January 9 - 12, 2006
Diffusion-Tensor Magnetic Resonance Imaging (DT-MRI) is a relatively recent
imaging modality. DT-MRI images are measurements of the diffusion tensor of
water in each voxel of an imaging volume. They can be viewed as noisy,
discrete, voxel-averaged samples of a continuous function from 3D space into
the positive definite symmetric matrices. These DT-MRI images can be used to
probe the structural and architectural features of fiber tissue such white
matter and the heart ventricles. We will present an overview of the
problems, methods and applications associated with DT-MRI data and their
Thermoacoustic tomography (TCT or TAT) is a new and promising method
of medical imaging. It is based on a hybrid imaging technique,
where the input and output signals have different physical nature.
In TAT, a microwave or radiofrequency electromagnetic pulse is sent
through the biological object triggering an acoustic wave measured in
the exteriror of the object. The resulting data is then used to recover
the absorption function.
The poster addresses several problems of image reconstruction in
thermoacoustic tomography. The presented results include injectivity
properties of the related spherical Radon transform, its range
description, reconstruction and incomplete data problems.
The purpose of this paper is to acquire image segmentation using a
modified Mumford-Shah model. A variational region intensity based
image segmentation model is proposed. The boundary of the given
image is extracted by using a modified Mumford-Shah segmentation
model. The proposed model is tested against synthetic data and simulated
normal noisy human-brain MRI images. The experimental results
provide preliminary evidence of the effectiveness of the presented
Diffraction tomography (DT) is a well-established imaging method
for determination of the complex-valued refractive index
distribution of a weakly scattering object.
The success of DT imaging in optical applications, however, has been limited
because it requires explicit knowledge of the phase of the measured wavefields.
To circumvent the phase-retrieval problem, a
theory of intensity DT (I-DT) has been proposed that
replaces explicit phase measurements on a single detector plane
by intensity measurements on two or more different parallel planes.
In this work, we propose novel I-DT reconstruction
theories that are applicable to non-conventional scanning geometries.
Such advancements can improve the effectiveness of existing
imaging systems and, perhaps more importantly, prompt and
facilitate the development of systems for novel applications.
Numerical simulations are conducted to demonstrate and validate
the proposed tomographic reconstruction algorithms.
Given a near-perfect X-ray source, such as a synchrotron, then what are the reasonable options for image reconstruction? Back-projection reconstruction has dominated, with lambda tomography not receiving the attention it deserves. Give the computation power a the beamline, is it reasonable to perform both reconstructions so as to discern object domains and interfaces? Second, all imaging methods reach a similar bottleneck, image analysis. Here, analysis means counting domains, identifying structure, following paths. If only the “yellow book” (Numerical Recipes: the art of scientific computing by Press, Flannery, Teukolsky, and Vettering) had another couple of chapters on algorithms for image analysis. Today, we start writing those chapters.
We present some sample data sets from our work at the LSU synchrotron, the Advanced Photon Source, and the National Synchrotron Light Source. Also, we discuss potential future issues for neutron tomography at the Spallation Neutron Source.
Metallic foams are a rather new class of porous and lightweight materials offering a unique combination of mechanical, thermal and
acoustical properties. Their high stiffness to weight ratio, acoustic damping properties and thermal resistance provide possible
applications in automobile industry for instance as crash energy absorbers or acoustic dampers, or in aerospace industry for
lightweight parts in rockets or aircrafts.
We will demonstrate methods which we use for the analysis of 3D datasets of Aluminum foams obtained at the synchrotron µCT facility
at the HASYLAB/DESY. It will be shown that by means of standard 3D image processing techniques it is possible to study and quantify
how different processing parameters like foaming temperature, time influence the structure formation and development of metallic
Given a near-perfect X-ray source, such as a synchrotron, then what are the reasonable options for image reconstruction? Back-projection reconstruction has dominated, with lambda tomography not receiving the attention it deserves. Give the computation power a the beamline, is it reasonable to perform both reconstructions so as to discern object domains and interfaces? Second, all imaging methods reach a similar bottleneck, image analysis. Here, analysis means counting domains, identifying structure, following paths. If only the "yellow book" (Numerical Recipes: the art of scientific computing by Press, Flannery, Teukolsky, and Vettering) had another couple of chapters on algorithms for image analysis. Today, we start writing those chapters.
Joint work with Dr. Ofer Levi, Industrial Engineering Department and Prof. Stanley Rotman Electrical Engineering Department, Ben-Gurion University of the Negev.
