6,325 research outputs found
Parallel Magnetic Resonance Imaging as Approximation in a Reproducing Kernel Hilbert Space
In Magnetic Resonance Imaging (MRI) data samples are collected in the spatial
frequency domain (k-space), typically by time-consuming line-by-line scanning
on a Cartesian grid. Scans can be accelerated by simultaneous acquisition of
data using multiple receivers (parallel imaging), and by using more efficient
non-Cartesian sampling schemes. As shown here, reconstruction from samples at
arbitrary locations can be understood as approximation of vector-valued
functions from the acquired samples and formulated using a Reproducing Kernel
Hilbert Space (RKHS) with a matrix-valued kernel defined by the spatial
sensitivities of the receive coils. This establishes a formal connection
between approximation theory and parallel imaging. Theoretical tools from
approximation theory can then be used to understand reconstruction in k-space
and to extend the analysis of the effects of samples selection beyond the
traditional g-factor noise analysis to both noise amplification and
approximation errors. This is demonstrated with numerical examples.Comment: 28 pages, 7 figure
Sheer shear: weak lensing with one mode
3D data compression techniques can be used to determine the natural basis of
radial eigenmodes that encode the maximum amount of information in a
tomographic large-scale structure survey. We explore the potential of the
Karhunen-Lo\`eve decomposition in reducing the dimensionality of the data
vector for cosmic shear measurements, and apply it to the final data from the
\cfh survey. We find that practically all of the cosmological information can
be encoded in one single radial eigenmode, from which we are able to reproduce
compatible constraints with those found in the fiducial tomographic analysis
(done with 7 redshift bins) with a factor of ~30 fewer datapoints. This
simplifies the problem of computing the two-point function covariance matrix
from mock catalogues by the same factor, or by a factor of ~800 for an
analytical covariance. The resulting set of radial eigenfunctions is close to
ell-independent, and therefore they can be used as redshift-dependent galaxy
weights. This simplifies the application of the Karhunen-Lo\`eve decomposition
to real-space and Fourier-space data, and allows one to explore the effective
radial window function of the principal eigenmodes as well as the associated
shear maps in order to identify potential systematics. We also apply the method
to extended parameter spaces and verify that additional information may be
gained by including a second mode to break parameter degeneracies. The data and
analysis code are publicly available at
https://github.com/emiliobellini/kl_sample.Comment: 15 pages, 16 figures. Accepted version on OJ
Operator theory and function theory in Drury-Arveson space and its quotients
The Drury-Arveson space , also known as symmetric Fock space or the
-shift space, is a Hilbert function space that has a natural -tuple of
operators acting on it, which gives it the structure of a Hilbert module. This
survey aims to introduce the Drury-Arveson space, to give a panoramic view of
the main operator theoretic and function theoretic aspects of this space, and
to describe the universal role that it plays in multivariable operator theory
and in Pick interpolation theory.Comment: Final version (to appear in Handbook of Operator Theory); 42 page
Medical imaging analysis with artificial neural networks
Given that neural networks have been widely reported in the research community of medical imaging, we provide a focused literature survey on recent neural network developments in computer-aided diagnosis, medical image segmentation and edge detection towards visual content analysis, and medical image registration for its pre-processing and post-processing, with the aims of increasing awareness of how neural networks can be applied to these areas and to provide a foundation for further research and practical development. Representative techniques and algorithms are explained in detail to provide inspiring examples illustrating: (i) how a known neural network with fixed structure and training procedure could be applied to resolve a medical imaging problem; (ii) how medical images could be analysed, processed, and characterised by neural networks; and (iii) how neural networks could be expanded further to resolve problems relevant to medical imaging. In the concluding section, a highlight of comparisons among many neural network applications is included to provide a global view on computational intelligence with neural networks in medical imaging
Model spaces: a survey
This is a brief and gentle introduction, aimed at graduate students, to the
subject of model subspaces of the Hardy space.Comment: 55 page
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