X-Ray CT Image Reconstruction via Wavelet Frame Based Regularization and Radon Domain Inpainting

Dong, Bin; Li, Jia; Shen, Zuowei

doi:10.1007/s10915-012-9579-6

Cited by 79 publications

(87 citation statements)

References 46 publications

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“…Comparing to the total variation based model, which is the other model that is widely used in image restoration, the analysis based model can generate higher quality images for various image restoration problems (see e.g. [9,42,43]). Furthermore, the analysis based model can be regarded as a special case of the proposed model (3.2).…”

Section: Numerical Simulationsmentioning

confidence: 99%

Image restoration: A wavelet frame based model for piecewise smooth functions and beyond

Cai

Dong

Shen

2016

Applied and Computational Harmonic Analysis

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104

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Recently, mapping a signal/image into a low rank Hankel/Toeplitz matrix has become an emerging alternative to the traditional sparse regularization, due to its ability to alleviate the basis mismatch between the true support in the continuous domain and the discrete grid. In this paper, we introduce a novel structured low rank matrix framework to restore piecewise smooth functions. Inspired by the total generalized variation to use sparse higher order derivatives, we derive that the Fourier samples of higher order derivatives satisfy an annihilation relation, resulting in a low rank multi-fold Hankel matrix. We further observe that the SVD of a low rank Hankel matrix corresponds to a tight wavelet frame system which can represent the image with sparse coefficients. Based on this observation, we also propose a wavelet frame analysis approach based continuous domain regularization model for the piecewise smooth image restoration. Finally, numerical results on image restoration tasks are presented as a proof-of-concept study to demonstrate that the proposed approach is compared favorably against several popular discrete regularization approaches and structured low rank matrix approaches.

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Section: Numerical Simulationsmentioning

confidence: 99%

Image restoration: A wavelet frame based model for piecewise smooth functions and beyond

Cai

Dong

Shen

2016

Applied and Computational Harmonic Analysis

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104

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“…Wavelet frame related algorithms have been developed to solve medical and biological image processing problems, e.g. medical image segmentation [44,113], X-ray computer tomography (CT) image reconstruction [47], and protein molecule 3D reconstruction from electron microscopy images [83]. Frames provide large flexibility in designing filters with improved performance in applications.…”

Section: Introductionmentioning

confidence: 99%

Duality for Frames

Fan

Heinecke

Shen

2015

J Fourier Anal Appl

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The subject of this article is the duality principle, which, well beyond its stand at the heart of Gabor analysis, is a universal principle in frame theory that gives insight into many phenomena. Its fiber matrix formulation for Gabor systems is the driving principle behind seemingly different results. We show how the classical duality identities, operator representations and constructions for dual Gabor frames are in fact aspects of the dual Gramian matrix fiberization and its sole duality principle, giving a unified view to all of them. We show that the same duality principle, via dual Gramian matrix analysis, holds for dual (or bi-) systems in abstract Hilbert spaces. The essence of the duality principle is the unitary equivalence of the frame operator and the Gramian of certain adjoint systems. An immediate consequence is, for example, that, even on this level of generality, dual frames are characterized in terms of biorthogonality relations of adjoint systems. We formulate the duality principle for irregular Gabor systems which have no structure whatsoever to the sampling of the shifts and modulations of the generating window. In case the shifts and modulations are sampled from lattices we show how the abstract matrices can be reduced to the simple structured fiber matrices of shift-invariant systems, thus arriving back in the well understood territory. Moreover, in the arena of multiresolution analysis J Fourier Anal Appl (MRA)-wavelet frames, the mixed unitary extension principle can be viewed as the duality principle in a sequence space. This perspective leads to a construction scheme for dual wavelet frames which is strikingly simple in the sense that it only needs the completion of an invertible constant matrix. Under minimal conditions on the MRA, our construction guarantees the existence and easy constructability of non-separable multivariate dual MRA-wavelet frames. The wavelets have compact support and we show examples for multivariate interpolatory refinable functions. Finally, we generalize the duality principle to the case of transforms that are no longer defined by discrete systems, but may have discrete adjoint systems.

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“…Hu et al [23] have compared the class of linear operators, which contains Radon, Bessel, and Riesz fractional integration transforms to deal with the inverse problem of the Radon transform and receive more effective reconstruction. Dong et al [24] have proposed a method that uses the analysis-based approach of wavelet frame method and Radon domain inpainting mechanism to reconstruct high-quality images with very small number of projections. Radon-based rotations require minimal interpolation and preserve all of the original image pixel intensities [25].…”

Section: Introductionmentioning

confidence: 99%

Projection-Based Medical Image Compression for Telemedicine Applications

2014

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Recent years have seen great development in the field of medical imaging and telemedicine. Despite the developments in storage and communication technologies, compression of medical data remains challenging. This paper proposes an efficient medical image compression method for telemedicine. The proposed method takes advantage of Radon transform whose basis functions are effective in representing the directional information. The periodic re-ordering of the elements of Radon projections requires minimal interpolation and preserves all of the original image pixel intensities. The dimension-reducing property allows the conversion of 2D processing task to a set of simple 1D task independently on each of the projections. The resultant Radon coefficients are then encoded using set partitioning in hierarchical trees (SPIHT) encoder. Experimental results obtained on a set of medical images demonstrate that the proposed method provides competing performance compared with conventional and state-of-the art compression methods in terms of compression ratio, peak signal-to-noise ratio (PSNR), and computational time.

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X-Ray CT Image Reconstruction via Wavelet Frame Based Regularization and Radon Domain Inpainting

Cited by 79 publications

References 46 publications

Image restoration: A wavelet frame based model for piecewise smooth functions and beyond

Image restoration: A wavelet frame based model for piecewise smooth functions and beyond

Duality for Frames

Projection-Based Medical Image Compression for Telemedicine Applications

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