniques that have been proposed suffer from high processing time, hardware cost and computational complexity. To address these problems, compressive sensing…

A classic problem is the estimation of a set of parameters from measurements collected by only a few sensors. The number of sensors is often limited by physical or economical constraints and their placement is of fundamental importance to…