526 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
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
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
Isotropic Polyharmonic B-Splines: Scaling Functions and Wavelets
In this paper, we use polyharmonic B-splines to build multidimensional wavelet bases. These functions are nonseparable, multidimensional basis functions that are localized versions of radial basis functions. We show that Rabut's elementary polyharmonic B-splines do not converge to a Gaussian as the order parameter increases, as opposed to their separable B-spline counterparts. Therefore, we introduce a more isotropic localization operator that guarantees this convergence, resulting into the isotropic polyharmonic B-splines. Next, we focus on the two-dimensional quincunx subsampling scheme. This configuration is of particular interest for image processing, because it yields a finer scale progression than the standard dyadic approach. However, up until now, the design of appropriate filters for the quincunx scheme has mainly been done using the McClellan transform. In our approach, we start from the scaling functions, which are the polyharmonic B-splines and, as such, explicitly known, and we derive a family of polyharmonic spline wavelets corresponding to different flavors of the semi-orthogonal wavelet transform; e.g., orthonormal, B-spline, and dual. The filters are automatically specified by the scaling relations satisfied by these functions. We prove that the isotropic polyharmonic B-spline wavelet converges to a combination of four Gabor atoms, which are well separated in the frequency domain. We also show that these wavelets are nearly isotropic and that they behave as an iterated Laplacian operator at low frequencies. We describe an efficient fast Fourier transform-based implementation of the discrete wavelet transform based on polyharmonic B-splines
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