Related papers: Optimal Compressive Imaging of Fourier Data
Compressed sensing is designed to measure sparse signals directly in a compressed form. However, most signals of interest are only "approximately sparse", i.e. even though the signal contains only a small fraction of relevant (large)…
What learning algorithms can be run directly on compressively-sensed data? In this work, we consider the question of accurately and efficiently computing low-rank matrix or tensor factorizations given data compressed via random projections.…
Modern reconstruction methods for magnetic resonance imaging (MRI) exploit the spatially varying sensitivity profiles of receive-coil arrays as additional source of information. This allows to reduce the number of time-consuming…
In this letter, we propose a turbo compressed sensing algorithm with partial discrete Fourier transform (DFT) sensing matrices. Interestingly, the state evolution of the proposed algorithm is shown to be consistent with that derived using…
We consider a compressive hyperspectral imaging reconstruction problem, where three-dimensional spatio-spectral information about a scene is sensed by a coded aperture snapshot spectral imager (CASSI). The CASSI imaging process can be…
In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the…
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…
A new digital image encryption method based on fast compressed sensing approach using structurally random matrices and Arnold transform is proposed. Considering the natural images to be compressed in any domain, the fast compressed sensing…
Compressive sampling has become a widely used approach to construct polynomial chaos surrogates when the number of available simulation samples is limited. Originally, these expensive simulation samples would be obtained at random locations…
A recent trend in the signal/image processing literature is the optimization of Fourier sampling schemes for specific datasets of signals. In this paper, we explain why choosing optimal non Cartesian Fourier sampling patterns is a difficult…
The sparse layouts of radio interferometers result in an incomplete sampling of the sky in Fourier space which leads to artifacts in the reconstructed images. Cleaning these systematic effects is essential for the scientific use of…
We study the problem of distributed and rate-adaptive feature compression for linear regression. A set of distributed sensors collect disjoint features of regressor data. A fusion center is assumed to contain a pretrained linear regression…
Learned image compression have attracted considerable interests in recent years. It typically comprises an analysis transform, a synthesis transform, quantization and an entropy coding model. The analysis transform and synthesis transform…
The field of medical image reconstruction has seen roughly four types of methods. The first type tended to be analytical methods, such as filtered back-projection (FBP) for X-ray computed tomography (CT) and the inverse Fourier transform…
Compressive sensing is a method to recover the original image from undersampled measurements. In order to overcome the ill-posedness of this inverse problem, image priors are used such as sparsity in the wavelet domain, minimum…
Certain applications such as Magnetic Resonance Imaging (MRI) require the reconstruction of functions from Fourier spectral data. When the underlying functions are piecewise-smooth, standard Fourier approximation methods suffer from the…
In this paper, we present the Monte-Carlo Compressive Optimization algorithm, a new method to solve a combinatorial optimization problem that is assumed compressible. The method relies on random queries to the objective function in order to…
Signal sampling and reconstruction is a fundamental engineering task at the heart of signal processing. The celebrated Shannon-Nyquist theorem guarantees perfect signal reconstruction from uniform samples, obtained at a rate twice the…
We propose a novel mesh refinement scheme based on signal processing for boundary integral simulations of inviscid droplet dynamics with axial symmetry. A key idea is to directly access the Fourier coefficients of a principal curvature as a…
Sonography techniques use multiple transducer elements for tissue visualization. Signals detected at each element are sampled prior to digital beamforming. The sampling rates required to perform high resolution digital beamforming are…