1,446 research outputs found
Development and implementation of efficient noise suppression methods for emission computed tomography
In PET and SPECT imaging, iterative reconstruction is now widely used due to its capability of incorporating into the reconstruction process a physics model and Bayesian statistics involved in photon detection. Iterative reconstruction methods rely on regularization terms to suppress image noise and render radiotracer distribution with good image quality. The choice of regularization method substantially affects the appearances of reconstructed images, and is thus a critical aspect of the reconstruction process. Major contributions of this work include implementation and evaluation of various new regularization methods. Previously, our group developed a preconditioned alternating projection algorithm (PAPA) to optimize the emission computed tomography (ECT) objective function with the non-differentiable total variation (TV) regularizer. The algorithm was modified to optimize the proposed reconstruction objective functions.
First, two novel TV-based regularizersâhigh-order total variation (HOTV) and infimal convolution total variation (ICTV)âwere proposed as alternative choices to the customary TV regularizer in SPECT reconstruction, to reduce âstaircaseâ artifacts produced by TV. We have evaluated both proposed reconstruction methods (HOTV-PAPA and ICTV-PAPA), and compared them with the TV regularized reconstruction (TV-PAPA) and the clinical standard, Gaussian post-filtered, expectation-maximization reconstruction method (GPF-EM) using both Monte Carlo-simulated data and anonymized clinical data. Model-observer studies using Monte Carlo-simulated data indicate that ICTV-PAPA is able to reconstruct images with similar or better lesion detectability, compared with clinical standard GPF-EM methods, but at lower detected count levels. This implies that switching from GPF-EM to ICTV-PAPA can reduce patient dose while maintaining image quality for diagnostic use.
Second, the 1 norm of discrete cosine transform (DCT)-induced framelet regularization was studied. We decomposed the image into high and low spatial-frequency components, and then preferentially penalized the high spatial-frequency components. The DCT-induced framelet transform of the natural radiotracer distribution image is sparse. By using this property, we were able to effectively suppress image noise without overly compromising spatial resolution or image contrast.
Finally, the fractional norm of the first-order spatial gradient was introduced as a regularizer. We implemented 2/3 and 1/2 norms to suppress image spatial variability. Due to the strong penalty of small differences between neighboring pixels, fractional-norm regularizers suffer from similar cartoon-like artifacts as with the TV regularizer. However, when penalty weights are properly selected, fractional-norm regularizers outperform TV in terms of noise suppression and contrast recovery
Post-Reconstruction Deconvolution of PET Images by Total Generalized Variation Regularization
Improving the quality of positron emission tomography (PET) images, affected
by low resolution and high level of noise, is a challenging task in nuclear
medicine and radiotherapy. This work proposes a restoration method, achieved
after tomographic reconstruction of the images and targeting clinical
situations where raw data are often not accessible. Based on inverse problem
methods, our contribution introduces the recently developed total generalized
variation (TGV) norm to regularize PET image deconvolution. Moreover, we
stabilize this procedure with additional image constraints such as positivity
and photometry invariance. A criterion for updating and adjusting automatically
the regularization parameter in case of Poisson noise is also presented.
Experiments are conducted on both synthetic data and real patient images.Comment: First published in the Proceedings of the 23rd European Signal
Processing Conference (EUSIPCO-2015) in 2015, published by EURASI
First order algorithms in variational image processing
Variational methods in imaging are nowadays developing towards a quite
universal and flexible tool, allowing for highly successful approaches on tasks
like denoising, deblurring, inpainting, segmentation, super-resolution,
disparity, and optical flow estimation. The overall structure of such
approaches is of the form ; where the functional is a data fidelity term also
depending on some input data and measuring the deviation of from such
and is a regularization functional. Moreover is a (often linear)
forward operator modeling the dependence of data on an underlying image, and
is a positive regularization parameter. While is often
smooth and (strictly) convex, the current practice almost exclusively uses
nonsmooth regularization functionals. The majority of successful techniques is
using nonsmooth and convex functionals like the total variation and
generalizations thereof or -norms of coefficients arising from scalar
products with some frame system. The efficient solution of such variational
problems in imaging demands for appropriate algorithms. Taking into account the
specific structure as a sum of two very different terms to be minimized,
splitting algorithms are a quite canonical choice. Consequently this field has
revived the interest in techniques like operator splittings or augmented
Lagrangians. Here we shall provide an overview of methods currently developed
and recent results as well as some computational studies providing a comparison
of different methods and also illustrating their success in applications.Comment: 60 pages, 33 figure
Joint Image Reconstruction and Segmentation Using the Potts Model
We propose a new algorithmic approach to the non-smooth and non-convex Potts
problem (also called piecewise-constant Mumford-Shah problem) for inverse
imaging problems. We derive a suitable splitting into specific subproblems that
can all be solved efficiently. Our method does not require a priori knowledge
on the gray levels nor on the number of segments of the reconstruction.
Further, it avoids anisotropic artifacts such as geometric staircasing. We
demonstrate the suitability of our method for joint image reconstruction and
segmentation. We focus on Radon data, where we in particular consider limited
data situations. For instance, our method is able to recover all segments of
the Shepp-Logan phantom from angular views only. We illustrate the
practical applicability on a real PET dataset. As further applications, we
consider spherical Radon data as well as blurred data
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