26 research outputs found
Noise-resilient approach for deep tomographic imaging
We propose a noise-resilient deep reconstruction algorithm for X-ray
tomography. Our approach shows strong noise resilience without obtaining noisy
training examples. The advantages of our framework may further enable
low-photon tomographic imaging.Comment: 2022 CLEO (the Conference on Lasers and Electro-Optics) conference
submissio
Controlled wavelet domain sparsity for x-ray tomography
Tomographic reconstruction is an ill-posed inverse problem that calls for regularization. One possibility is to require sparsity of the unknown in an orthonormal wavelet basis. This, in turn, can be achieved by variational regularization, where the penalty term is the sum of the absolute values of the wavelet coefficients. The primal-dual fixed point algorithm showed that the minimizer of the variational regularization functional can be computed iteratively using a soft-thresholding operation. Choosing the soft-thresholding parameter mu > 0 is analogous to the notoriously difficult problem of picking the optimal regularization parameter in Tikhonov regularization. Here, a novel automatic method is introduced for choosing mu, based on a control algorithm driving the sparsity of the reconstruction to an a priori known ratio of nonzero versus zero wavelet coefficients in the unknown.Peer reviewe
Data-proximal complementary -TV reconstruction for limited data CT
In a number of tomographic applications, data cannot be fully acquired,
resulting in a severely underdetermined image reconstruction. In such cases,
conventional methods lead to reconstructions with significant artifacts. To
overcome these artifacts, regularization methods are applied that incorporate
additional information. An important example is TV reconstruction, which is
known to be efficient at compensating for missing data and reducing
reconstruction artifacts. At the same time, however, tomographic data is also
contaminated by noise, which poses an additional challenge. The use of a single
regularizer must therefore account for both the missing data and the noise.
However, a particular regularizer may not be ideal for both tasks. For example,
the TV regularizer is a poor choice for noise reduction across multiple scales,
in which case curvelet regularization methods are well suited. To
address this issue, in this paper we introduce a novel variational
regularization framework that combines the advantages of different
regularizers. The basic idea of our framework is to perform reconstruction in
two stages, where the first stage mainly aims at accurate reconstruction in the
presence of noise, and the second stage aims at artifact reduction. Both
reconstruction stages are connected by a data proximity condition. The proposed
method is implemented and tested for limited-view CT using a combined
curvelet-TV approach. We define and implement a curvelet transform adapted to
the limited-view problem and illustrate the advantages of our approach in
numerical experiments