We present new multi-scale geometric tools for both analysis and synthesis of 3-D data which may be scattered or observed in voxel arrays,
which are typically very noisy, and which may contain one-dimensional structures such as line segments and filaments.
These tools mainly rely on the 3-D Beamlet Transform (developed by Donoho et al.) offering the collection of line integrals along a strat
egic multi-scale set of line segments, the Beamlet set (running through the image at different orientations, positions and lengths).
3D Beamlets methods can be applied in a wide variety of application fields that involve 3D imaging, in this work we focus on applying Bea
mlet methods for the problem of dim target multi-frame detection and develop specialized tools for this application. We use tools from Gra
ph theory and apply them to the special graph generated by the beamlets set.
Computed tomography entails the reconstruction of a function from measurements of its line integrals. In this talk we explore the
question: How many and which line integrals should be measured in order to achieve a desired resolution in the reconstructed image?
Answering this question may help to reduce the amount of measurements and thereby the radiation dose, or to obtain a better image
from the data one already has. Our exploration leads us to a mathematically and practically fruitful interaction of Shannon
sampling theory and tomography. For example, sampling theory helps to identify efficient data acquisition schemes, provides a
qualitative understanding of certain artifacts in tomographic images, and facilitates the error analysis of some reconstruction
algorithms. On the other hand, applications in tomography have stimulated new research in sampling theory, e.g., on nonuniform
sampling theorems and estimates for the aliasing error. Our dual aim is an exposition of the main principles involved as well as
the presentation of some new insights.
Joint with Bernhard G. Bodmann, Donald J. Kouri, and Manos
Recent studies have shown that as much as 85% of heart attacks are caused
by the rupture of lesions comprising fatty deposits capped by a thin layer
of fibrous tissue-- so-called vulnerable plaques. An imaging modality for
the reliable and early detection of vulnerable plaques is therefore of
significant clinical relevance. As a move in that direction, we develop a
texture-based algorithm for labeling tissues in high resolution CT volume
scans based upon variations in the local statistics of the wavelet
coefficients. We use a fast wavelet transform associated with isotropic,
three-dimensional wavelets; as a result, the algorithm is able to process
large volume sets in their entirety, as opposed to two-dimensional
cross-sections, and retains an orientation independent sensitivity to
features at all levels. The algorithm has been applied to the
classification of tissues in scans of coronary artery specimens taken
using a General Electric RS-9 Micro CT scanner with a linear resolution of
27 micrometers. In the current revision, it has shown promise for reliably
distinguishing fibromuscular, lipid, and calcified tissues.
Many inverse problems from acoustics, elasticity or electromagnetism can be reduced to the inverse scattering problem for the Helmholtz
equation. We consider scattering by inclusions or obstacles in an homogeneous background medium. The factorization method establishes
explicite relation between the spectral properties of the far field operator or its derivatives and the shape of the scatterer. This
relation allows to reconstruct unknown scattering object pointwise. The factorization method works pretty well for any type of boundary
condition and is dimension independent.
Breakout groups 1/11/2006
Many materials (such as metals) are
they consist of crystaline grains at various
The interaction of these grains with X-rays can be
as diffraction spots. Discrete tomography can be used
recover the internal oriention arrangement of the
form such diffraction measurements.
This poster presents a new method for the recognition and reconstruction
of simple geometric shapes from 3D data. Line element geometry, which
generalizes both line geometry and the Laguerre geometry of oriented
planes, enables us to recognize a wide class of surfaces (spiral surfaces,
cones, helical surfaces, rotational surfaces, cylinders, etc.) by fitting
linear subspaces in an appropriate seven-dimensional image space. In
combination with standard techniques such as PCA and RANSAC, line element
geometry is employed to effectively perform the segmentation of complex
objects according to surface type.
We present a framework to segment 3D point clouds into 0D,1D and 2D connected components (isolated points, curves, and surfaces) and
then to assign robust estimates of the Gauss and mean curvatures and the principal curvature directions at each surface point. The
framework is point-based. It does not use surface reconstruction, works on noisy data, no-human-in-the-loop is required to deal with
non-uniformly sampled clouds and boundary points. The topology and geometry recovery are parallelizable with low overhead.
A new local tomography function g is proposed. It is shown that g still
contains non-local artifacts, but their level is an order of magnitude
smaller than those of the previously known local tomography function. We
also investigate local tomography reconstruction in the dynamic case, i.e.
when the object f being scanned is undergoing some changes during the scan.
