Magnetic resonance imaging (MRI) has rapidly become an important tool in clinical medicine and biological research. Its functional variant (functional magnetic resonance imaging; fMRI) is currently the most widely used method for brain mapping and studying the neural basis of human cognition. While the method is widespread, there is insuf � cient knowledge of the physiological basis of the fMRI signal to interpret the data con � dently with respect to neural activity. This paper reviews the basic principles of MRI and fMRI, and subsequently discusses in some detail the relationship between the blood-oxygenlevel-dependent (BOLD) fMRI signal and the neural activity elicited during sensory stimulation. To examine this relationship, we conducted the � rst simultaneous intracortical recordings of neural signals and BOLD responses. Depending on the temporal characteristics of the stimulus, a moderate to strong correlation was found between the neural activity measured with microelectrodes and the BOLD signal averaged over a small area around the microelectrode tips. However, the BOLD signal had signi � cantly higher variability than the neural activity, indicating that human fMRI combined with traditional statistical methods underestimates the reliability of the neuronal activity. To understand the relative contribution of several types of neuronal signals to the haemodynamic response, we compared local � eld potentials (LFPs), single- and multi-unit activity (MUA) with high spatio-temporal fMRI responses recorded simultaneously in monkey visual cortex. At recording sites characterized by transient responses, only the LFP signal was signi � cantly correlated with the haemodynamic response. Furthermore, the LFPs had the largest magnitude signal and linear systems analysis showed that the LFPs were better than the MUAs at predicting the fMRI responses. These � ndings, together with an analysis of the neural signals, indicate that the BOLD signal primarily measures the input and processing of neuronal information within a region and not the output signal transmitted to other brain regions.

The rapid collection of brain images from healthy and diseased subjects has stimulated the development of powerful mathematical algorithms to compare, pool and average brain data across whole populations. Brain structure is so complex and variable that new approaches in computer vision, partial differential equations, and statistical field theory are being formulated to detect and visualize disease-specific patterns. We present some novel mathematical strategies for computational anatomy, focusing on the creation of population-based brain atlases. These atlases describe how the brain varies with age, gender, genetics, and over time. We review applications in Alzheimer's disease, schizophrenia and brain development, outlining some current challenges in the field.

Phase unwrapping is the inference of absolute phase from modulo-2π phase. This paper introduces a new energy minimization framework for phase unwrapping. The considered objective functions are first-order Markov random fields. We provide an exact energy minimization algorithm, whenever the corresponding clique potentials are convex, namely for the phase unwrapping classical L p norm, with p ≥ 1. Its complexity is KT(n, 3n), where K is the length of the absolute phase domain measured in 2π units and T (n, m) is the complexity of a max-flow computation in a graph with n nodes and m edges. For nonconvex clique potentials, often used owing to their discontinuity preserving ability, we face an NP-hard problem for which we devise an approximate solution. Both algorithms solve integer optimization problems, by computing a sequence of binary optimizations, each one solved by graph cut techniques. Accordingly, we name the two algorithms PUMA, for phase unwrapping max-flow/min-cut. A set of experimental results illustrates the effectiveness of the proposed approach and its competitiveness in comparison with state-of-the-art phase unwrapping algorithms.

Abstract — In magnetic resonance imaging (MRI), the spatial inhomogeneity of the static magnetic field can cause degraded images if the reconstruction is based on inverse Fourier trans-formation. This paper presents and discusses a range of fast reconstruction algorithms that attempt to avoid such degra-dation by taking the field inhomogeneity into account. Some of these algorithms are new, others are modified versions of known algorithms. Speed and accuracy of all these algorithms are demonstrated using spiral MRI. Index Terms—Conjugate phase reconstruction, magnetic reso-nance imaging, off-resonance correction, simulated phase evolu-tion and rewinding. I.

ABSTRACT Optical coherence tomography (OCT) is an optical ranging technique analogous to radar -detection of back-scattered light produces a signal that is temporally localized at timesof-flight corresponding to the location of scatterers in the object. However the interferometric collection technique used in OCT allows, in principle, the coherent collection of data, i.e. amplitude and phase information can be extracted. Interferometric Synthetic Aperture Microscopy (ISAM) adds phasestable data collection to OCT instrumentation and employs physics-based processing analogous to that used in Synthetic Aperture Radar (SAR). That is, the complex nature of the coherent data is exploited to give gains in image quality. Specifically, diffraction-limited resolution is achieved throughout the sample, not just within focal volume of the illuminating field. Simulated and experimental verifications of this effect are presented. ISAM's computational focusing obviates the trade-off between lateral resolution and depth-of-focus seen in traditional OCT.

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We show how improved sequences for magnetic resonance imaging can be found through optimization of Bayesian design scores. Combining approximate Bayesian inference and natural image statistics with high-performance numerical computation, we propose the first Bayesian experimental design framework for this problem of high relevance to clinical and brain research. Our solution requires large-scale approximate inference for dense, non-Gaussian models. We propose a novel scalable variational inference algorithm, and show how powerful methods of numerical mathematics can be modified to compute primitives in our framework. Our approach is evaluated on raw data from a 3T MR scanner. 1

The current technical and methodological status of functional magnetic resonance imaging (fMRI) is reviewed. The mechanisms underlying the effects of deoxyhemoglobin concentration and cerebral blood flow changes are discussed, and methods for monitoring these changes are described and compared. Methods for post-processing fMRI data are outlined. Potential problems and solutions related to vessels and motion are discussed in detail.

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Abstract—In dynamic magnetic resonance imaging (MRI) studies, the motion kinetics or the contrast variability are often hard to predict, hampering an appropriate choice of the image update rate or the temporal resolution. A constant azimuthal profile spacing (111.246), based on the Golden Ratio, is inves-tigated as optimal for image reconstruction from an arbitrary number of profiles in radial MRI. The profile order is evalu-ated and compared with a uniform profile distribution in terms of signal-to-noise ratio (SNR) and artifact level. The favorable characteristics of such a profile order are exemplified in two appli-cations on healthy volunteers. First, an advanced sliding window reconstruction scheme is applied to dynamic cardiac imaging, with a reconstruction window that can be flexibly adjusted ac-cording to the extent of cardiac motion that is acceptable. Second, a contrast-enhancing-space filter is presented that permits reconstructing an arbitrary number of images at arbitrary time points from one raw data set. The filter was utilized to depict the T1-relaxation in the brain after a single inversion prepulse. While a uniform profile distribution with a constant angle increment is optimal for a fixed and predetermined number of profiles, a profile distribution based on the Golden Ratio proved to be an appropriate solution for an arbitrary number of profiles. Index Terms—Projection reconstruction, radial signal-to-noise ratio (MRI), real-time imaging, time-resolved imaging. I.