PEAR: PEriodic And fixed Rank separation for fast fMRI

In functional MRI (fMRI), faster acquisition via undersampling of data can improve the spatial-temporal resolution trade-off and increase statistical robustness through increased degrees-of-freedom. High quality reconstruction of fMRI data from undersampled measurements requires proper modeling of the data. We present an fMRI reconstruction approach based on modeling the fMRI signal as a sum of periodic and fixed rank components, for improved reconstruction from undersampled measurements. We decompose the fMRI signal into a component which a has fixed rank and a component consisting of a sum of periodic signals which is sparse in the temporal Fourier domain. Data reconstruction is performed by solving a constrained problem that enforces a fixed, moderate rank on one of the components, and a limited number of temporal frequencies on the other. Our approach is coined PEAR - PEriodic And fixed Rank separation for fast fMRI. Experimental results include purely synthetic simulation, a simulation with real timecourses and retrospective undersampling of a real fMRI dataset. Evaluation was performed both quantitatively and visually versus ground truth, comparing PEAR to two additional recent methods for fMRI reconstruction from undersampled measurements. Results demonstrate PEAR's improvement in estimating the timecourses and activation maps versus the methods compared against at acceleration ratios of R=8,16 (for simulated data) and R=6.66,10 (for real data). PEAR results in reconstruction with higher fidelity than when using a fixed-rank based model or a conventional Low-rank+Sparse algorithm. We have shown that splitting the functional information between the components leads to better modeling of fMRI, over state-of-the-art methods

A Holographic Diffuser Generalised Optical Differentiation Wavefront Sensor

The wavefront sensors used today at the biggest World's telescopes have either a high dynamic range or a high sensitivity, and they are subject to a linear trade off between these two parameters. A new class of wavefront sensors, the Generalised Optical Differentiation Wavefront Sensors, has been devised, in a way not to undergo this linear trade off and to decouple the dynamic range from the sensitivity. This new class of WFSs is based on the light filtering in the focal plane from a dedicated amplitude filter, which is a hybrid between a linear filter, whose physical dimension is related to the dynamic range, and a step in the amplitude, whose size is related to the sensitivity. We propose here a possible technical implementation of this kind of WFS, making use of a simple holographic diffuser to diffract part of the light in a ring shape around the pin of a pyramid wavefront sensor. In this way, the undiffracted light reaches the pin of the pyramid, contributing to the high sensitivity regime of the WFS, while the diffused light is giving a sort of static modulation of the pyramid, allowing to have some signal even in high turbulence conditions. The holographic diffuser zeroth order efficiency is strictly related to the sensitivity of the WFS, while the diffusing angle of the diffracted light gives the amount of modulation and thus the dynamic range. By properly choosing these two parameters it is possible to build a WFS with high sensitivity and high dynamic range in a static fashion. Introducing dynamic parts in the setup allows to have a set of different diffuser that can be alternated in front of the pyramid, if the change in the seeing conditions requires it.Comment: 11 pages, 5 figure

Randomized Dynamic Mode Decomposition

This paper presents a randomized algorithm for computing the near-optimal low-rank dynamic mode decomposition (DMD). Randomized algorithms are emerging techniques to compute low-rank matrix approximations at a fraction of the cost of deterministic algorithms, easing the computational challenges arising in the area of `big data'. The idea is to derive a small matrix from the high-dimensional data, which is then used to efficiently compute the dynamic modes and eigenvalues. The algorithm is presented in a modular probabilistic framework, and the approximation quality can be controlled via oversampling and power iterations. The effectiveness of the resulting randomized DMD algorithm is demonstrated on several benchmark examples of increasing complexity, providing an accurate and efficient approach to extract spatiotemporal coherent structures from big data in a framework that scales with the intrinsic rank of the data, rather than the ambient measurement dimension. For this work we assume that the dynamics of the problem under consideration is evolving on a low-dimensional subspace that is well characterized by a fast decaying singular value spectrum

Efficiency improvement of the frequency-domain BEM for rapid transient elastodynamic analysis

The frequency-domain fast boundary element method (BEM) combined with the exponential window technique leads to an efficient yet simple method for elastodynamic analysis. In this paper, the efficiency of this method is further enhanced by three strategies. Firstly, we propose to use exponential window with large damping parameter to improve the conditioning of the BEM matrices. Secondly, the frequency domain windowing technique is introduced to alleviate the severe Gibbs oscillations in time-domain responses caused by large damping parameters. Thirdly, a solution extrapolation scheme is applied to obtain better initial guesses for solving the sequential linear systems in the frequency domain. Numerical results of three typical examples with the problem size up to 0.7 million unknowns clearly show that the first and third strategies can significantly reduce the computational time. The second strategy can effectively eliminate the Gibbs oscillations and result in accurate time-domain responses