Properties of g are studied, the notion of visible singularities is suitably
generalized, and a relationship between the wave fronts of f and g is
established. It is shown that the changes in f do not cause any smearing of
the singularities of g. Results of numerical experiments are presented.
Blob3D is a software project begun at the University of Texas at Austin in
1999 for facilitating measurements of discrete features of interest in
volumetric data sets. It is designed in particular to deal with cases
where features are touching or impinging, and to allow up to tens of
thousands of features to be processed in a reasonable amount of
time. Processing is broken into three stages: segmentation of a phase of
interest, separation of touching objects, and extraction of measurements
from the interpreted volume. For each stage a variety of
three-dimensional algorithms have been created that account for vagaries of
CT data, and program design is intended to enable relatively
straightforward addition of new methods as they are developed. Separation
is the most time-intensive step, as it utilizes manual and semi-automated
methods that rely heavily on the user. This approach is most appropriate
in many instances where the natural variation and complexity of the
features require expert interpretation, but further automation is a future
goal. Although designed in particular for geological applications using
X-ray CT data, Blob3D is sufficiently general that it can be applied to
other data types and in other fields.
Breakout groups 1/10/2005
Breakout groups 1/12/2006
The presentation introduces edge-forming schemes for image
zooming by arbitrary magnification factors.
Image zooming via conventional interpolation methods often
produces the so-called checkerboard effect, in particular,
when the magnification factor is large.
In order to remove the artifact and to form reliable edges, a
nonlinear convex-concave model and its numerical algorithm are
suggested along with anisotropic edge-forming numerical schemes.
The algorithm is analyzed for stability and choices of
It has been numerically verified that the resulting algorithm can
form clear edges in 2 to 3 iterations of a linearized ADI method.
Various results are given to show effectiveness and reliability
of the algorithm, for both gray-scale and color images.
This is a joint work with Dr. Youngjoon Cha.
During the phenomenon of grain growth, larger grains tend to
grow at the expense of their smaller neighbors, resulting in a steady
increase in the average grain size. Because the growth of any given
grain is affected by that of its neighbors, the behavior of the
ensemble of grains is a strong function of nearest-neighbor size
correlations. Quantitative information concerning these correlations
can be extracted only from a truly three-dimensional characterization
of the sample microstructure. We have used x-ray microtomography to
measure the size correlations in a polycrystalline specimen of Al
alloyed with 2 at.% Sn. The tin atoms segregate to the grain
boundaries, where they impart a strong contrast in x-ray attenuation
that can be reconstructed tomographically; however, the nonuniform
nature of the segregation process presents a formidable challenge to
the automated segmentation of the reconstructions. By employing an
iterative region-growing algorithm followed by a novel
grain-boundary-network optimization routine (based on a phase-field
simulation of grain growth), we were able to measure the size, topology
and local connectivity of nearly 5000 contiguous Al grains, from which
the nearest-neighbor size correlations could be computed. The
resulting information was incorporated into a non-mean-field theory for
grain growth, the accuracy of which was evaluated by comparing its
predictions to the observed microstructure of the Al-Sn samples.
Joint with Gaik Ambartsoumian.
In thermoacoustic tomography TAT (sometimes called TCT), one triggers
an ultrasound signal from the medium by radiating it with a short EM
pulse. Mathematically speaking, under ideal conditions, the imaging
problem boils down to inversion of a spherical Radon transform. The talk
will survey known results and open problems in this area.
We propose a novel active contour model for image segmentation. The proposed model is based on an assumption that the image is locally binary. Our method is able to segment images with non-homogeneous regions, which is difficult for existing region based active contour models. Experimental results demonstrate the effectiveness of our method, and comparative study shows its advantage over previous methods.
Medical images can involve high levels of noise and unclear edges and
therefore their segmentation is often challenging. In this
presentation, we consider the method of background subtraction (MBS) in
order to minimize difficulties arising in the application of
segmentation methods to medical imagery. When an appropriate background
is subtracted from the given image, the residue can be considered as a
perturbation of a binary image, for which most segmentation methods can
detect desired edges effectively. New strategies are presented for the
computation of the background and tested along with active contour
models. Various numerical examples are presented to show effectiveness
of the MBS for segmentation of medical imagery. The method can be
extended to an efficient surface detection of 3-D medical images.
