43,061 research outputs found
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
Investigation of iterative image reconstruction in three-dimensional optoacoustic tomography
Iterative image reconstruction algorithms for optoacoustic tomography (OAT),
also known as photoacoustic tomography, have the ability to improve image
quality over analytic algorithms due to their ability to incorporate accurate
models of the imaging physics, instrument response, and measurement noise.
However, to date, there have been few reported attempts to employ advanced
iterative image reconstruction algorithms for improving image quality in
three-dimensional (3D) OAT. In this work, we implement and investigate two
iterative image reconstruction methods for use with a 3D OAT small animal
imager: namely, a penalized least-squares (PLS) method employing a quadratic
smoothness penalty and a PLS method employing a total variation norm penalty.
The reconstruction algorithms employ accurate models of the ultrasonic
transducer impulse responses. Experimental data sets are employed to compare
the performances of the iterative reconstruction algorithms to that of a 3D
filtered backprojection (FBP) algorithm. By use of quantitative measures of
image quality, we demonstrate that the iterative reconstruction algorithms can
mitigate image artifacts and preserve spatial resolution more effectively than
FBP algorithms. These features suggest that the use of advanced image
reconstruction algorithms can improve the effectiveness of 3D OAT while
reducing the amount of data required for biomedical applications
Gradient-based quantitative image reconstruction in ultrasound-modulated optical tomography: first harmonic measurement type in a linearised diffusion formulation
Ultrasound-modulated optical tomography is an emerging biomedical imaging
modality which uses the spatially localised acoustically-driven modulation of
coherent light as a probe of the structure and optical properties of biological
tissues. In this work we begin by providing an overview of forward modelling
methods, before deriving a linearised diffusion-style model which calculates
the first-harmonic modulated flux measured on the boundary of a given domain.
We derive and examine the correlation measurement density functions of the
model which describe the sensitivity of the modality to perturbations in the
optical parameters of interest. Finally, we employ said functions in the
development of an adjoint-assisted gradient based image reconstruction method,
which ameliorates the computational burden and memory requirements of a
traditional Newton-based optimisation approach. We validate our work by
performing reconstructions of optical absorption and scattering in two- and
three-dimensions using simulated measurements with 1% proportional Gaussian
noise, and demonstrate the successful recovery of the parameters to within
+/-5% of their true values when the resolution of the ultrasound raster probing
the domain is sufficient to delineate perturbing inclusions.Comment: 12 pages, 6 figure
Accelerated High-Resolution Photoacoustic Tomography via Compressed Sensing
Current 3D photoacoustic tomography (PAT) systems offer either high image
quality or high frame rates but are not able to deliver high spatial and
temporal resolution simultaneously, which limits their ability to image dynamic
processes in living tissue. A particular example is the planar Fabry-Perot (FP)
scanner, which yields high-resolution images but takes several minutes to
sequentially map the photoacoustic field on the sensor plane, point-by-point.
However, as the spatio-temporal complexity of many absorbing tissue structures
is rather low, the data recorded in such a conventional, regularly sampled
fashion is often highly redundant. We demonstrate that combining variational
image reconstruction methods using spatial sparsity constraints with the
development of novel PAT acquisition systems capable of sub-sampling the
acoustic wave field can dramatically increase the acquisition speed while
maintaining a good spatial resolution: First, we describe and model two general
spatial sub-sampling schemes. Then, we discuss how to implement them using the
FP scanner and demonstrate the potential of these novel compressed sensing PAT
devices through simulated data from a realistic numerical phantom and through
measured data from a dynamic experimental phantom as well as from in-vivo
experiments. Our results show that images with good spatial resolution and
contrast can be obtained from highly sub-sampled PAT data if variational image
reconstruction methods that describe the tissues structures with suitable
sparsity-constraints are used. In particular, we examine the use of total
variation regularization enhanced by Bregman iterations. These novel
reconstruction strategies offer new opportunities to dramatically increase the
acquisition speed of PAT scanners that employ point-by-point sequential
scanning as well as reducing the channel count of parallelized schemes that use
detector arrays.Comment: submitted to "Physics in Medicine and Biology
Fast Mojette Transform for Discrete Tomography
A new algorithm for reconstructing a two dimensional object from a set of one
dimensional projected views is presented that is both computationally exact and
experimentally practical. The algorithm has a computational complexity of O(n
log2 n) with n = N^2 for an NxN image, is robust in the presence of noise and
produces no artefacts in the reconstruction process, as is the case with
conventional tomographic methods. The reconstruction process is approximation
free because the object is assumed to be discrete and utilizes fully discrete
Radon transforms. Noise in the projection data can be suppressed further by
introducing redundancy in the reconstruction. The number of projections
required for exact reconstruction and the response to noise can be controlled
without comprising the digital nature of the algorithm. The digital projections
are those of the Mojette Transform, a form of discrete linogram. A simple
analytical mapping is developed that compacts these projections exactly into
symmetric periodic slices within the Discrete Fourier Transform. A new digital
angle set is constructed that allows the periodic slices to completely fill all
of the objects Discrete Fourier space. Techniques are proposed to acquire these
digital projections experimentally to enable fast and robust two dimensional
reconstructions.Comment: 22 pages, 13 figures, Submitted to Elsevier Signal Processin
On the Adjoint Operator in Photoacoustic Tomography
Photoacoustic Tomography (PAT) is an emerging biomedical "imaging from
coupled physics" technique, in which the image contrast is due to optical
absorption, but the information is carried to the surface of the tissue as
ultrasound pulses. Many algorithms and formulae for PAT image reconstruction
have been proposed for the case when a complete data set is available. In many
practical imaging scenarios, however, it is not possible to obtain the full
data, or the data may be sub-sampled for faster data acquisition. In such
cases, image reconstruction algorithms that can incorporate prior knowledge to
ameliorate the loss of data are required. Hence, recently there has been an
increased interest in using variational image reconstruction. A crucial
ingredient for the application of these techniques is the adjoint of the PAT
forward operator, which is described in this article from physical, theoretical
and numerical perspectives. First, a simple mathematical derivation of the
adjoint of the PAT forward operator in the continuous framework is presented.
Then, an efficient numerical implementation of the adjoint using a k-space time
domain wave propagation model is described and illustrated in the context of
variational PAT image reconstruction, on both 2D and 3D examples including
inhomogeneous sound speed. The principal advantage of this analytical adjoint
over an algebraic adjoint (obtained by taking the direct adjoint of the
particular numerical forward scheme used) is that it can be implemented using
currently available fast wave propagation solvers.Comment: submitted to "Inverse Problems
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