219 research outputs found
Image Compressive Sensing Recovery Using Adaptively Learned Sparsifying Basis via L0 Minimization
From many fewer acquired measurements than suggested by the Nyquist sampling
theory, compressive sensing (CS) theory demonstrates that, a signal can be
reconstructed with high probability when it exhibits sparsity in some domain.
Most of the conventional CS recovery approaches, however, exploited a set of
fixed bases (e.g. DCT, wavelet and gradient domain) for the entirety of a
signal, which are irrespective of the non-stationarity of natural signals and
cannot achieve high enough degree of sparsity, thus resulting in poor CS
recovery performance. In this paper, we propose a new framework for image
compressive sensing recovery using adaptively learned sparsifying basis via L0
minimization. The intrinsic sparsity of natural images is enforced
substantially by sparsely representing overlapped image patches using the
adaptively learned sparsifying basis in the form of L0 norm, greatly reducing
blocking artifacts and confining the CS solution space. To make our proposed
scheme tractable and robust, a split Bregman iteration based technique is
developed to solve the non-convex L0 minimization problem efficiently.
Experimental results on a wide range of natural images for CS recovery have
shown that our proposed algorithm achieves significant performance improvements
over many current state-of-the-art schemes and exhibits good convergence
property.Comment: 31 pages, 4 tables, 12 figures, to be published at Signal Processing,
Code available: http://idm.pku.edu.cn/staff/zhangjian/ALSB
An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems
We propose a new fast algorithm for solving one of the standard approaches to
ill-posed linear inverse problems (IPLIP), where a (possibly non-smooth)
regularizer is minimized under the constraint that the solution explains the
observations sufficiently well. Although the regularizer and constraint are
usually convex, several particular features of these problems (huge
dimensionality, non-smoothness) preclude the use of off-the-shelf optimization
tools and have stimulated a considerable amount of research. In this paper, we
propose a new efficient algorithm to handle one class of constrained problems
(often known as basis pursuit denoising) tailored to image recovery
applications. The proposed algorithm, which belongs to the family of augmented
Lagrangian methods, can be used to deal with a variety of imaging IPLIP,
including deconvolution and reconstruction from compressive observations (such
as MRI), using either total-variation or wavelet-based (or, more generally,
frame-based) regularization. The proposed algorithm is an instance of the
so-called "alternating direction method of multipliers", for which convergence
sufficient conditions are known; we show that these conditions are satisfied by
the proposed algorithm. Experiments on a set of image restoration and
reconstruction benchmark problems show that the proposed algorithm is a strong
contender for the state-of-the-art.Comment: 13 pages, 8 figure, 8 tables. Submitted to the IEEE Transactions on
Image Processin
(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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