Abstract
X-ray computed tomography (CT) is widely used in medical applications, where many efforts have been made for decades to eliminate artifacts caused by incomplete projection. In this paper, we propose a new CT image reconstruction model based on nonlocal low-rank regularity and data-driven tight frame (NLR-DDTF). Unlike the Spatial-Radon domain data-driven tight frame regularization, the proposed NLR-DDTF model uses an asymmetric treatment for image reconstruction and Radon domain inpainting, which combines the nonlocal low-rank approximation method for spatial domain CT image reconstruction and data-driven tight frame-based regularization for Radon domain image inpainting. An alternative direction minimization algorithm is designed to solve the proposed model. Several numerical experiments and comparisons are provided to illustrate the superior performance of the NLR-DDTF method.
Highlights
In order to exploit this kind of prior knowledge of f, the authors of [1] proposed an image inpainting method on the projection image f, following with another inverse problem for image restoration in the spatial domain
In [1,5], the sparse approximation methods were proposed for both the computed tomography (CT) image u and projection image f, which are based on the pre-constructed wavelet frames or datadriven tight frames
All these problems are handled by the alternative direction multiplier method technique, which is converted into several sub-problems and solved iteratively and alternately
Summary
Medical imaging applications of X-ray computed tomography (CT) include cranial, chest, cardiac abdominal and pelvic imaging. In order to exploit this kind of prior knowledge of f , the authors of [1] proposed an image inpainting method on the projection image f , following with another inverse problem for image restoration in the spatial domain This wavelet frame-based regularity with Radon domain inpainting was shown to be useful for reconstructing high quality images from a very small number of projections, κ min k RΛc ( Pu − f )k22 + k RΛ ( Pu) − f 0 k22 + k RΛ f − f 0 k22 +.
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