the considerable practical challenges of sensitivity based imaging, including the signal-to-noise ratio (SNR) issue, sensitivity assessment, and hardware requirements. Only in 1997 did Sodickson et al. To overcome the restrictions of previously proposed methods, in this work we reformulate the problem of image

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m]]l]]s¶D]]¿÷mB]iv]b]oD]m¶¨]iv]§]iv]r]j]t¿rv]]irj]]t]]m] / | ap]]r¿]ÎNy]s¶D]]mb¶r]ix} Û]Ix]]rd]mb]} p—N]t]o%ism] in]ty]m] / || Û]Is]¡uÎc]rN]]riv]nd]p]*N]m]st¶ I always bow to Śri ̄ Śāradāmbā, the limitless ocean of the nectar of compassion, who bears a rosary, a vessel of nectar, the symbol

Algebraic algorithms deal with numbers, vectors, matrices, polynomials, for-mal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation with matri-ces and polynomials is fundamental for modern computations in Sciences and

[ A review of past and recent strategies for sub-Nyquist sampling] Signal processing methods have changed substantially over the last several decades. In modern applications, an increasing number of functions is being pushed forward to sophisticated software algorithms, leaving only delicate finely-tuned tasks for the circuit level. Sampling theory, the gate to the digital world, is the key enabling this revolution, encompassing all aspects related to the conversion of continuous-time signals to discrete streams of numbers. The famous Shannon-Nyquist theorem has become a landmark: a mathematical statement which has had one of the most profound impacts on industrial development of digital signal processing (DSP) systems. Over the years, theory and practice in the field of sampling have developed in parallel routes. Contributions by many research groups suggest a multitude of methods, other than uniform sampling, to acquire analog signals [1]–[6]. The math has deepened, leading to abstract signal spaces and innovative sampling techniques. Within generalized sampling theory, bandlimited signals have no special preference, other than historic. At the same time, the market adhered to the Nyquist paradigm; state-of-the-art analog to digital conversion (ADC) devices provide values of their input at equalispaced time points [7], [8]. The footprints of Shannon-Nyquist are evident

I hereby declare that I have created this work completely on my own and used no other sources or tools than the ones listed, and that I have marked any citations accordingly. Hiermit versichere ich, dass ich die vorliegende Arbeit selbständig verfasst und keine anderen als die angegebenen Quellen

ii iv vTo my parents vi vii Acknowledgements I would first and foremost extend my whole-hearted gratitude to my advisors, An-drea Arpaci-Dusseau and Remzi Arpaci-Dusseau. Andrea and Remzi are the reason that I had the opportunity for this exceptional Ph.D. journey. To this day, I still re

. However, for many practical signal acquisition applications, including medical imaging and remote sensing, this assumption is violated as the projections must be taken in groups. In this paper, we consider such applications and derive requirements on the number of measurements needed for successful

Caractérisation des problèmes conjoints de détection et d'estimation

First, I would like to thank my advisors Prof. Gal A. Kaminka and Dr. David Sarne for their excellent guidance and constant support in the past two years. I learned quite a bit about scientific research, all thanks to their great instruction. Working with them was a real pleasure, not only