Denoising of Frame Coefficients Using $\ell^1$ Data-Fidelity Term and Edge-Preserving Regularization

2007 ◽  
Vol 6 (2) ◽  
pp. 547-576 ◽  
Author(s):  
Sylvain Durand ◽  
Mila Nikolova
Keyword(s):  
Edge Preserving ◽  
Data Fidelity ◽  
Fidelity Term

scholarly journals Edge-preserving reconstruction with contour-line smoothing and non-quadratic data-fidelity

2013 ◽  
Vol 7 (4) ◽  
pp. 1331-1366 ◽  
Author(s):  
Marc C. Robini ◽  
◽  
Yuemin Zhu ◽  
Jianhua Luo ◽  
Keyword(s):  
Contour Line ◽  
Edge Preserving ◽  
Data Fidelity

A multi-frame super-resolution based on new variational data fidelity term

2020 ◽  
Vol 87 ◽  
pp. 446-467
Author(s):  
M. Hakim ◽  
A. Ghazdali ◽  
A. Laghrib
Keyword(s):  
Super Resolution ◽  
Data Fidelity ◽  
Fidelity Term

Fourth-order partial differential equations based anisotropic diffusion model for low-dose CT images

2018 ◽  
Vol 32 (25) ◽  
pp. 1850300 ◽  
Author(s):  
Yadunath Pathak ◽  
K. V. Arya ◽  
Shailendra Tiwari
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Fourth Order ◽  
Gaussian Noise ◽  
Anisotropic Diffusion ◽  
Low Dose ◽  
X Ray ◽  
Mixed Noise ◽  
Data Fidelity ◽  
Fidelity Term

The low-dose X-ray Computed Tomography (CT) is one of the most effective and indispensable imaging tools for clinical diagnosis. The reduced number of photons in low-dose X-ray CT imaging introduces the vulnerability towards Poisson and Gaussian noise. The majority of research till date focuses on reconstructing the images by reducing the effect of either Poisson or Gaussian noise. Thus, there is a need for a reconstruction framework that can counter the effects of both types of noises simultaneously. In this paper, an approach is proposed to handle the mixed noise (i.e. Poisson and Gaussian noises). Variational framework is utilized as energy minimization function. Minimizing the log likelihood gives data-fidelity term which portrays the distribution of noise in low-dose X-ray CT images. The problem of data-fidelity term as well as mixed noise issue in the sinogram data is resolved simultaneously by proposing a novel filter. The proposed filter modifies the Anisotropic Diffusion (AD) model based on Convolution Virtual Electric Field AD called as MADC. The modification in AD is achieved by applying fourth-order partial differential equations. To evaluate the effectiveness of the proposed MADC technique, both qualitative and quantitative evaluations are performed on three simulated test phantoms and one real standard thorax phantom of size [Formula: see text]. Afterwards, the performance of the proposed technique is compared with competitive denoising techniques. The experimental results reveal that the proposed framework significantly preserves the edges of reconstructed images and introduces lesser number of gradient reversal artifacts.

scholarly journals IPGM: Inertial Proximal Gradient Method for Convolutional Dictionary Learning

Electronics ◽  
2021 ◽  
Vol 10 (23) ◽  
pp. 3021
Author(s):  
Jing Li ◽  
Xiao Wei ◽  
Fengpin Wang ◽  
Jinjia Wang
Keyword(s):  
Dictionary Learning ◽  
Gradient Method ◽  
Inertial Force ◽  
Proximal Gradient Method ◽  
Recent Success ◽  
Alternating Direction ◽  
Inertial Algorithm ◽  
Derivative Formula ◽  
Data Fidelity ◽  
Fidelity Term

Inspired by the recent success of the proximal gradient method (PGM) and recent efforts to develop an inertial algorithm, we propose an inertial PGM (IPGM) for convolutional dictionary learning (CDL) by jointly optimizing both an ℓ2-norm data fidelity term and a sparsity term that enforces an ℓ1 penalty. Contrary to other CDL methods, in the proposed approach, the dictionary and needles are updated with an inertial force by the PGM. We obtain a novel derivative formula for the needles and dictionary with respect to the data fidelity term. At the same time, a gradient descent step is designed to add an inertial term. The proximal operation uses the thresholding operation for needles and projects the dictionary to a unit-norm sphere. We prove the convergence property of the proposed IPGM algorithm in a backtracking case. Simulation results show that the proposed IPGM achieves better performance than the PGM and slice-based methods that possess the same structure and are optimized using the alternating-direction method of multipliers (ADMM).

