876 research outputs found
Iterative CT reconstruction using shearlet-based regularization
In computerized tomography, it is important to reduce the image noise without increasing the acquisition dose. Extensive research has been done into total variation minimization for image denoising and sparse-view reconstruction. However, TV minimization methods show superior denoising performance for simple images (with little texture), but result in texture information loss when applied to more complex images. Since in medical imaging, we are often confronted with textured images, it might not be beneficial to use TV. Our objective is to find a regularization term outperforming TV for sparse-view reconstruction and image denoising in general. A recent efficient solver was developed for convex problems, based on a split-Bregman approach, able to incorporate regularization terms different from TV. In this work, a proof-of-concept study demonstrates the usage of the discrete shearlet transform as a sparsifying transform within this solver for CT reconstructions. In particular, the regularization term is the 1-norm of the shearlet coefficients. We compared our newly developed shearlet approach to traditional TV on both sparse-view and on low-count simulated and measured preclinical data. Shearlet-based regularization does not outperform TV-based regularization for all datasets. Reconstructed images exhibit small aliasing artifacts in sparse-view reconstruction problems, but show no staircasing effect. This results in a slightly higher resolution than with TV-based regularization
Reconstruction of Binary Functions and Shapes from Incomplete Frequency Information
The characterization of a binary function by partial frequency information is
considered. We show that it is possible to reconstruct binary signals from
incomplete frequency measurements via the solution of a simple linear
optimization problem. We further prove that if a binary function is spatially
structured (e.g. a general black-white image or an indicator function of a
shape), then it can be recovered from very few low frequency measurements in
general. These results would lead to efficient methods of sensing,
characterizing and recovering a binary signal or a shape as well as other
applications like deconvolution of binary functions blurred by a low-pass
filter. Numerical results are provided to demonstrate the theoretical
arguments.Comment: IEEE Transactions on Information Theory, 201
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