205 research outputs found
Shearlet-based compressed sensing for fast 3D cardiac MR imaging using iterative reweighting
High-resolution three-dimensional (3D) cardiovascular magnetic resonance
(CMR) is a valuable medical imaging technique, but its widespread application
in clinical practice is hampered by long acquisition times. Here we present a
novel compressed sensing (CS) reconstruction approach using shearlets as a
sparsifying transform allowing for fast 3D CMR (3DShearCS). Shearlets are
mathematically optimal for a simplified model of natural images and have been
proven to be more efficient than classical systems such as wavelets. Data is
acquired with a 3D Radial Phase Encoding (RPE) trajectory and an iterative
reweighting scheme is used during image reconstruction to ensure fast
convergence and high image quality. In our in-vivo cardiac MRI experiments we
show that the proposed method 3DShearCS has lower relative errors and higher
structural similarity compared to the other reconstruction techniques
especially for high undersampling factors, i.e. short scan times. In this
paper, we further show that 3DShearCS provides improved depiction of cardiac
anatomy (measured by assessing the sharpness of coronary arteries) and two
clinical experts qualitatively analyzed the image quality
Sampling and Reconstruction of Sparse Signals on Circulant Graphs - An Introduction to Graph-FRI
With the objective of employing graphs toward a more generalized theory of
signal processing, we present a novel sampling framework for (wavelet-)sparse
signals defined on circulant graphs which extends basic properties of Finite
Rate of Innovation (FRI) theory to the graph domain, and can be applied to
arbitrary graphs via suitable approximation schemes. At its core, the
introduced Graph-FRI-framework states that any K-sparse signal on the vertices
of a circulant graph can be perfectly reconstructed from its
dimensionality-reduced representation in the graph spectral domain, the Graph
Fourier Transform (GFT), of minimum size 2K. By leveraging the recently
developed theory of e-splines and e-spline wavelets on graphs, one can
decompose this graph spectral transformation into the multiresolution low-pass
filtering operation with a graph e-spline filter, and subsequent transformation
to the spectral graph domain; this allows to infer a distinct sampling pattern,
and, ultimately, the structure of an associated coarsened graph, which
preserves essential properties of the original, including circularity and,
where applicable, the graph generating set.Comment: To appear in Appl. Comput. Harmon. Anal. (2017
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