Aggregated motion estimation for real-time MRI reconstruction

Real-time magnetic resonance imaging (MRI) methods generally shorten the measuring time by acquiring less data than needed according to the sampling theorem. In order to obtain a proper image from such undersampled data, the reconstruction is commonly defined as the solution of an inverse problem, which is regularized by a priori assumptions about the object. While practical realizations have hitherto been surprisingly successful, strong assumptions about the continuity of image features may affect the temporal fidelity of the estimated images. Here we propose a novel approach for the reconstruction of serial real-time MRI data which integrates the deformations between nearby frames into the data consistency term. The method is not required to be affine or rigid and does not need additional measurements. Moreover, it handles multi-channel MRI data by simultaneously determining the image and its coil sensitivity profiles in a nonlinear formulation which also adapts to non-Cartesian (e.g., radial) sampling schemes. Experimental results of a motion phantom with controlled speed and in vivo measurements of rapid tongue movements demonstrate image improvements in preserving temporal fidelity and removing residual artifacts.Comment: This is a preliminary technical report. A polished version is published by Magnetic Resonance in Medicine. Magnetic Resonance in Medicine 201

Quick Adaptive Ternary Segmentation: An Efficient Decoding Procedure For Hidden Markov Models

Hidden Markov models (HMMs) are characterized by an unobservable (hidden) Markov chain and an observable process, which is a noisy version of the hidden chain. Decoding the original signal (i.e., hidden chain) from the noisy observations is one of the main goals in nearly all HMM based data analyses. Existing decoding algorithms such as the Viterbi algorithm have computational complexity at best linear in the length of the observed sequence, and sub-quadratic in the size of the state space of the Markov chain. We present Quick Adaptive Ternary Segmentation (QATS), a divide-and-conquer procedure which decodes the hidden sequence in polylogarithmic computational complexity in the length of the sequence, and cubic in the size of the state space, hence particularly suited for large scale HMMs with relatively few states. The procedure also suggests an effective way of data storage as specific cumulative sums. In essence, the estimated sequence of states sequentially maximizes local likelihood scores among all local paths with at most three segments. The maximization is performed only approximately using an adaptive search procedure. The resulting sequence is admissible in the sense that all transitions occur with positive probability. To complement formal results justifying our approach, we present Monte-Carlo simulations which demonstrate the speedups provided by QATS in comparison to Viterbi, along with a precision analysis of the returned sequences. An implementation of QATS in C++ is provided in the R-package QATS and is available from GitHub

Detection and inference of changes in high-dimensional linear regression with non-sparse structures

For data segmentation in high-dimensional linear regression settings, the regression parameters are often assumed to be sparse segment-wise, which enables many existing methods to estimate the parameters locally via $\ell_1$-regularised maximum likelihood-type estimation and then contrast them for change point detection. Contrary to this common practice, we show that the sparsity of neither regression parameters nor their differences, a.k.a. differential parameters, is necessary for consistency in multiple change point detection. In fact, both statistically and computationally, better efficiency is attained by a simple strategy that scans for large discrepancies in local covariance between the regressors and the response. We go a step further and propose a suite of tools for directly inferring about the differential parameters post-segmentation, which are applicable even when the regression parameters themselves are non-sparse. Theoretical investigations are conducted under general conditions permitting non-Gaussianity, temporal dependence and ultra-high dimensionality. Numerical results from simulated and macroeconomic datasets demonstrate the competitiveness and efficacy of the proposed methods