4,683 research outputs found
Generic iterative subset algorithms for discrete tomography
AbstractDiscrete tomography deals with the reconstruction of images from their projections where the images are assumed to contain only a small number of grey values. In particular, there is a strong focus on the reconstruction of binary images (binary tomography). A variety of binary tomography problems have been considered in the literature, each using different projection models or additional constraints. In this paper, we propose a generic iterative reconstruction algorithm that can be used for many different binary reconstruction problems. In every iteration, a subproblem is solved based on at most two of the available projections. Each of the subproblems can be solved efficiently using network flow methods. We report experimental results for various reconstruction problems. Our results demonstrate that the algorithm is capable of reconstructing complex objects from a small number of projections
Efficient Inversion of Multiple-Scattering Model for Optical Diffraction Tomography
Optical diffraction tomography relies on solving an inverse scattering
problem governed by the wave equation. Classical reconstruction algorithms are
based on linear approximations of the forward model (Born or Rytov), which
limits their applicability to thin samples with low refractive-index contrasts.
More recent works have shown the benefit of adopting nonlinear models. They
account for multiple scattering and reflections, improving the quality of
reconstruction. To reduce the complexity and memory requirements of these
methods, we derive an explicit formula for the Jacobian matrix of the nonlinear
Lippmann-Schwinger model which lends itself to an efficient evaluation of the
gradient of the data- fidelity term. This allows us to deploy efficient methods
to solve the corresponding inverse problem subject to sparsity constraints
Structured random measurements in signal processing
Compressed sensing and its extensions have recently triggered interest in
randomized signal acquisition. A key finding is that random measurements
provide sparse signal reconstruction guarantees for efficient and stable
algorithms with a minimal number of samples. While this was first shown for
(unstructured) Gaussian random measurement matrices, applications require
certain structure of the measurements leading to structured random measurement
matrices. Near optimal recovery guarantees for such structured measurements
have been developed over the past years in a variety of contexts. This article
surveys the theory in three scenarios: compressed sensing (sparse recovery),
low rank matrix recovery, and phaseless estimation. The random measurement
matrices to be considered include random partial Fourier matrices, partial
random circulant matrices (subsampled convolutions), matrix completion, and
phase estimation from magnitudes of Fourier type measurements. The article
concludes with a brief discussion of the mathematical techniques for the
analysis of such structured random measurements.Comment: 22 pages, 2 figure
A Multi-GPU Programming Library for Real-Time Applications
We present MGPU, a C++ programming library targeted at single-node multi-GPU
systems. Such systems combine disproportionate floating point performance with
high data locality and are thus well suited to implement real-time algorithms.
We describe the library design, programming interface and implementation
details in light of this specific problem domain. The core concepts of this
work are a novel kind of container abstraction and MPI-like communication
methods for intra-system communication. We further demonstrate how MGPU is used
as a framework for porting existing GPU libraries to multi-device
architectures. Putting our library to the test, we accelerate an iterative
non-linear image reconstruction algorithm for real-time magnetic resonance
imaging using multiple GPUs. We achieve a speed-up of about 1.7 using 2 GPUs
and reach a final speed-up of 2.1 with 4 GPUs. These promising results lead us
to conclude that multi-GPU systems are a viable solution for real-time MRI
reconstruction as well as signal-processing applications in general.Comment: 15 pages, 10 figure
Enhancing Compressed Sensing 4D Photoacoustic Tomography by Simultaneous Motion Estimation
A crucial limitation of current high-resolution 3D photoacoustic tomography
(PAT) devices that employ sequential scanning is their long acquisition time.
In previous work, we demonstrated how to use compressed sensing techniques to
improve upon this: images with good spatial resolution and contrast can be
obtained from suitably sub-sampled PAT data acquired by novel acoustic scanning
systems if sparsity-constrained image reconstruction techniques such as total
variation regularization are used. Now, we show how a further increase of image
quality can be achieved for imaging dynamic processes in living tissue (4D
PAT). The key idea is to exploit the additional temporal redundancy of the data
by coupling the previously used spatial image reconstruction models with
sparsity-constrained motion estimation models. While simulated data from a
two-dimensional numerical phantom will be used to illustrate the main
properties of this recently developed
joint-image-reconstruction-and-motion-estimation framework, measured data from
a dynamic experimental phantom will also be used to demonstrate their potential
for challenging, large-scale, real-world, three-dimensional scenarios. The
latter only becomes feasible if a carefully designed combination of tailored
optimization schemes is employed, which we describe and examine in more detail
Quantifying admissible undersampling for sparsity-exploiting iterative image reconstruction in X-ray CT
Iterative image reconstruction (IIR) with sparsity-exploiting methods, such
as total variation (TV) minimization, investigated in compressive sensing (CS)
claim potentially large reductions in sampling requirements. Quantifying this
claim for computed tomography (CT) is non-trivial, because both full sampling
in the discrete-to-discrete imaging model and the reduction in sampling
admitted by sparsity-exploiting methods are ill-defined. The present article
proposes definitions of full sampling by introducing four sufficient-sampling
conditions (SSCs). The SSCs are based on the condition number of the system
matrix of a linear imaging model and address invertibility and stability. In
the example application of breast CT, the SSCs are used as reference points of
full sampling for quantifying the undersampling admitted by reconstruction
through TV-minimization. In numerical simulations, factors affecting admissible
undersampling are studied. Differences between few-view and few-detector bin
reconstruction as well as a relation between object sparsity and admitted
undersampling are quantified.Comment: Revised version that was submitted to IEEE Transactions on Medical
Imaging on 8/16/201
Solving ill-posed inverse problems using iterative deep neural networks
We propose a partially learned approach for the solution of ill posed inverse
problems with not necessarily linear forward operators. The method builds on
ideas from classical regularization theory and recent advances in deep learning
to perform learning while making use of prior information about the inverse
problem encoded in the forward operator, noise model and a regularizing
functional. The method results in a gradient-like iterative scheme, where the
"gradient" component is learned using a convolutional network that includes the
gradients of the data discrepancy and regularizer as input in each iteration.
We present results of such a partially learned gradient scheme on a non-linear
tomographic inversion problem with simulated data from both the Sheep-Logan
phantom as well as a head CT. The outcome is compared against FBP and TV
reconstruction and the proposed method provides a 5.4 dB PSNR improvement over
the TV reconstruction while being significantly faster, giving reconstructions
of 512 x 512 volumes in about 0.4 seconds using a single GPU
Matroid Regression
We propose an algebraic combinatorial method for solving large sparse linear
systems of equations locally - that is, a method which can compute single
evaluations of the signal without computing the whole signal. The method scales
only in the sparsity of the system and not in its size, and allows to provide
error estimates for any solution method. At the heart of our approach is the
so-called regression matroid, a combinatorial object associated to sparsity
patterns, which allows to replace inversion of the large matrix with the
inversion of a kernel matrix that is constant size. We show that our method
provides the best linear unbiased estimator (BLUE) for this setting and the
minimum variance unbiased estimator (MVUE) under Gaussian noise assumptions,
and furthermore we show that the size of the kernel matrix which is to be
inverted can be traded off with accuracy
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