314 research outputs found
Enhanced imaging of microcalcifications in digital breast tomosynthesis through improved image-reconstruction algorithms
PURPOSE: We develop a practical, iterative algorithm for image-reconstruction
in under-sampled tomographic systems, such as digital breast tomosynthesis
(DBT).
METHOD: The algorithm controls image regularity by minimizing the image total
-variation (TpV), a function that reduces to the total variation when
or the image roughness when . Constraints on the image, such as
image positivity and estimated projection-data tolerance, are enforced by
projection onto convex sets (POCS). The fact that the tomographic system is
under-sampled translates to the mathematical property that many widely varied
resultant volumes may correspond to a given data tolerance. Thus the
application of image regularity serves two purposes: (1) reduction of the
number of resultant volumes out of those allowed by fixing the data tolerance,
finding the minimum image TpV for fixed data tolerance, and (2) traditional
regularization, sacrificing data fidelity for higher image regularity. The
present algorithm allows for this dual role of image regularity in
under-sampled tomography.
RESULTS: The proposed image-reconstruction algorithm is applied to three
clinical DBT data sets. The DBT cases include one with microcalcifications and
two with masses.
CONCLUSION: Results indicate that there may be a substantial advantage in
using the present image-reconstruction algorithm for microcalcification
imaging.Comment: Submitted to Medical Physic
How little data is enough? Phase-diagram analysis of sparsity-regularized X-ray CT
We introduce phase-diagram analysis, a standard tool in compressed sensing,
to the X-ray CT community as a systematic method for determining how few
projections suffice for accurate sparsity-regularized reconstruction. In
compressed sensing a phase diagram is a convenient way to study and express
certain theoretical relations between sparsity and sufficient sampling. We
adapt phase-diagram analysis for empirical use in X-ray CT for which the same
theoretical results do not hold. We demonstrate in three case studies the
potential of phase-diagram analysis for providing quantitative answers to
questions of undersampling: First we demonstrate that there are cases where
X-ray CT empirically performs comparable with an optimal compressed sensing
strategy, namely taking measurements with Gaussian sensing matrices. Second, we
show that, in contrast to what might have been anticipated, taking randomized
CT measurements does not lead to improved performance compared to standard
structured sampling patterns. Finally, we show preliminary results of how well
phase-diagram analysis can predict the sufficient number of projections for
accurately reconstructing a large-scale image of a given sparsity by means of
total-variation regularization.Comment: 24 pages, 13 figure
Toward optimal X-ray flux utilization in breast CT
A realistic computer-simulation of a breast computed tomography (CT) system
and subject is constructed. The model is used to investigate the optimal number
of views for the scan given a fixed total X-ray fluence. The reconstruction
algorithm is based on accurate solution to a constrained, TV-minimization
problem, which has received much interest recently for sparse-view CT data.Comment: accepted to the 11th International Meeting on Fully Three-Dimensional
Image Reconstruction in Radiology and Nuclear Medicine 201
Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm
The primal-dual optimization algorithm developed in Chambolle and Pock (CP),
2011 is applied to various convex optimization problems of interest in computed
tomography (CT) image reconstruction. This algorithm allows for rapid
prototyping of optimization problems for the purpose of designing iterative
image reconstruction algorithms for CT. The primal-dual algorithm is briefly
summarized in the article, and its potential for prototyping is demonstrated by
explicitly deriving CP algorithm instances for many optimization problems
relevant to CT. An example application modeling breast CT with low-intensity
X-ray illumination is presented.Comment: Resubmitted to Physics in Medicine and Biology. Text has been
modified according to referee comments, and typos in the equations have been
correcte
Noise properties of CT images reconstructed by use of constrained total-variation, data-discrepancy minimization
PURPOSE: The authors develop and investigate iterative image reconstruction algorithms based on data-discrepancy minimization with a total-variation (TV) constraint. The various algorithms are derived with different data-discrepancy measures reflecting the maximum likelihood (ML) principle. Simulations demonstrate the iterative algorithms and the resulting image statistical properties for low-dose CT data acquired with sparse projection view angle sampling. Of particular interest is to quantify improvement of image statistical properties by use of the ML data fidelity term. METHODS: An incremental algorithm framework is developed for this purpose. The instances of the incremental algorithms are derived for solving optimization problems including a data fidelity objective function combined with a constraint on the image TV. For the data fidelity term the authors, compare application of the maximum likelihood principle, in