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Compressed Sensing Magnetic Resonance Imaging (CS-MRI) significantly accelerates MR data acquisition at a sampling rate much lower than the Nyquist criterion. A major challenge for CS-MRI lies in solving the severely ill-posed inverse…

Magnetic resonance imaging (MRI) has revolutionized medical imaging, providing a non-invasive and highly detailed look into the human body. However, the long acquisition times of MRI present challenges, causing patient discomfort, motion…

Magnetic resonance imaging (MRI) is an essential medical tool with inherently slow data acquisition process. Slow acquisition process requires patient to be long time exposed to scanning apparatus. In recent years significant efforts are…

Fast Magnetic Resonance Imaging (MRI) is highly in demand for many clinical applications in order to reduce the scanning cost and improve the patient experience. This can also potentially increase the image quality by reducing the motion…

Compressed sensing (CS) is a new signal acquisition paradigm that enables the reconstruction of signals and images from a low number of samples. A particularly exciting application of CS is Magnetic Resonance Imaging (MRI), where CS…

Task-adapted compressed sensing magnetic resonance imaging (CS-MRI) is emerging to address the specific demands of downstream clinical tasks with significantly fewer k-space measurements than required by Nyquist sampling. However, existing…

Dynamic Magnetic Resonance Imaging (MRI) is a crucial non-invasive method used to capture the movement of internal organs and tissues, making it a key tool for medical diagnosis. However, dynamic MRI faces a major challenge: long…

Compressed sensing (CS) theory assures us that we can accurately reconstruct magnetic resonance images using fewer k-space measurements than the Nyquist sampling rate requires. In traditional CS-MRI inversion methods, the fact that the…

Compressive sensing (CS) is an effective approach for fast Magnetic Resonance Imaging (MRI). It aims at reconstructing MR images from a small number of under-sampled data in k-space, and accelerating the data acquisition in MRI. To improve…

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 (CS) has been playing a key role in accelerating the magnetic resonance imaging (MRI) acquisition process. With the resurgence of artificial intelligence, deep neural networks and CS algorithms are being integrated to…

Compressed Sensing MRI reconstructs images of the body's internal anatomy from undersampled measurements, thereby reducing scan time. Recently, deep learning has shown great potential for reconstructing high-fidelity images from highly…

Magnetic resonance imaging (MRI) is a non-invasive imaging modality and provides comprehensive anatomical and functional insights into the human body. However, its long acquisition times can lead to patient discomfort, motion artifacts, and…

Compressive sensing (CS) reconstructs images from sub-Nyquist measurements by solving a sparsity-regularized inverse problem. Traditional CS solvers use iterative optimizers with hand crafted sparsifiers, while early data-driven methods…

Compressed sensing magnetic resonance imaging (CS-MRI) is a theoretical framework that can accurately reconstruct images from undersampled k-space data with a much lower sampling rate than the one set by the classical Nyquist-Shannon…

Compressed sensing (CS) MRI relies on adequate undersampling of the k-space to accelerate the acquisition without compromising image quality. Consequently, the design of optimal sampling patterns for these k-space coefficients has received…

The structure of Magnetic Resonance Images (MRI) and especially their compressibility in an appropriate representation basis enables the application of the compressive sensing theory, which guarantees exact image recovery from incomplete…

Popular methods in compressed sensing (CS) are dependent on deep learning (DL), where large amounts of data are used to train non-linear reconstruction models. However, ensuring generalisability over and access to multiple datasets is…

To accelerate MRI, the field of compressed sensing is traditionally concerned with optimizing the image quality after a partial undersampling of the measurable $\textit{k}$-space. In our work, we propose to change the focus from the quality…

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…