Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This first book on greedy approximation gives a systematic presentation of the fundamental results. It also contains an introduction to two hot topics in numerical mathematics: learning theory and compressed sensing. Nonlinear approximation is becoming increasingly important, especially since two types are frequently employed in applications: adaptive methods are used in PDE solvers, while m-term approximation is used in image/signal/data processing, as well as in the design of neural networks. The fundamental question of nonlinear approximation is how to devise good constructive methods (algorithms) and recent results have established that greedy type algorithms may be the solution. The author has drawn on his own teaching experience to write a book ideally suited to graduate courses. The reader does not require a broad background to understand the material. Important open problems are included to give students and professionals alike ideas for further research.

Approximation theory. --- Theory of approximation --- Functional analysis --- Functions --- Polynomials --- Chebyshev systems --- Compressed sensing (Telecommunication) --- Compressive sensing (Telecommunication) --- Sensing, Compressed (Telecommunication) --- Sparse sampling (Telecommunication) --- Signal processing

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The objective of this 5th edition of the book, as with the prior editions, is to teach through images a practical approach to magnetic resonance (MR) physics and image quality. Unlike other texts covering this topic, the focus is on clinical images rather than equations. A practical approach to MR physics is developed through images, emphasizing knowledge of fundamentals important to achieve high image quality. Pulse diagrams are also included, which many at first find difficult to understand. Readers are encouraged to glance at these as they go through the text. With time and repetition, as a reader progresses through the book, the value of these and the knowledge thus available will become evident (and the diagrams themselves easier to understand). The text is organized into concise chapters, each discussing an important point relevant to clinical MR and illustrated largely with images from routine patient exams. The topics covered encompass the breadth of the field, from imaging basics and pulse sequences to advanced topics including contrast-enhanced MR angiography, spectroscopy, perfusion and advanced parallel imaging/data sparsity techniques. Discussion of the latest hardware and software innovations, for example next generation low field MR, deep learning, MR-PET, 7 T, interventional MR, 4D flow, CAIPIRINHA, spiral techniques, radial acquisition, simultaneous multislice, compressed sensing and MR fingerprinting, is included because these topics are critical to current clinical practice as well as to future advances. Included in the fifth edition are a large number of new topics, keeping the text up to date in this increasingly complex field. The text has also been thoroughly revised to include additional relevant clinical images, to improve the clarity of descriptions, and to increase the depth of content. The book is highly recommended for radiologists, physicists, and technologists interested in the background of image acquisition used in standard as well as specialized clinical settings. .

Magnetic resonance imaging. --- Medical radiology. --- Compressed sensing (Telecommunication) --- Compressive sensing (Telecommunication) --- Sensing, Compressed (Telecommunication) --- Sparse sampling (Telecommunication) --- Signal processing --- Clinical radiology --- Radiology, Medical --- Radiology (Medicine) --- Medical physics --- Clinical magnetic resonance imaging --- Diagnostic magnetic resonance imaging --- Functional magnetic resonance imaging --- Imaging, Magnetic resonance --- Medical magnetic resonance imaging --- MR imaging --- MRI (Magnetic resonance imaging) --- NMR imaging --- Nuclear magnetic resonance --- Nuclear magnetic resonance imaging --- Cross-sectional imaging --- Diagnostic imaging --- Diagnostic use --- Radiology. --- Medical physics. --- Neurology. --- Nervous system --- Medical Physics. --- Neurosurgery. --- Surgery. --- Nerves --- Neurosurgery --- Medicine --- Neuropsychiatry --- Health physics --- Health radiation physics --- Medical radiation physics --- Radiotherapy physics --- Radiation therapy physics --- Biophysics --- Physics --- Radiological physics --- Radiation --- Surgery --- Diseases