scholarly journals A Constrained Convex Optimization Approach to Hyperspectral Image Restoration with Hybrid Spatio-Spectral Regularization

2020 ◽  
Vol 12 (21) ◽  
pp. 3541
Author(s):  
Saori Takeyama ◽  
Shunsuke Ono ◽  
Itsuo Kumazawa
Keyword(s):  
Convex Optimization ◽  
Image Restoration ◽  
Optimization Problem ◽  
Hyperspectral Image ◽  
Optimization Problems ◽  
Low Rank ◽  
Optimization Approach ◽  
Regularization Term ◽  
Data Fidelity ◽  
Fidelity Term

We propose a new constrained optimization approach to hyperspectral (HS) image restoration. Most existing methods restore a desirable HS image by solving some optimization problems, consisting of a regularization term(s) and a data-fidelity term(s). The methods have to handle a regularization term(s) and a data-fidelity term(s) simultaneously in one objective function; therefore, we need to carefully control the hyperparameter(s) that balances these terms. However, the setting of such hyperparameters is often a troublesome task because their suitable values depend strongly on the regularization terms adopted and the noise intensities on a given observation. Our proposed method is formulated as a convex optimization problem, utilizing a novel hybrid regularization technique named Hybrid Spatio-Spectral Total Variation (HSSTV) and incorporating data-fidelity as hard constraints. HSSTV has a strong noise and artifact removal ability while avoiding oversmoothing and spectral distortion, without combining other regularizations such as low-rank modeling-based ones. In addition, the constraint-type data-fidelity enables us to translate the hyperparameters that balance between regularization and data-fidelity to the upper bounds of the degree of data-fidelity that can be set in a much easier manner. We also develop an efficient algorithm based on the alternating direction method of multipliers (ADMM) to efficiently solve the optimization problem. We illustrate the advantages of the proposed method over various HS image restoration methods through comprehensive experiments, including state-of-the-art ones.

scholarly journals Proximal Newton Methods for X-Ray Imaging with Non-Smooth Regularization

2020 ◽  
Vol 2020 (14) ◽  
pp. 7-1-7-7
Author(s):  
Tao Ge ◽  
Umberto Villa ◽  
Ulugbek S. Kamilov ◽  
Joseph A. O’Sullivan
Keyword(s):  
Image Reconstruction ◽  
Proximal Algorithms ◽  
X Ray ◽  
X Ray Imaging ◽  
Tv Regularization ◽  
X Ray Computed ◽  
Tomography Reconstruction ◽  
Data Fidelity ◽  
Fidelity Term ◽  
Thresholding Algorithm

Non-smooth regularization is widely used in image reconstruction to eliminate the noise while preserving subtle image structures. In this work, we investigate the use of proximal Newton (PN) method to solve an optimization problem with a smooth data-fidelity term and total variation (TV) regularization arising from image reconstruction applications. Specifically, we consider a nonlinear Poisson-modeled single-energy X-ray computed tomography reconstruction problem with the data-fidelity term given by the I-divergence. The PN algorithm is compared to state-of-the-art first-order proximal algorithms, such as the wellestablished fast iterative shrinkage and thresholding algorithm (FISTA), both in terms of number of iterations and time to solutions. We discuss the key factors that influence the performance of PN, including the strength of regularization, the stopping criterion for both sub-problem and main-problem, and the use of exact or approximated Hessian operators.

Sparse reconstruction method based on integrating data fidelity term and sparse constraint term

2017 ◽  
Vol 25 (9) ◽  
pp. 2437-2447
Author(s):  
高红霞 GAO Hong-xia ◽  
谢剑河 XIE Jian-he ◽  
曾润浩 ZENG Run-hao ◽  
吴梓灵 WU Zi-ling ◽  
马 鸽 MA Ge
Keyword(s):  
Sparse Reconstruction ◽  
Reconstruction Method ◽  
Sparse Constraint ◽  
Data Fidelity ◽  
Fidelity Term
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