In this paper, we present an unified framework for joint segmentation and
The registration component of the method relies on two forces for
aligning the input images: one from the image similarity measure,
and the other from an image homogeneity constraint. The former,
based on local correlation, aims to find the detailed intensity
correspondence for the input images. The latter, generated from
the evolving segmentation contours, provides an extra guidance in
assisting the alignment process towards a more meaningful, stable
and noise-tolerant procedure. We present several 2D/3D example on
synthetic and real data.
Work in collaboration with Evren Ozarslan of the National Institutes of Health and Baba Vemuri of the University of Florida.
Magnetic resonance can be used to measure the rate and direction of molecular translational diffusion. Combining this diffusion measurement with magnetic resonance imaging methods allows the visualization of 3D motion of molecules in structured environments, like biological tissue. In its simplest form, the 3D measure of diffusion can be modeled as a real, symmetry rank-2 tensor of diffusion rate and direction at each image voxel. At a minimum, this model requires seven unique measurements of diffusion to fit the model (Basser, et al., J Magn Reson 1994;B:247–254). The resulting rank-2 tensor can be used to visualize diffusion as an ellipsoid at each voxel and fiber connections can be inferred by connecting the path, defined by the long axis (principle eigenvector) of the ellipse, passing through each voxel.
However, the rank-2 model of diffusion fails to accurately represent diffusion in complex structured environments, like nervous tissue with many crossing fibers. This limitation can be overcome by extending the angular resolution of diffusion measurements (Tuch, et al., Proceedings of the 7th Annual Meeting of Inter Soc Magn Reson Med, Philadelphia, 1999. p 321.) and by modeling the diffusion with higher rank tensors (Ozarslan et al., Magn. Reson. Med. 2003; 50:955-965 & Magn. Reson. Med. 2005;53;866-876). At each voxel in this more complete model, the 3D diffusion is represented by an "orientation distribution function" (ODF) indicating the probability of diffusion rate and direction. The diffusion ODF can be used to infer fiber connectivity but the issue of probable path selection remains a challenge. Plus the chosen procedure for path selection will influence with the level of resolution required for the measurements. In this presentation, methods of diffusion measurement and examples of diffusion-weighted magnetic resonance images from brain and spinal cord will be presented to illustrate the potential and challenges for path selecting leading to fiber mapping in the central nervous system.
Already in 1968 one recognized that the transmission electron
microscope could be used in a tomographic setting as a tool for
structure determination of macromolecules. However, its usage in
mainstream structural biology has been limited and the reason is mostly
due to the incomplete data problems that leads to severe ill-posedness
of the inverse problem. Despite these problems its importance is
beginning to increase, especially in drug discovery.
In order to understand the difficulties of electron tomography one
needs to properly formulate the forward problem that models the
measured intensity in the microscope. The electron-specimen interaction
is modelled as a diffraction tomography problem and the picture is
completed by adding a description of the optical system of the
transmission electron microscope. For weakly scattering specimens one
can further simplify the forward model by employing the first order
Born approximation which enables us to explicitly express the forward
operator in terms of the propagation operator from diffraction
tomography acting on the specimen convolved with a point spread
function, derived from the optics in the microscope. We next turn to
the algorithmic and mathematical difficulties that one faces in dealing
with the resulting inverse problem, especially the incomplete data
problems that leads to severe ill-posedness. Even though we briefly
mention single particle methods, our focus is will be on electron
tomography of general weakly scattering specimens and we mention some
of the progress that has been made in the field. Finally, if time
permits, we provide some examples of reconstructions from electron
tomography and demonstrate some of the biological interpretations that
one can make.
Thermoacoustic tomography (TCT) is a hybrid imaging technique that has been
proposed as an alternative to xray mammography. Ideally, electromagnetic (EM)
energy is deposited into the breast tissue uniformly in space, but impulsively
in time. This heats the tissue causing thermal expansion. Cancerous masses
absorb more energy than healthy tissue, creating a pressure wave, which is
detected by standard ultrasound transducers placed on the surface of a
hemisphere surrounding the breast. Assuming constant sound speed and zero
attenuation, the data represent integrals of the tissue's EM absorptivity over
spheres centered about the receivers (ultrasound transducers).
