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Iterative Hard Thresholding (IHT) is a class of projected gradient descent methods for optimizing sparsity-constrained minimization models, with the best known efficiency and scalability in practice. As far as we know, the existing…
Iterative hard thresholding (IHT) is a projected gradient descent algorithm, known to achieve state of the art performance for a wide range of structured estimation problems, such as sparse inference. In this work, we consider IHT as a…
Compressed sensing (CS) or sparse signal reconstruction (SSR) is a signal processing technique that exploits the fact that acquired data can have a sparse representation in some basis. One popular technique to reconstruct or approximate the…
The idea of compressed sensing is to exploit representations in suitable (overcomplete) dictionaries that allow to recover signals far beyond the Nyquist rate provided that they admit a sparse representation in the respective dictionary.…
We present a new recovery analysis for a standard compressed sensing algorithm, Iterative Hard Thresholding (IHT) (Blumensath and Davies, 2008), which considers the fixed points of the algorithm. In the context of arbitrary measurement…
Commonly employed reconstruction algorithms in compressed sensing (CS) use the $L_2$ norm as the metric for the residual error. However, it is well-known that least squares (LS) based estimators are highly sensitive to outliers present in…
We propose a simple modification to the iterative hard thresholding (IHT) algorithm, which recovers asymptotically sparser solutions as a function of the condition number. When aiming to minimize a convex function $f(x)$ with condition…
We investigate the problem of reconstructing signals from a subsampled convolution of their modulated versions and a known filter. The problem is studied as applies to specific imaging systems relying on spatial phase modulation by randomly…
We propose a compressive sensing algorithm that exploits geometric properties of images to recover images of high quality from few measurements. The image reconstruction is done by iterating the two following steps: 1) estimation of normal…
Adaptive thresholding methods have proved to yield high SNRs and fast convergence in finding the solution to the Compressed Sensing (CS) problems. Recently, it was observed that the robustness of a class of iterative sparse recovery…
In this paper we consider the problem of exact recovery of a fixed sparse vector with the measurement matrices sequentially arriving along with corresponding measurements. We propose an extension of the iterative hard thresholding (IHT)…
In this work, we show that reconstructing a sparse signal from quantized compressive measurement can be achieved in an unified formalism whatever the (scalar) quantization resolution, i.e., from 1-bit to high resolution assumption. This is…
A spectrally sparse signal of order $r$ is a mixture of $r$ damped or undamped complex sinusoids. This paper investigates the problem of reconstructing spectrally sparse signals from a random subset of $n$ regular time domain samples, which…
We consider the inverse scattering problem for sparse scatterers. An image reconstruction algorithm is proposed that is based on a nonlinear generalization of iterative hard thresholding. The convergence and error of the method was analyzed…
In this paper, we analyze the generalization performance of the Iterative Hard Thresholding (IHT) algorithm widely used for sparse recovery problems. The parameter estimation and sparsity recovery consistency of IHT has long been known in…
Recent work by Rauhut and Ward developed a notion of weighted sparsity and a corresponding notion of Restricted Isometry Property for the space of weighted sparse signals. Using these notions, we pose a best weighted sparse approximation…
Compressed sensing has shown great potentials in accelerating magnetic resonance imaging. Fast image reconstruction and high image quality are two main issues faced by this new technology. It has been shown that, redundant image…
The question of fast convergence in the classical problem of high dimensional linear regression has been extensively studied. Arguably, one of the fastest procedures in practice is Iterative Hard Thresholding (IHT). Still, IHT relies…
This study addresses the blind deconvolution problem with modulated inputs, focusing on a measurement model where an unknown blurring kernel $\boldsymbol{h}$ is convolved with multiple random modulations…
Compressed sensing aims to undersample certain high-dimensional signals, yet accurately reconstruct them by exploiting signal characteristics. Accurate reconstruction is possible when the object to be recovered is sufficiently sparse in a…