A New Detail-Preserving Regularization Scheme

Weihong Guo, Jing Qin, and Wotao Yin

Publised in SIAM Journal on Imaging Sciences


It is a challenging task to reconstruct images from their noisy, blurry, and/or incomplete measurements, especially those with important details and features such as medical MR and CT images.

We propose a novel regularization model that integrates two recently-developed regularization tools total generalized variation (TGV) by Bredies, Kunish, and Pock and the shearlet transform by Labate, Lim, Kutyniok, and Weiss. The proposed model recovers both edges and fine details of images much better than the existing regularization models based on total variation (TV) and wavelets.

Specifically, while TV preserves sharp edges and suffers the oil-painting artifact, TGV “selectively regularizes” different image regions at different levels and thus largely avoids oil-painting artifact. Unlike the wavelet transform, which represents isotropic image features much more sparsely than anisotropic ones, the shearlet transform can also efficiently represent anisotropic features such as edges, curves, and so on. The proposed model based on TVG and Shearlets has been tested in the compressive sensing context and reconstructed high-quality images from fewer measurements than the state-of-the-art methods. It also applies to other image processing tasks such as denoising, deblurring, change detection, object tracking, etc. The proposed model is solved by variable splitting and the alternating direction method of multiplier (ADMM). For certain sensing operators including the partial Fourier transform, all the ADMM subproblems have closed-form solutions. Convergence of the algorithm is presented.

The numerical simulation presented in this paper uses the incomplete Fourier, discrete cosine, and wavelet measurements of magnetic resonance (MR) images and natural images. The proposed method is demonstrated to preserve various image features including edges and textures much better than TV/wavelet based methods.


W. Guo, J. Qin, and W. Yin, A new detail-preserving regularity scheme, SIAM Journal on Imaging Sciences, 7(2), 2014. DOI:10.1137/120904263.

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