Related papers: Sparse Wavelet Representations of Spatially Varyin…
Sparse representation of 3D images is considered within the context of data reduction. The goal is to produce high quality approximations of 3D images using fewer elementary components than the number of intensity points in the 3D array.…
Sparsity is one of the key concepts that allows the recovery of signals that are subsampled at a rate significantly lower than required by the Nyquist-Shannon sampling theorem. Our proposed framework uses arbitrary multiscale transforms,…
We propose a new algorithm for recovery of sparse signals from their compressively sensed samples. The proposed algorithm benefits from the strategy of gradual movement to estimate the positions of non-zero samples of sparse signal. We…
We develop a sparse spectral method for a class of fractional differential equations, posed on $\mathbb{R}$, in one dimension. These equations can include sqrt-Laplacian, Hilbert, derivative and identity terms. The numerical method utilizes…
In this article, we review the literature on design and analysis of recursive algorithms for reconstructing a time sequence of sparse signals from compressive measurements. The signals are assumed to be sparse in some transform domain or in…
In this paper we discuss an application of Stochastic Approximation to statistical estimation of high-dimensional sparse parameters. The proposed solution reduces to resolving a penalized stochastic optimization problem on each stage of a…
The discrete curvelet transform decomposes an image into a set of fundamental components that are distinguished by direction and size as well as a low-frequency representation. The curvelet representation is approximately sparse; thus, it…
Image convolution with complex kernels is a fundamental operation in photography, scientific imaging, and animation effects, yet direct dense convolution is computationally prohibitive on resource-limited devices. Existing approximations,…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
Sparse coding of images is traditionally done by cutting them into small patches and representing each patch individually over some dictionary given a pre-determined number of nonzero coefficients to use for each patch. In lack of a way to…
Image deblurring is a fundamental problem in imaging, usually solved with com-putationally intensive optimization procedures. We show that the minimization can be significantly accelerated by leveraging the fact that images and blur…
Sub-pixel registration is a crucial step for applications such as super-resolution in remote sensing, motion compensation in magnetic resonance imaging, and non-destructive testing in manufacturing, to name a few. Recently, these…
Clustering images according to their acquisition devices is a well-known problem in multimedia forensics, which is typically faced by means of camera Sensor Pattern Noise (SPN). Such an issue is challenging since SPN is a noise-like signal,…
Many applications like audio and image processing show that sparse representations are a powerful and efficient signal modeling technique. Finding an optimal dictionary that generates at the same time the sparsest representations of data…
In this paper, we study the problem of image recovery from given partial (corrupted) observations. Recovering an image using a low-rank model has been an active research area in data analysis and machine learning. But often, images are not…
In this paper, we propose a Bayesian MAP estimator for solving the deconvolution problems when the observations are corrupted by Poisson noise. Towards this goal, a proper data fidelity term (log-likelihood) is introduced to reflect the…
In imaging modalities recording diffraction data, the original image can be reconstructed assuming known phases. When phases are unknown, oversampling and a constraint on the support region in the original object can be used to solve a…
The high complexity of various inverse problems poses a significant challenge to model-based reconstruction schemes, which in such situations often reach their limits. At the same time, we witness an exceptional success of data-based…
Image reconstruction based on indirect, noisy, or incomplete data remains an important yet challenging task. While methods such as compressive sensing have demonstrated high-resolution image recovery in various settings, there remain issues…
Regularization approaches have demonstrated their effectiveness for solving ill-posed problems. However, in the context of variational restoration methods, a challenging question remains, which is how to find a good regularizer. While total…