The inversion problem for TCT is therefore to recover the EM absorptivity
from integrals over spheres centered on a hemisphere. We present an
inversion formula for the complete data case, where integrals are measured
for centers on the entire sphere. We discuss differences between ideal and
clinically measurable TCT data and options for accurately reconstructing the
Crystalline materials such as most metals, ceramics, rocks, drugs, and bones are composed of a 3D space-filling network of small
crystallites r the grains. The geometry of this network governs a range of physical properties such as hardness and lifetime before
failure. Our group has pursued an experimental method r 3DXRD r which for the first time enable structural characterisation of the
grains in 3D. Furthermore, changes in grain morphology can be followed during typical industrial processes such as annealing or
3DXRD is based on reconstruction principles. In comparison to conventional tomography the use of higher dimensional spaces is
required. The projections are subject to group symmetry and their number is inherently limited. The grains exhibit a number of
geometric properties which can be utilised. Furthermore the problem at hand can be reformulated in terms of both vector-type and
scalar-type reconstructions. In conjunction these effects make 3DXRD reconstruction mathematically challenging.
The 3DXRD method will be presented with a few applications. The algorithms developed so far r for simplifying cases r will be
summarised with focus on continuous reconstruction methods.
The speaker will provide an overview of the Radon transform, showing
its relationship with X-ray tomography and other tomographic problems.
He will also describe the filtered back projection inversion formula
and contrast it with Lambda tomography. Finally, he plans to give an
elementary introduction to microlocal analysis and its implications
for limited data tomography. Sample reconstructions (tomography
pictures) will be provided to illustrate the ideas.
Joint work with Juan Cardelino and Marcelo Bertalmio.
Some of the most succesful algorithms for the automated
segmentation of images use an Active Regions approach, where a
curve is evolved so as to maximize the disparity of its interior
and exterior. But these techniques require the manual selection of
several parameters, which make impractical the work with long
image sequences or with a very dissimilar set of sequences.
Unfortunately this is precisely the case with 3D biological
image sequences. In this work we improve on previous Active
Regions algorithms in two aspects: by introducing a way to compute
and update the optimum weights for the different channels involved
(color, texture, etc.) and by estimating if the moving curve has
lost any object so as to launch a re-initialization step. Our
method is shown to outperform previous approaches. Several
examples of biological image sequences, quite long and different
among themselves, are presented.
The use of Sobolev gradients and negative norms
has proven to be a very useful preconditioning strategy
for a variety of problems from mechanics and CFD, including
transonic flow, minimal surface, and Ginzburg-Landau.
We summarize results of applying this methodology in a
variational approach for image decomposition f=u+v+w.
Conventional attenuation-based x-ray micro-CT is limited in terms of the image contrast it can convey for differentiating different
tissue components, spaces and functions. Multi-modality imaging (e.g., radionuclide emission and/or x-ray scatter) can expand the
information that can be obtained about those tissue aspects, but a challenge is accurate co-registration of the multiple images needed
for the CT image data to be used to enhance the other modality's specificity. Poly-capillary optics consist of bundles of hollow glass
capillaries (nominally 25µm in lumen diameter) which can "bend" x-rays or gamma rays by virtue of reflection of the photons within those
capillaries. This approach serves both to exclude unwanted radiation (i.e., collimates the radiation) and to allow passage of radiation
along accurately described paths - either parallel or focused. As both x-rays from an external x-ray source and from gamma ray emitters
and x-ray scatterers within an object can be imaged with this approach, the images from these three modalities are perfectly
co-registered. This allows use of the x-ray image to provide for attenuation correction of the internally generated radiation, as well
as restricting that emission to specific anatomic structures and spaces by virtue of a priori physiological knowledge.
Many imaging techniques acquire information about an underlying image
by making indirect linear measurements. For example, in computed
tomography we observe line integrals through the image, while in MRI
we observe samples of the image's Fourier transform.
To acquire an N-pixel image, we will in general need to make at least
What happens if the number of measurements is (much) less than N
(that is, the measurements are incomplete)? We will present
theoretical results showing that if the image is sparse, it can be
reconstructed from a very limited set of measurements essentially as
well as from a full set by solving a certain convex optimization
program. By "sparse", we mean that the image can be closely
approximated using a small number of elements from a known orthobasis
(a wavelet system, for example).
Although the reconstruction procedure is nonlinear, it is
exceptionally stable in the presence of noise, both in theory and in
We will conclude with several practical examples of how the theory
can be applied to "real-world" imaging problems.
