497 research outputs found
Sparse image reconstruction on the sphere: implications of a new sampling theorem
We study the impact of sampling theorems on the fidelity of sparse image
reconstruction on the sphere. We discuss how a reduction in the number of
samples required to represent all information content of a band-limited signal
acts to improve the fidelity of sparse image reconstruction, through both the
dimensionality and sparsity of signals. To demonstrate this result we consider
a simple inpainting problem on the sphere and consider images sparse in the
magnitude of their gradient. We develop a framework for total variation (TV)
inpainting on the sphere, including fast methods to render the inpainting
problem computationally feasible at high-resolution. Recently a new sampling
theorem on the sphere was developed, reducing the required number of samples by
a factor of two for equiangular sampling schemes. Through numerical simulations
we verify the enhanced fidelity of sparse image reconstruction due to the more
efficient sampling of the sphere provided by the new sampling theorem.Comment: 11 pages, 5 figure
Implications for compressed sensing of a new sampling theorem on the sphere
A sampling theorem on the sphere has been developed recently, requiring half
as many samples as alternative equiangular sampling theorems on the sphere. A
reduction by a factor of two in the number of samples required to represent a
band-limited signal on the sphere exactly has important implications for
compressed sensing, both in terms of the dimensionality and sparsity of
signals. We illustrate the impact of this property with an inpainting problem
on the sphere, where we show the superior reconstruction performance when
adopting the new sampling theorem compared to the alternative.Comment: 1 page, 2 figures, Signal Processing with Adaptive Sparse Structured
Representations (SPARS) 201
Decoding of Emotional Information in Voice-Sensitive Cortices
The ability to correctly interpret emotional signals from others is crucial for successful social interaction. Previous neuroimaging studies showed that voice-sensitive auditory areas [1-3] activate to a broad spectrum of vocally expressed emotions more than to neutral speech melody (prosody). However, this enhanced response occurs irrespective of the specific emotion category, making it impossible to distinguish different vocal emotions with conventional analyses [4-8]. Here, we presented pseudowords spoken in five prosodic categories (anger, sadness, neutral, relief, joy) during event-related functional magnetic resonance imaging (fMRI), then employed multivariate pattern analysis [9, 10] to discriminate between these categories on the basis of the spatial response pattern within the auditory cortex. Our results demonstrate successful decoding of vocal emotions from fMRI responses in bilateral voice-sensitive areas, which could not be obtained by using averaged response amplitudes only. Pairwise comparisons showed that each category could be classified against all other alternatives, indicating for each emotion a specific spatial signature that generalized across speakers. These results demonstrate for the first time that emotional information is represented by distinct spatial patterns that can be decoded from brain activity in modality-specific cortical areas
Harmonic analysis of spherical sampling in diffusion MRI
In the last decade diffusion MRI has become a powerful tool to non-invasively
study white-matter integrity in the brain. Recently many research groups have
focused their attention on multi-shell spherical acquisitions with the aim of
effectively mapping the diffusion signal with a lower number of q-space
samples, hence enabling a crucial reduction of acquisition time. One of the
quantities commonly studied in this context is the so-called orientation
distribution function (ODF). In this setting, the spherical harmonic (SH)
transform has gained a great deal of popularity thanks to its ability to
perform convolution operations efficiently and accurately, such as the
Funk-Radon transform notably required for ODF computation from q-space data.
However, if the q-space signal is described with an unsuitable angular
resolution at any b-value probed, aliasing (or interpolation) artifacts are
unavoidably created. So far this aspect has been tackled empirically and, to
our knowledge, no study has addressed this problem in a quantitative approach.
The aim of the present work is to study more theoretically the efficiency of
multi-shell spherical sampling in diffusion MRI, in order to gain understanding
in HYDI-like approaches, possibly paving the way to further optimization
strategies.Comment: 1 page, 2 figures, 19th Annual Meeting of International Society for
Magnetic Resonance in Medicin
Practical Box Splines for Reconstruction on the Body Centered Cubic Lattice
We introduce a family of box splines for efficient, accurate, and smooth reconstruction of volumetric data sampled on the body-centered cubic (BCC) lattice, which is the favorable volumetric sampling pattern due to its optimal spectral sphere packing property. First, we construct a box spline based on the four principal directions of the BCC lattice that allows for a linear reconstruction. Then, the design is extended for higher degrees of continuity. We derive the explicit piecewise polynomial representations of the and box splines that are useful for practical reconstruction applications. We further demonstrate that approximation in the shift-invariant space—generated by BCC-lattice shifts of these box splines—is twice as efficient as using the tensor-product B-spline solutions on the Cartesian lattice (with comparable smoothness and approximation order and with the same sampling density). Practical evidence is provided demonstrating that the BCC lattice not only is generally a more accurate sampling pattern, but also allows for extremely efficient reconstructions that outperform tensor-product Cartesian reconstructions
Surfing the Brain—An Overview of Wavelet-Based Techniques for fMRI Data Analysis
The measurement of brain activity in a noninvasive way is an essential element in modern neurosciences. Modalities such as electroencephalography (EEG) and magnetoencephalography (MEG) recently gained interest, but two classical techniques remain predominant. One of them is positron emission tomography (PET), which is costly and lacks temporal resolution but allows the design of tracers for specific tasks; the other main one is functional magnetic resonance imaging (fMRI), which is more affordable than PET from a technical, financial, and ethical point of view, but which suffers from poor contrast and low signal-to-noise ratio (SNR). For this reason, advanced methods have been devised to perform the statistical analysis of fMRI data
An Orthogonal Family of Quincunx Wavelets with Continuously Adjustable Order
We present a new family of two-dimensional and three-dimensional orthogonal wavelets which uses quincunx sampling. The orthogonal refinement filters have a simple analytical expression in the Fourier domain as a function of the order λ, which may be noninteger. We can also prove that they yield wavelet bases of for any λ>0. The wavelets are fractional in the sense that the approximation error at a given scale a decays like ; they also essentially behave like fractional derivative operators. To make our construction practical, we propose an fast Fourier transform-based implementation that turns out to be surprisingly fast. In fact, our method is almost as efficient as the standard Mallat algorithm for separable wavelets
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