109 research outputs found
Multicontrast MRI reconstruction with structure-guided total variation
Magnetic resonance imaging (MRI) is a versatile imaging technique that allows
different contrasts depending on the acquisition parameters. Many clinical
imaging studies acquire MRI data for more than one of these contrasts---such as
for instance T1 and T2 weighted images---which makes the overall scanning
procedure very time consuming. As all of these images show the same underlying
anatomy one can try to omit unnecessary measurements by taking the similarity
into account during reconstruction. We will discuss two modifications of total
variation---based on i) location and ii) direction---that take structural a
priori knowledge into account and reduce to total variation in the degenerate
case when no structural knowledge is available. We solve the resulting convex
minimization problem with the alternating direction method of multipliers that
separates the forward operator from the prior. For both priors the
corresponding proximal operator can be implemented as an extension of the fast
gradient projection method on the dual problem for total variation. We tested
the priors on six data sets that are based on phantoms and real MRI images. In
all test cases exploiting the structural information from the other contrast
yields better results than separate reconstruction with total variation in
terms of standard metrics like peak signal-to-noise ratio and structural
similarity index. Furthermore, we found that exploiting the two dimensional
directional information results in images with well defined edges, superior to
those reconstructed solely using a priori information about the edge location.Engineering and Physical Sciences Research Council (Grant ID: EP/H046410/1)This is the final version of the article. It first appeared from Society for Industrial and Applied Mathematics via http://dx.doi.org/10.1137/15M1047325
Conditional Score-Based Reconstructions for Multi-contrast MRI
Magnetic resonance imaging (MRI) exam protocols consist of multiple
contrast-weighted images of the same anatomy to emphasize different tissue
properties. Due to the long acquisition times required to collect fully sampled
k-space measurements, it is common to only collect a fraction of k-space for
some, or all, of the scans and subsequently solve an inverse problem for each
contrast to recover the desired image from sub-sampled measurements. Recently,
there has been a push to further accelerate MRI exams using data-driven priors,
and generative models in particular, to regularize the ill-posed inverse
problem of image reconstruction. These methods have shown promising
improvements over classical methods. However, many of the approaches neglect
the multi-contrast nature of clinical MRI exams and treat each scan as an
independent reconstruction. In this work we show that by learning a joint
Bayesian prior over multi-contrast data with a score-based generative model we
are able to leverage the underlying structure between multi-contrast images and
thus improve image reconstruction fidelity over generative models that only
reconstruct images of a single contrast
A function space framework for structural total variation regularization with applications in inverse problems
In this work, we introduce a function space setting for a wide class of
structural/weighted total variation (TV) regularization methods motivated by
their applications in inverse problems. In particular, we consider a
regularizer that is the appropriate lower semi-continuous envelope (relaxation)
of a suitable total variation type functional initially defined for
sufficiently smooth functions. We study examples where this relaxation can be
expressed explicitly, and we also provide refinements for weighted total
variation for a wide range of weights. Since an integral characterization of
the relaxation in function space is, in general, not always available, we show
that, for a rather general linear inverse problems setting, instead of the
classical Tikhonov regularization problem, one can equivalently solve a
saddle-point problem where no a priori knowledge of an explicit formulation of
the structural TV functional is needed. In particular, motivated by concrete
applications, we deduce corresponding results for linear inverse problems with
norm and Poisson log-likelihood data discrepancy terms. Finally, we provide
proof-of-concept numerical examples where we solve the saddle-point problem for
weighted TV denoising as well as for MR guided PET image reconstruction
Edge-weighted pFISTA-Net for MRI Reconstruction
Deep learning based on unrolled algorithm has served as an effective method
for accelerated magnetic resonance imaging (MRI). However, many methods ignore
the direct use of edge information to assist MRI reconstruction. In this work,
we present the edge-weighted pFISTA-Net that directly applies the detected edge
map to the soft-thresholding part of pFISTA-Net. The soft-thresholding value of
different regions will be adjusted according to the edge map. Experimental
results of a public brain dataset show that the proposed yields reconstructions
with lower error and better artifact suppression compared with the
state-of-the-art deep learning-based methods. The edge-weighted pFISTA-Net also
shows robustness for different undersampling masks and edge detection
operators. In addition, we extend the edge weighted structure to joint
reconstruction and segmentation network and obtain improved reconstruction
performance and more accurate segmentation results
Mathematics of biomedical imaging today—a perspective
Biomedical imaging is a fascinating, rich and dynamic research area, which has huge importance in biomedical research and clinical practice alike. The key technology behind the processing, and automated analysis and quantification of imaging data is mathematics. Starting with the optimisation of the image acquisition and the reconstruction of an image from indirect tomographic measurement data, all the way to the automated segmentation of tumours in medical images and the design of optimal treatment plans based on image biomarkers, mathematics appears in all of these in different flavours. Non-smooth optimisation in the context of sparsity-promoting image priors, partial differential equations for image registration and motion estimation, and deep neural networks for image segmentation, to name just a few. In this article, we present and review mathematical topics that arise within the whole biomedical imaging pipeline, from tomographic measurements to clinical support tools, and highlight some modern topics and open problems. The article is addressed to both biomedical researchers who want to get a taste of where mathematics arises in biomedical imaging as well as mathematicians who are interested in what mathematical challenges biomedical imaging research entails
A function space framework for structural total variation regularization with applications in inverse problems
In this work, we introduce a function space setting for a wide class of
structural/weighted total variation (TV) regularization methods motivated by
their applications in inverse problems. In particular, we consider a
regularizer that is the appropriate lower semi-continuous envelope
(relaxation) of a suitable total variation type functional initially defined
for sufficiently smooth functions. We study examples where this relaxation
can be expressed explicitly, and we also provide refinements for weighted
total variation for a wide range of weights. Since an integral
characterization of the relaxation in function space is, in general, not
always available, we show that, for a rather general linear inverse problems
setting, instead of the classical Tikhonov regularization problem, one can
equivalently solve a saddle-point problem where no a priori knowledge of an
explicit formulation of the structural TV functional is needed. In
particular, motivated by concrete applications, we deduce corresponding
results for linear inverse problems with norm and Poisson log-likelihood data
discrepancy terms. Finally, we provide proof-of-concept numerical examples
where we solve the saddle-point problem for weighted TV denoising as well as
for MR guided PET image reconstruction
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