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Compressive spectral imaging (CSI) has emerged as an alternative spectral image acquisition technology, which reduces the number of measurements at the cost of requiring a recovery process. In general, the reconstruction methods are based…
Compressed sensing is a powerful tool in applications such as magnetic resonance imaging (MRI). It enables accurate recovery of images from highly undersampled measurements by exploiting the sparsity of the images or image patches in a…
This chapter develops a theoretical analysis of the convex programming method for recovering a structured signal from independent random linear measurements. This technique delivers bounds for the sampling complexity that are similar with…
In this manuscript, we analyze the sparse signal recovery (compressive sensing) problem from the perspective of convex optimization by stochastic proximal gradient descent. This view allows us to significantly simplify the recovery analysis…
The paper analyses the possibility to recover different biomedical signals if limited number of samples is available. Having in mind that monitoring of health condition is done by measuring and observing key parameters such as heart…
Sparse coding and dictionary learning are popular techniques for linear inverse problems such as denoising or inpainting. However in many cases, the measurement process is nonlinear, for example for clipped, quantized or 1-bit measurements.…
Magnetic resonance imaging (MRI) reconstruction is an active inverse problem which can be addressed by conventional compressed sensing (CS) MRI algorithms that exploit the sparse nature of MRI in an iterative optimization-based manner.…
Compressed Sensing suggests that the required number of samples for reconstructing a signal can be greatly reduced if it is sparse in a known discrete basis, yet many real-world signals are sparse in a continuous dictionary. One example is…
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…
This paper presents a deep learning method for faster magnetic resonance imaging (MRI) by reducing k-space data with sub-Nyquist sampling strategies and provides a rationale for why the proposed approach works well. Uniform subsampling is…
We describe an acquisition/processing procedure for image reconstruction in dynamic Magnetic Resonance Imaging (MRI). The approach requires sliding window to record a set of trajectories in the k-space, standard regularization to…
This paper presents modification of the TwIST algorithm for Compressive Sensing MRI images reconstruction. Compressive Sensing is new approach in signal processing whose basic idea is recovering signal form small set of available samples.…
This paper addresses the problem of simultaneous signal recovery and dictionary learning based on compressive measurements. Multiple signals are analyzed jointly, with multiple sensing matrices, under the assumption that the unknown signals…
Over the past several decades, many different types of computational imaging approaches have been proposed for improving MRI. In this paper, we provide an overview of methods that assume that MRI Fourier data is linearly predictable. Linear…
Real-time magnetic resonance imaging (MRI) methods generally shorten the measuring time by acquiring less data than needed according to the sampling theorem. In order to obtain a proper image from such undersampled data, the reconstruction…
Compressed Sensing MRI (CS-MRI) has shown promise in reconstructing under-sampled MR images, offering the potential to reduce scan times. Classical techniques minimize a regularized least-squares cost function using an expensive iterative…
Is it possible to detect a feature in an image without ever looking at it? Images are known to have sparser representation in Wavelets and other similar transforms. Compressed Sensing is a technique which proposes simultaneous acquisition…
This paper deals with the Compressive Sensing implementation in the Face Recognition problem. Compressive Sensing is new approach in signal processing with a single goal to recover signal from small set of available samples. Compressive…
Compressed sensing is a paradigm within signal processing that provides the means for recovering structured signals from linear measurements in a highly efficient manner. Originally devised for the recovery of sparse signals, it has become…
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,…