132 research outputs found
Joint Sensing Matrix and Sparsifying Dictionary Optimization for Tensor Compressive Sensing.
Tensor compressive sensing (TCS) is a multidimensional framework of compressive sensing (CS), and it is
advantageous in terms of reducing the amount of storage, easing
hardware implementations, and preserving multidimensional
structures of signals in comparison to a conventional CS system.
In a TCS system, instead of using a random sensing matrix and
a predefined dictionary, the average-case performance can be
further improved by employing an optimized multidimensional
sensing matrix and a learned multilinear sparsifying dictionary.
In this paper, we propose an approach that jointly optimizes
the sensing matrix and dictionary for a TCS system. For the
sensing matrix design in TCS, an extended separable approach
with a closed form solution and a novel iterative nonseparable
method are proposed when the multilinear dictionary is fixed.
In addition, a multidimensional dictionary learning method that
takes advantages of the multidimensional structure is derived,
and the influence of sensing matrices is taken into account in the
learning process. A joint optimization is achieved via alternately
iterating the optimization of the sensing matrix and dictionary.
Numerical experiments using both synthetic data and real images
demonstrate the superiority of the proposed approache
(k,q)-Compressed Sensing for dMRI with Joint Spatial-Angular Sparsity Prior
Advanced diffusion magnetic resonance imaging (dMRI) techniques, like
diffusion spectrum imaging (DSI) and high angular resolution diffusion imaging
(HARDI), remain underutilized compared to diffusion tensor imaging because the
scan times needed to produce accurate estimations of fiber orientation are
significantly longer. To accelerate DSI and HARDI, recent methods from
compressed sensing (CS) exploit a sparse underlying representation of the data
in the spatial and angular domains to undersample in the respective k- and
q-spaces. State-of-the-art frameworks, however, impose sparsity in the spatial
and angular domains separately and involve the sum of the corresponding sparse
regularizers. In contrast, we propose a unified (k,q)-CS formulation which
imposes sparsity jointly in the spatial-angular domain to further increase
sparsity of dMRI signals and reduce the required subsampling rate. To
efficiently solve this large-scale global reconstruction problem, we introduce
a novel adaptation of the FISTA algorithm that exploits dictionary
separability. We show on phantom and real HARDI data that our approach achieves
significantly more accurate signal reconstructions than the state of the art
while sampling only 2-4% of the (k,q)-space, allowing for the potential of new
levels of dMRI acceleration.Comment: To be published in the 2017 Computational Diffusion MRI Workshop of
MICCA
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