We describe a method of integrating KarhunenLoève Transform (KLT) into compressive sensing, which can as a result leverage KLT’s optimality in revealing the sparsity of a signal. We present two complementary results: (1) by using the KLT to find the optimal basis for decoding we can drastically reduce the number of measurements for compressive sensing used in applications such as spectrum sensi...

Compressive Sensing is a recently developed technique that exploits the sparsity of naturally occurring signals and images to solve inverse problems when the number of samples is less than the size of the original signal. We apply this technique to solve underdetermined inverse problems that commonly occur in remote sensing, including superresolution, image fusion and deconvolution. We use l 1-...

Compressive sensing (CS) has been a way to lower sampling rate leading to data reduction for processing in multiple-input multiple-output (MIMO) radar systems. In this paper, we further reduce the computational complexity of a pulse-Doppler collocated MIMO radar by introducing a two-dimensional (2D) compressive sensing. To do so, we first introduce a new 2D formulation for the compressed receiv...

Compressive sensing is a new field in signal processing and applied mathematics. It allows one to simultaneously sample and compress signals which are known to have a sparse representation in a known basis or dictionary along with the subsequent recovery by linear programming (requiring polynomial (P) time) of the original signals with low or no error [1, 2, 3]. In a discrete setting, sparsity ...

The 1-bit compressive sensing has been studied recently in the field of sparse signal recovery. Since the amplitude information of sparse signals in 1-bit models is not available, the solution to the 1-bit models is no longer unique in general. As a result, the aim of 1-bit compressive sensing is to recover the signal within a positive scalar factor by using some decoding methods. In this paper...

in this paper, a novel time-varying channel estimation approach based on Kalman filter compressive sensing is proposed for the high sampling problem of ultra wideband (UWB) system considering the sparse of the channel impulse response. The direct sequence UWB signal is formulated to the mathematical model of compressed sensing after down sampling. The receiver recovery the channel impulse respo...

Compressive sensing, also known as compressive sampling, has made a tremendous impact on signal processing and statistical learning, and has facilitated numerous applications in areas ranging frommedical imaging and computational biology to astronomy. Recently, there has been a growing interest in applying the principles of compressive sensing to an even wider range of topics, including those i...

An efficient method and system for compressive sensing of hyperspectral data is presented. Compression efficiency is achieved by randomly encoding both the spatial and the spectral domains of the hyperspectral datacube. Separable sensing architecture is used to reduce the computational complexity associated with the compressive sensing of a large volume of data, which is typical of hyperspectra...

The recent theory of compressive sensing leverages upon the structure of signals to acquire them with much fewer measurements than was previously thought necessary, and certainly well below the traditional Nyquist-Shannon sampling rate. However, most implementations developed to take advantage of this framework revolve around controlling the measurements with carefully engineered material or ac...

Compressive sensing is considered a huge breakthrough in signal acquisition. It allows recording an image consisting of N(2) pixels using much fewer than N(2) measurements if it can be transformed to a basis where most pixels take on negligibly small values. Standard compressive sensing techniques suffer from the computational overhead needed to reconstruct an image with typical computation tim...