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This thesis focuses on developing efficient algorithmic tools for processing large datasets. In many modern data analysis tasks, the sheer volume of available datasets far outstrips our abilities to process them. This scenario commonly arises in tasks incl ...
We find an optimal upper bound on the volume of the John ellipsoid of a k-dimensional section of the n-dimensional cube, and an optimal lower bound on the volume of the Lowner ellipsoid of a projection of the n-dimensional cross-polytope onto a k-dimension ...
The theme of this thesis revolves around three important manifestations of light, namely its corpuscular, wave and electromagnetic nature. Our goal is to exploit these principles to analyze, design and build imaging modalities by developing new signal proc ...
Reconstructing continuous signals based on a small number of discrete samples is a fundamental problem across science and engineering. We are often interested in signals with "simple" Fourier structure - e.g., those involving frequencies within a bounded r ...
Purpose MP2RAGE T-1-weighted imaging has been shown to be beneficial for various applications, mainly because of its good grey-white matter contrast, its B-1-robustness and ability to derive T(1)maps. Even using parallel imaging, the method requires long a ...
While the recent theory of compressed sensing provides an opportunity to overcome the Nyquist limit in recovering sparse signals, a solution approach usually takes the form of an inverse problem of an unknown signal, which is crucially dependent on specifi ...
Compressed sensing is provided a data-acquisition paradigm for sparse signals. Remarkably, it has been shown that the practical algorithms provide robust recovery from noisy linear measurements acquired at a near optimal sampling rate. In many real-world a ...
Foundations of signal processing are heavily based on Shannon's sampling theorem for acquisition, representation and reconstruction. This theorem states that signals should not contain frequency components higher than the Nyquist rate, which is half of the ...
Sparse recovery is a powerful tool that plays a central role in many applications, including source estimation in radio astronomy, direction of arrival estimation in acoustics or radar, super-resolution microscopy, and X-ray crystallography. Conventional a ...
One of the greatest challenges in the design of modern wearable devices is energy efficiency. While data processing and communication have received a lot of attention from the industry and academia, leading to highly efficient microcontrollers and transmis ...
