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A new algorithm is developed to jointly recover a temporal sequence of images from noisy and under-sampled Fourier data. Specifically, we consider the case where each data set is missing vital information that prevents its (individual)…
Natural images tend to mostly consist of smooth regions with individual pixels having highly correlated spectra. This information can be exploited to recover hyperspectral images of natural scenes from their incomplete and noisy…
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…
Modulo imaging enables high dynamic range (HDR) acquisition by cyclically wrapping saturated intensities, but accurate reconstruction remains challenging due to ambiguities between natural image edges and artificial wrap discontinuities.…
We consider the demixing problem of two (or more) structured high-dimensional vectors from a limited number of nonlinear observations where this nonlinearity is due to either a periodic or an aperiodic function. We study certain families of…
The characterization of a binary function by partial frequency information is considered. We show that it is possible to reconstruct binary signals from incomplete frequency measurements via the solution of a simple linear optimization…
We consider the problem of reconstructing an image from compressive measurements using a multi-resolution grid. In this context, the reconstructed image is divided into multiple regions, each one with a different resolution. This problem…
This dissertation is devoted to provide advanced nonconvex nonsmooth variational models of (Magnetic Resonance Image) MRI reconstruction, efficient learnable image reconstruction algorithms and parameter training algorithms that improve the…
High dynamic range (HDR) images capture much more intensity levels than standard ones. Current methods predominantly generate HDR images from 8-bit low dynamic range (LDR) sRGB images that have been degraded by the camera processing…
Magnetic resonance imaging (MRI) reconstruction is a fundamental task aimed at recovering high-quality images from undersampled or low-quality MRI data. This process enhances diagnostic accuracy and optimizes clinical applications. In…
We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…
Digital cameras can only capture a limited range of real-world scenes' luminance, producing images with saturated pixels. Existing single image high dynamic range (HDR) reconstruction methods attempt to expand the range of luminance, but…
Multi-segment reconstruction (MSR) problem consists of recovering a signal from noisy segments with unknown positions of the observation windows. One example arises in DNA sequence assembly, which is typically solved by matching short reads…
Reconstructing high-quality magnetic resonance images (MRI) from undersampled raw data is of great interest from both technical and clinical point of views. To this date, however, it is still a mathematically and computationally challenging…
Reconstructing continuous signals from a small number of discrete samples is a fundamental problem across science and engineering. In practice, we are often interested in signals with 'simple' Fourier structure, such as bandlimited,…
The goal of this paper is to present a non-iterative and more importantly an extremely fast algorithm to reconstruct images from compressively sensed (CS) random measurements. To this end, we propose a novel convolutional neural network…
The recent development of the on-chip micro-polarizer technology has made it possible to acquire four spatially aligned and temporally synchronized polarization images with the same ease of operation as a conventional camera. In this paper,…
Phase retrieval, a nonlinear problem prevalent in imaging applications, has been extensively studied using random models, some of which with i.i.d. sensing matrix components. While these models offer robust reconstruction guarantees, they…
Image restoration refers to the process of reconstructing noisy, destroyed, or missing parts of an image, which is an ill-posed inverse problem. A specific regularization term and image degradation are typically assumed to achieve…
In this paper we present a fast and efficient method for the reconstruction of Magnetic Resonance Images (MRI) from severely under-sampled data. From the Compressed Sensing theory we have mathematically modeled the problem as a constrained…