In general geophysical images provide two kinds of information: (a) structural
images of discontinuities that define various lithology units and (b) physical
property distribution within these units. Depending on the resolution of the
geophysical survey, large scale changes can usually be detected that are often
correlated with stratigraphic architecture of the subsurface. Knowledge of
these architectural elements provides information about subsurface. Total
variation (TV) regularization is one possibility to preserve discontinuity in
the images. Another goal is to interpret these images is to obtain features
that have varying scale information. Wavelets have the attractive quality of
being able to resolve scale information in signal or data set. Moreover,
heterogeneity produces non-stationary signal that can be effectively analyzed
using wavelets due to its localization property. In this work we will present a
new methodology for computing a time-frequency map for non-stationary signals
using the continuous wavelet transform (CWT) that is more advantageous than
conventional method of producing a time-frequency map using the Short Time
Fourier Transform (STFT). This map is generated by transforming the time-scale
map by taking the Fourier transform of the inverse CWT to produce a
time-frequency map. We refer to such a map as the time-frequency CWT (TFCWT).
Imaging using total variation regularization operator followed by spectral
decomposition using TFCWT can be used as an effective interpretive tool.
In this talk I will describe recent results in the segmentation
of relevant structures in electron tomography.
We have developed novel techniques based on
PDEs to work with this extremely hard data.
I will describe the problem and the proposed solution,
both at a tutorial level for a general audience.
This is joint work with A. Bartesaghi and S. Subramaniam from NCI at NIH.
We present an algorithm for constructing orthogonal wavelet frames from MRA’s in L2(R), as well as for the associated filter banks. This construction gives rise to a vector-valued wavelet transform (VDWT) for vector valued data, such asimages. We present numerical results of image data compression using the VDWT.
Joint work with:
Joachim Weickert, Christian Feddern, Bernhard Burgeth, Christoph Schnoerr,
Curvature-driven PDE filters like mean-curvature motion (MCM), and median
filters are well-studied as structure-preserving filters for grey-value
images. They are related via a remarkable approximation result by Guichard
We show generalisations of both types of filters to multivariate,
specifically matrix-valued images. We discuss properties and algorithmic
aspects, and demonstrate their usefulness for the filtering of
Work in collaboration with the PSC-VB team and the Duke Center for In
Vivo Microscopy (CIVM) with support from the National Library of Medicine.
Volumetric datasets (CT, MRI, EM, etc.) on the gigabyte scale are relatively
common in the basic and clinic al Life Sciences, and datasets on the terabyte
scale will become increasingly common in the near future. At these scales
visualization and analysis using typical users desktop systems is difficult.
We have been developing a client-server system, the PSC Volume Browser
(PSC-VB), that links the graphics power of user's PCs with remote high
performance servers and supercomputing resources to enable the routine sharing,
visualization, and anaylsis of of large volumetric and time series datasets.
PSC-VB provides the framework for efficient data transfer and data manipulation
using both client and server side processing. The system is designed to link
extensible toolsets for data analysis including the National Library of
Medicine Insight Segmentation and Registration Toolkit (ITK) and user
provided processing modules.
We are currently using PSC-VB for analysis of mouse cardiac function
using time series micro-CT volumes and mouse embryo development micro-MRI
volumes captured at the Duke CIVM. This talk will provide an overview of
the PSC-VB system and its specific application to the CIVM time series
data analysis as well as preliminary efforts to build very large data
volumes from serial section electron microscopy images. Although our
current applications involve biological data the general framework is
applicable to other data modalities and has been used to view, for example,
earthquake ground motions and electro magnetic fields.
Common reflection angle migration (CRAM) is a computationally efficient
imaging technology developed at ExxonMobil which, as its name implies,
enables us to form
images of the subsurface in which all reflection events are imaged at the
same reflection angle.
It is most useful in complex imaging situations, such as beneath salt
masses where signal/noise
is a key issue and CRAM often enables us to separate signal and noise by
contrasting different common reflection angle volumes. Our poster shows a
of how this works in practice.
Recently several research groups independently proposed a
sinogram decomposition approach for different problems in medical imaging.
Sinogram is the set of projections of the reconstructed object. The main
idea is to treat a sinogram as a family of the sinogram curves (s-curves).
Each s-curve is obtained by tracing a single object point in the sinogram.
There are many operators that can be defined on a the space of s-curves:
backprojection (sum), minimum/maximum, etc. Therefore, the sinogram
decomposition approach can be used in many applications: reconstruction from
noisy data, sinogram completion for truncation correction and field-of-view
extension, and artifact correction. In this poster we will derive equations
of s-curves in fan-beam geometry, native for medical CT scanners,
parameterize the family of s-curves through a given sinogram pixel, and
consider some of the applications, where we suggest ways for estimation of
missing data using this approach.