Sparsity/undersampling tradeoffs in anisotropic undersampling, with applications in MR imaging/spectroscopy

Monajemi, Hatef; Donoho, David L.

doi:10.1093/imaiai/iay013

Cited by 6 publications

(8 citation statements)

References 43 publications

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“…This procedure differs from standard practice in NUS, where only the indirect dimensions are subsampled, and the uniformly sampled direct dimension is Fourier transformed to yield a set of independent reconstructions. 10 In fact, Bayesian inference makes no distinction between the direct and indirect dimensions of a NUS dataset: only the measured data are considered, and there is no concept of "missing" data. 4 Pooling all data into a single model increases the chances of successful parameter inference.…”

Section: N-dimensional Signalsmentioning

confidence: 99%

“…2 Because uniform sampling (US) requires insupportably long measurement times to obtain high resolution data, spectroscopists are increasingly moving to nonuniform sampling (NUS) techniques, where a much smaller subset of grid points is measured. 9,10 In an essentially independent line of research, data from NMR experiments have been modeled using Bayesian probability theory. 5,6 When the subset of measured grid points, called the sampling schedule, 7,8 is chosen judiciously, the desired spectral information can often be estimated successfully.…”

Section: Introductionmentioning

confidence: 99%

“…Characterizing the "zone of success" of recovery algorithms and effectively choosing sampling schedules are both areas of active research in the compressed sensing and signal processing fields. 9,10 In an essentially independent line of research, data from NMR experiments have been modeled using Bayesian probability theory. 4,[11][12][13][14][15][16][17] In Bayesian probability theory, the probability of some event is seen as representing our degree of belief that the event is true.…”

Section: Introductionmentioning

confidence: 99%

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Variational Bayesian analysis of nonuniformly sampled NMR data

Worley

2017

Concepts Magnetic Resonance

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Nonuniform sampling (NUS) offers NMR spectroscopists a means of accelerating data collection and increasing spectral quality in multidimensional (nD) experiments. The data from NUS experiments are incomplete by design, and must be reconstructed prior to use. While most existing reconstruction techniques compute point estimates of the true signal, Bayesian statistics offers a means of estimating posterior distributions over the signal, which enable more rigorous quantitation and uncertainty estimation. In this article, we describe the variational approach to approximating Bayesian posterior distributions, and illustrate how it can be applied to extend existing results from Bayesian spectrum analysis and compressed sensing. The new NUS reconstruction algorithms resulting from variational Bayes are computationally efficient, and offer new insights into the concepts of spectral sparsity and optimal sampling in NMR experiments. K E Y W O R D Sactive learning, Bayesian inference, compressed sensing, variational approximation

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Section: N-dimensional Signalsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Variational Bayesian analysis of nonuniformly sampled NMR data

Worley

2017

Concepts Magnetic Resonance

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“…3 More generally, massive experimentation can solve complex problems lying beyond the reach of any theory. Successful examples of ambitious computational experimentation as a fundamental method of scientific discovery abound: in (Brunton, Proctor, & Kutz, 2016), the authors take a data science approach to discover governing equations of various dynamical systems including the strongly nonlinear Lorenz-63 model; in (Monajemi, Jafarpour, Gavish, Collaboration, & Donoho, 2013) and (Monajemi & Donoho, 2018), the authors conducted data science studies involving several million CPU hours to discover fundamentally more practical sensing methods in the area of Compressed Sensing; in (Huang et al, 2015), MCEs solved a 30year-old puzzle in the design of a particular protein.…”

