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A successful class of image denoising methods is based on Bayesian approaches working in wavelet representations. However, analytical estimates can be obtained only for particular combinations of analytical models of signal and noise, thus…
We consider the problem of robust deconvolution, and particularly the recovery of an unknown deterministic signal convolved with a known filter and corrupted by additive noise. We present a novel, non-iterative data-driven approach.…
Reconstructing the unknown spectrum of a given X-ray source is a common problem in a wide range of X-ray imaging tasks. For high-energy sources, transmission measurements are mostly used to recover the X-ray spectrum, as a solution to an…
Many imaging modalities involve reconstruction of unknown objects from collections of noisy projections related by random rotations. In one of these modalities, cryogenic electron microscopy (cryo-EM), the extremely low signal-to-noise…
Machine learning, and more specifically deep learning, have shown remarkable performance in sensing, communications, and inference. In this paper, we consider the application of the deep unfolding technique in the problem of signal…
Image denoising is a fundamental problem in image processing whose primary objective is to remove the noise while preserving the original image structure. In this work, we proposed a new architecture for image denoising. We have used…
Efficient estimation of wideband spectrum is of great importance for applications such as cognitive radio. Recently, sub-Nyquist sampling schemes based on compressed sensing have been proposed to greatly reduce the sampling rate. However,…
Recently, the application of low rank minimization to image denoising has shown remarkable denoising results which are equivalent or better than those of the existing state-of-the-art algorithms. However, due to iterative nature of low rank…
Denoising algorithms play a crucial role in medical image processing and analysis. However, classical denoising algorithms often ignore explanatory and critical medical features preservation, which may lead to misdiagnosis and legal…
Computed Tomography (CT) is widely used in engineering and medicine for imaging the interior of objects, patients, or animals. If the employed X-ray source is monoenergetic, image reconstruction essentially means the inversion of a ray…
Modern signal and image acquisition systems are able to capture data that is no longer real-valued, but may take values on a manifold. However, whenever measurements are taken, no matter whether manifold-valued or not, there occur tiny…
We consider the applications of a numerical-analytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of Vlasov-Poisson/Maxwell equations. We calculate the…
This paper investigates the phase retrieval problem, which aims to recover a signal from the magnitudes of its linear measurements. We develop statistically and computationally efficient algorithms for the situation when the measurements…
An efficient despeckling method using a quantum-inspired adaptive threshold function is presented for reducing noise of ultrasound images. In the first step, the ultrasound image is decorrelated by an spectrum equalization procedure due to…
Poisson noise commonly occurs in images captured by photon-limited imaging systems such as in astronomy and medicine. As the distribution of Poisson noise depends on the pixel intensity value, noise levels vary from pixels to pixels. Hence,…
We develop a method for sparse image reconstruction from polychromatic computed tomography (CT) measurements under the blind scenario where the material of the inspected object and the incident-energy spectrum are unknown. We obtain a…
Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency,…
Model-based methods are widely used for reconstruction in compressed sensing (CS) magnetic resonance imaging (MRI), using regularizers to describe the images of interest. The reconstruction process is equivalent to solving a composite…
For time series data observed at non-random and possibly non-equidistant time points, we estimate the trend function nonparametrically. Under the assumption of a bounded total variation of the function and low-order moment conditions on the…
Cosmic microwave background (CMB) radiation data obtained by different experiments contain, besides the desired signal, a superposition of microwave sky contributions. We present a fast and robust method, using a wavelet decomposition on…