the form of weighted least-squares (WLSQ) and Poisson-likelihood (PL), with the use of unweighted least-squares (LSQ). RESULTS: The incremental algorithms are applied to projection data generated by a simulation modeling the breast computed tomography (bCT) imaging application. The only source of data inconsistency in the bCT projections is due to noise, and a Poisson distribution is assumed for the transmitted x-ray photon intensity. In the simulations involving the incremental algorithms an ensemble of images, reconstructed from 1000 noise realizations of the x-ray transmission data, is used to estimate the image statistical properties. The WLSQ and PL incremental algorithms are seen to reduce image variance as compared to that of LSQ without sacrificing image bias. The difference is also seen at few iterations—short of numerical convergence of the corresponding optimization problems. CONCLUSIONS: The proposed incremental algorithms prove effective and efficient for iterative image reconstruction in low-dose CT applications particularly with sparse-view projection data
Problem Identification and Decomposition within the Requirements Generation Process
Only recently has the real importance of the requirements generation process and its requisite activities been recognized. That importance is underscored by the evolving partitions and refinements of the once all-encompassing (and somewhat miss-named) Requirements Analysis phase of the software development lifecycle. Continuing along that evolutionary line, we propose an additional refinement to the requirements generation model that focuses on problem identification and its decomposition into an associated set of user needs that drive the requirements generation process. Problem identification stresses the importance of recognizing and identifying the difference between a perceived state of the system and the desired one. We mention pre- and post-conditions that help identify and bound the problem and then present some methods and techniques that assist in refining that boundary and also in recognizing essential characteristics of the problem. We continue by presenting a process by which the identified problem and its characteristics are decomposed and translated into a set of user needs that provide the basis for the solution description, i.e, the set of requirements. Finally, to place problem identification and decomposition in perspective, we present them within the framework of the Requirements Generation Model
A parametric level-set method for partially discrete tomography
This paper introduces a parametric level-set method for tomographic
reconstruction of partially discrete images. Such images consist of a
continuously varying background and an anomaly with a constant (known)
grey-value. We represent the geometry of the anomaly using a level-set
function, which we represent using radial basis functions. We pose the
reconstruction problem as a bi-level optimization problem in terms of the
background and coefficients for the level-set function. To constrain the
background reconstruction we impose smoothness through Tikhonov regularization.
The bi-level optimization problem is solved in an alternating fashion; in each
iteration we first reconstruct the background and consequently update the
level-set function. We test our method on numerical phantoms and show that we
can successfully reconstruct the geometry of the anomaly, even from limited
data. On these phantoms, our method outperforms Total Variation reconstruction,
DART and P-DART.Comment: Paper submitted to 20th International Conference on Discrete Geometry
for Computer Imager
GPU-based Iterative Cone Beam CT Reconstruction Using Tight Frame Regularization
X-ray imaging dose from serial cone-beam CT (CBCT) scans raises a clinical
concern in most image guided radiation therapy procedures. It is the goal of
this paper to develop a fast GPU-based algorithm to reconstruct high quality
CBCT images from undersampled and noisy projection data so as to lower the
imaging dose. For this purpose, we have developed an iterative tight frame (TF)
based CBCT reconstruction algorithm. A condition that a real CBCT image has a
sparse representation under a TF basis is imposed in the iteration process as
regularization to the solution. To speed up the computation, a multi-grid
method is employed. Our GPU implementation has achieved high computational
efficiency and a CBCT image of resolution 512\times512\times70 can be
reconstructed in ~5 min. We have tested our algorithm on a digital NCAT phantom
and a physical Catphan phantom. It is found that our TF-based algorithm is able
to reconstrct CBCT in the context of undersampling and low mAs levels. We have
also quantitatively analyzed the reconstructed CBCT image quality in terms of
modulation-transfer-function and contrast-to-noise ratio under various scanning
conditions. The results confirm the high CBCT image quality obtained from our
TF algorithm. Moreover, our algorithm has also been validated in a real
clinical context using a head-and-neck patient case. Comparisons of the
developed TF algorithm and the current state-of-the-art TV algorithm have also
been made in various cases studied in terms of reconstructed image quality and
computation efficiency.Comment: 24 pages, 8 figures, accepted by Phys. Med. Bio
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