A New Detail-Preserving Regularization Scheme

  title={A New Detail-Preserving Regularization Scheme},
  author={Weihong Guo and Jing Qin and Wotao Yin},
  journal={SIAM J. Imaging Sci.},
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 magnetic resonance (MR) and CT images. We propose a novel regularization model that integrates two recently developed regularization tools: total generalized variation (TGV) by Bredies, Kunisch, and Pock; and shearlet transform by Labate, Lim, Kutyniok, and Weiss. The proposed model recovers both edges and fine details of… 
Two-stage Geometric Information Guided Image Reconstruction
Geometric information extracted from the results of stage I serves as an initial prior for stage II which alternates image reconstruction and geometric information update in a mutually beneficial way and is applicable to other types of measurements as well.
Constrained Minimization Problem for Image Restoration Based on Non-Convex Hybrid Regularization
Numerical experiments show that the proposed hybrid regularization model can restrain blocking artifacts while projecting sharp edges, and the restoration quality outperforms several state-of-the-art methods.
Evolution from total variation to nonlinear sparsifying transform for sparse-view CT image reconstruction
This study investigated the image quality differences between the conventional TV minimization and the NLST-based CS, as well as imagequality differences among different kinds of NLST -based CS algorithms in the sparse-view CT image reconstruction.
Image Denoising via Nonlocal Low Rank Approximation With Local Structure Preserving
A re-weighted TGV regularized nuclear norm minimization model for local structure preserving image denoising is proposed and the over-smoothing problem aroused by a low-rank model can be effectively solved.
Image Restoration under Cauchy Noise with Sparse Representation Prior and Total Generalized Variation
This article introduces a novel variational model for restoring images degraded by Cauchy noise and/or blurring. The model integrates a nonconvex data-fidelity term with two regularization terms, a
Generalized Hessian-Schatten Norm Regularization for Image Reconstruction
Regularization plays a crucial role in reliably utilizing imaging systems for scientific and medical investigations. It helps to stabilize the process of computationally undoing any degradation


Sparse directional image representations using the discrete shearlet transform
Total Variation Wavelet Inpainting
Two related variational models are proposed, which combine the total variation (TV) minimization technique with wavelet representations, and can have effective and automatic control over geometric features of the inpainted images including sharp edges, even in the presence of substantial loss of wavelet coefficients.
Hybrid regularization for mri reconstruction with static field inhomogeneity correction
This work introduces a combined TV-framelet regularization to the undersampled MR reconstruction problem in inhomogeneous fields and shows that the inclusion of a frameletRegularization term decreases computation time and improves image quality over the traditional total variation (TV)-based approach.
Edge Guided Reconstruction for Compressive Imaging
The edge detector of EdgeCS is designed to faithfully return partial edges from intermediate image reconstructions even though these reconstructions may still have noise and artifacts.
Image restoration: Total variation, wavelet frames, and beyond
This paper is designed to establish connections between these two major image restoration approaches: variational methods and wavelet frame based methods to provide new interpretations and understanding of both approaches, and hence, lead to new applications for both approaches.
A Combined First and Second Order Variational Approach for Image Reconstruction
The numerical discussion confirms that the proposed higher-order model competes with models of its kind in avoiding the creation of undesirable artifacts and blocky-like structures in the reconstructed images—a known disadvantage of the ROF model—while being simple and efficiently numerically solvable.
Alternating Direction Method for Image Inpainting in Wavelet Domains
An unconstrained, TV-regularized, $\ell_2$-data-fitting model to recover the image, solved by the alternating direction method (ADM), and extensions of this ADM scheme to solving two closely related constrained models.
Sparse MRI: The application of compressed sensing for rapid MR imaging
Practical incoherent undersampling schemes are developed and analyzed by means of their aliasing interference and demonstrate improved spatial resolution and accelerated acquisition for multislice fast spin‐echo brain imaging and 3D contrast enhanced angiography.
The contourlet transform: an efficient directional multiresolution image representation
A "true" two-dimensional transform that can capture the intrinsic geometrical structure that is key in visual information is pursued and it is shown that with parabolic scaling and sufficient directional vanishing moments, contourlets achieve the optimal approximation rate for piecewise smooth functions with discontinuities along twice continuously differentiable curves.
Sparse Components of Images and Optimal Atomic Decompositions
This paper applies mathematical analysis to a specific formalization of SCA using synthetic image models, hoping to gain insight into what might emerge from a higher-resolution SCA based on n by n image patches for large n but a constant field of view.