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Nonlinear image recovery with half-quadratic regularization

D. Geman, Chengda Yang
1995 IEEE Transactions on Image Processing  
One popular method for the recovery of an ideal intensity image from corrupted or indirect measurements is regularization: minimize an objective function which enforces a roughness penalty in addition  ...  In contrast, nonlinear estimates are more accurate, but often far less accessible.  ...  and common observation: nonlinear estimates are superior to linear ones for many image recovery problems but are generally far more dicult to compute.  ... 
doi:10.1109/83.392335 pmid:18290044 fatcat:mc2pgmyf6vb5rfmksunl3eqkly

Analysis of Resolution and Noise Properties of Nonquadratically Regularized Image Reconstruction Methods for PET

Sangtae Ahn, R.M. Leahy
2008 IEEE Transactions on Medical Imaging  
resolution in quadratic regularization.  ...  However, there has been little research on the quantitative analysis of nonquadratic regularization due to its nonlinearity.  ...  For a quantitative comparison, we computed the recovery coefficient (RC) [48] and full-width half-maximum (FWHM) of the perturbation responses.  ... 
doi:10.1109/tmi.2007.911549 pmid:18334436 fatcat:h72yvpcfancb5oh4klxdcvth2a

Impulse noise treatment in magnetotelluric inversion

Hugo Hidalgo-Silva, Enrique Gómez-Treviño
2021 Open Geosciences  
The application of total variation regularization along with L1-norm penalized data fitting (TVL1) is the usual approach for the impulse noise treatment in image recovery.  ...  The nonconvex operator is solved by following a half-quadratic procedure of minimization.  ...  Author contributions: HHS developed and implemented the algorithms, and EGT assisted with the analysis and interpretation of results.  ... 
doi:10.1515/geo-2020-0225 fatcat:qvbgd636tza3dkvilsk6qe7e6e

Regularized image reconstruction for PS model-based cardiovascular MRI

Anthony G. Christodoulou, Bo Zhao, Zhi-Pei Liang
2011 2011 IEEE International Symposium on Biomedical Imaging: From Nano to Macro  
An important practical question is which regularization scheme to use for PS model-based cardiovascular imaging.  ...  It has been shown that ℓ 1 regularization is useful for finding sparse solutions, and ℓ 2 regularization is widely used to incorporate anatomical constraints.  ...  In this paper, we solve it by combining a half-quadratic optimization algorithm with a continuation procedure [11, 12] .  ... 
doi:10.1109/isbi.2011.5872353 pmid:25283177 pmcid:PMC4184476 dblp:conf/isbi/ChristodoulouZL11 fatcat:wlwrqq43nfed5gvlztng5glkaa

Image Deblurring in the Presence of Impulsive Noise

Leah Bar, Nahum Kiryati, Nir Sochen
2006 International Journal of Computer Vision  
The suggested approach integrates and extends the robust statistics, line process (half quadratic) and anisotropic diffusion points of view.  ...  Consider the problem of image deblurring in the presence of impulsive noise. Standard image deconvolution methods rely on the Gaussian noise model and do not perform well with impulsive noise.  ...  The experimental results demonstrate effective image recovery, with various blur models and noise levels.  ... 
doi:10.1007/s11263-006-6468-1 fatcat:43m7qgw555c7jaq4dgt5oermky

An ℓ_p Variable Projection Method for Large-Scale Separable Nonlinear Inverse Problems [article]

Malena Espanol, Mirjeta Pasha
2021 arXiv   pre-print
We adopt a majorization minimization method that relies on constructing a quadratic tangent majorant to approximate a general ℓ_p regularized problem by an ℓ_2 regularized problem that can be solved by  ...  Numerical examples on large-scale two-dimensional imaging problems arising from blind deconvolution are used to highlight the performance of the proposed approach in both quality of the reconstructed image  ...  In [2] , the separable nonlinear least squares problem is reformulated as a sparse-recovery problem by the 1 -norm minimization.  ... 
arXiv:2105.14155v1 fatcat:u3idswntbzcfro7nycuoo7lysu

Nonlinear approach to difference imaging in diffuse optical tomography

Meghdoot Mozumder, Tanja Tarvainen, Aku Seppänen, Ilkka Nissilä, Simon R. Arridge, Ville Kolehmainen
2015 Journal of Biomedical Optics  
Difference imaging aims at recovery of the change in the optical properties of a body based on measurements before and after the change.  ...  To overcome the limitations of the linear approach, we investigate a nonlinear approach for difference imaging where the images of the optical parameters before and after the change are reconstructed simultaneously  ...  (b) Estimated optical coefficients with nonlinear difference imaging using quadratic smoothness regularization for modeling δx ROI .  ... 
doi:10.1117/1.jbo.20.10.105001 pmid:26440615 fatcat:xvmj7k27szbt5k46qqiw5bt4ry

A Memory Gradient algorithm for ℓ2 — ℓ0 regularization with applications to image restoration

Emilie Chouzenoux, Jean-Christophe Pesquet, Hugues Talbot, Anna Jezierska
2011 2011 18th IEEE International Conference on Image Processing  
In this paper, we consider a class of differentiable criteria for sparse image recovery problems. The regularization is applied to a linear transform of the target image.  ...  The fast convergence properties of the proposed optimization algorithm are illustrated through image restoration examples.  ...  First, we compare the MM-MG algorithm given by (6) and (9) where J = 1, with the Beck-Teboulle (BT) gradient-based algorithm [13] and with the fast version of half quadratic (HQ) algorithm [11]  ... 
doi:10.1109/icip.2011.6116230 dblp:conf/icip/ChouzenouxPTJ11 fatcat:co2wgcriubdkze25ys4axbqmcu