Section: Introductionmentioning

confidence: 99%

Ambitious Data Science Can Be Painless

Monajemi¹,

Murri²,

Jonas³

et al. 2019

Harvard Data Science Review

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Modern data science research, at the cutting edge, can involve massive computational experimentation; an ambitious PhD in computational fields may conduct experiments consuming several million CPU hours. Traditional computing practices, in which researchers use laptops, PCs, or campus-resident resources with shared policies, are awkward or inadequate for experiments at the massive scale and varied scope that we now see in the most ambitious data science. On the other hand, modern cloud computing promises seemingly unlimited computational resources that can be custom configured, and seems to offer a powerful new venue for ambitious data-driven science. Exploiting the cloud fully, it seems the amount of raw experimental work that could be completed in a fixed amount of calendar time ought to expand by several orders of magnitude.As potentially powerful as cloud-based experimentation may be in the abstract, it has not yet become a standard option for researchers in many academic disciplines. The prospect of actually conducting massive computational experiments in today's cloud systems with today's standard approaches forcefully confronts the potential user with daunting challenges. The user schooled in traditional interactive personal computing likely expects that a cloud experiment will involve an intricate collection of moving parts seemingly requiring extensive monitoring and involvement. Leading considerations include: (i) the seeming complexity of today's cloud computing interface, (ii) the difficulty of executing and managing an overwhelmingly large number of computational jobs, and (iii) the difficulty of keeping track of, collating, and combining a massive collection of separate results. Starting a massive experiment 'bare-handed' seems therefore highly problematic and prone to rapid 'researcher burn out'. New software stacks are emerging that render massive cloud-based experiments relatively painless. Such stacks simplify experimentation by systematizing experiment definition, automating distribution and management of all tasks, and allowing easy harvesting of results and documentation. In this article, we discuss several painless computing stacks that abstract away the difficulties of massive experimentation, thereby allowing a proliferation of ambitious experiments for scientific discovery. * This article is based on a series of lectures given in a Stanford course Stats285 in the Fall of 2017. † Corresponding

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“…In order to solve the above problems of under-sampled with phase discontinuity generated from Hilbert transform in single interference fringe phase retrieval methods [27], a new method was put forward in this paper. The shear interference principle was used to build a two-dimensional compound optical field firstly.…”

Section: Introductionmentioning

confidence: 99%

Under-Sampled Phase Retrieval of Single Interference Fringe Based on Hilbert Transform

2019

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Phase retrieval from single interference fringe is important and effective method in obtaining the real phase distribution. The original phase can be retrieved by the line integral of its gradient expressed as sine and cosine components, which were gained by the Hilbert transform twice from a single interference fringe pattern. However, this method fails when the phase transformation of the interference fringe is too fast. In this paper, a novel method to recover the continuous phase of the whole field is proposed to solve the above problems. The shear interference technique is introduced into the phase retrieval method to build an exponential 2-D complex light field of natural base for the phase slope obtained by the Hilbert transform. Then, the expressions of phase slopes in x-and y-directions are constructed as a discrete Poisson equation. Therefore, the calculation of phase retrieval is equivalent to solve the discrete Poisson equation mathematically. Finally, the real phase is gotten by the weighted discrete cosine transform (WDCT) of the discrete Poisson equation. The simulation results verify the validity of this method and show that the proposed method can achieve the phase retrieval of the phase discontinuity in x-and y-directions, which leads to the under-sampled problem. It can restore the whole field phase distribution rapidly and accurately. Moreover, this method is applied to phase retrieval of interferometric synthetic aperture radar (InSAR) with the under-sampled problem in this paper. The experimental results show that this method can recover the phase of InSAR with the under-sampled problems caused by terrain abrupt change and so on. Compared with other commonly used methods, it achieved satisfactory results. This method provides a new idea for solving the under-sampled problem in the phase retrieval from a single-frame interference fringe.

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Sparsity/undersampling tradeoffs in anisotropic undersampling, with applications in MR imaging/spectroscopy

Cited by 6 publications

References 43 publications

Variational Bayesian analysis of nonuniformly sampled NMR data

Variational Bayesian analysis of nonuniformly sampled NMR data

Ambitious Data Science Can Be Painless

Under-Sampled Phase Retrieval of Single Interference Fringe Based on Hilbert Transform

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