An accelerated version of alternating direction method of multipliers for TV minimization in EIT

Ashkan Javaherian, Manuchehr Soleimani, Knut Moeller, Amir Movafeghi, Reza Faghihi
2016 Applied Mathematical Modelling  
The results demonstrate the superiority of the accelerated algorithm over existing TV solvers in EIT with regard to both accuracy and speed.  ...  Existing total variation (TV) solvers that have been applied in Electrical Impedance Tomography (EIT) smooth the TV function in order to cope with its nondifferentiability around the origin, and thus imposes  ...  The NtD map is nonlinear with respect to , so it is linearized by computing the Jacobian around 0  .  ... 
doi:10.1016/j.apm.2016.05.052 fatcat:3t3oijoqwnagbhfr64xo4pbdta

Sparsity-based three-dimensional image reconstruction for near-field MIMO radar imaging

2019 Turkish Journal of Electrical Engineering and Computer Sciences  
Sparsity is enforced using total variation regularization, and the reflectivity distribution is reconstructed iteratively without requiring computation with huge matrices.  ...  Since the underlying scenes can be typically represented sparsely in some transform domain, sparsity priors can effectively regularize the image formation problem and hence enable high-quality reconstructions  ...  ., which was funded by TÜBİTAK under a TEYDEB 1511 program with grant number 3140481.  ... 
doi:10.3906/elk-1902-85 fatcat:bxdfuorzabad5hl2hragpcfqje

Another Robust NMF: Rethinking the Hyperbolic Tangent Function and Locality Constraint

xingyu shen, xiang zhang, long lan, Qing Liao, zhigang luo
2019 IEEE Access  
Following the paradigm of the half-quadratic algorithm, we easily solve an adaptive weighted NMF instead of original tanhNMF.  ...  INDEX TERMS Non-negative matrix factorization, robust NMF, the hyperbolic tangent function, half-quadratic algorithm, locality constraint.  ...  Geman and Reynolds in 1992 [28] originally presented the half-quadratic minimization in the multiplicative form to perform image reconstruction with non-convex regularization problem.  ... 
doi:10.1109/access.2019.2903309 fatcat:fqhugbbpzfeljch3so2mxdrq4e

Multichannel regularized recovery of compressed video sequences

Mun Gi Choi, Yongyi Yang, N.P. Galatsanos
2001 IEEE transactions on circuits and systems - 2, Analog and digital signal processing  
Several forms of temporal regularization with different computational complexity are considered.  ...  In this paper, we propose a multichannel regularized recovery approach to ameliorate coding artifacts in compressed video.  ...  Observe that each term involved in (11) and ( 8 ) is a quadratic and convex function of the image vectors . As a result, the regularization terms and are quadratic and convex functions of .  ... 
doi:10.1109/82.933797 fatcat:doqlfop2f5dmhljytj54zeoiu4

A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration

Junfeng Yang, Wotao Yin, Yin Zhang, Yilun Wang
2009 SIAM Journal of Imaging Sciences  
In the MTV case, we show that the model can be derived from an extended half-quadratic transform of Geman and Yang [14] .  ...  For color images with three channels and when applied to the MTV model (either locally weighted or not), the per-iteration computational complexity of this algorithm is dominated by nine fast Fourier transforms  ...  Based upon our previous work in [32] for singlechannel images, we show that this algorithm can be derived from a general half-quadratic formulation, and is applicable to a variety of regularization functions  ... 
doi:10.1137/080730421 fatcat:ey5vkp2btrakbhmqmgxq52a7q4

Sparse SAR imaging based on L 1/2 regularization

JinShan Zeng, Jian Fang, ZongBen Xu
2012 Science China Information Sciences  
Compared to the conventional SAR imaging technique, the new method implements SAR imaging effectively at much lower sampling rate than the Nyquist rate, and produces high-quality images with reduced sidelobes  ...  The approach is based on L 1/2 regularization to reconstruct the scattering field, which optimizes a quadratic error term of the SAR observation process subject to the interested scene sparsity.  ...  One improved method based on non-quadratic penalty (namely, L p regularization with p ∈ (0, 2)) for SAR imaging was proposed to preserve such features in [11] , with extension to passive radar for multiple  ... 
doi:10.1007/s11432-012-4632-5 fatcat:rbzoeeylnbfvjdinh3j5govkwy

Convergence of an Iterative Method for Variational Deconvolution and Impulsive Noise Removal

Leah Bar, Nir Sochen, Nahum Kiryati
2007 Multiscale Modeling & simulation  
Image restoration, i.e. the recovery of images that have been degraded by blur and noise, is a challenging inverse problem.  ...  The variational formulation yields a nonlinear integro-differential equation. This equation was linearized by fixed point iteration.  ...  In the half quadratic regularization two auxiliary variables b = (b x , b y ) are introduced in order to make the manipulation of the regularizer simpler (quadratic in u).  ... 
doi:10.1137/060671607 fatcat:fxftxfwiuzg63gw5q5cnhc3x74
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