Efficient Minimization Method for a Generalized Total Variation Functional

Rodríguez, Paul; Wohlberg, Brendt

doi:10.1109/tip.2008.2008420

Cited by 210 publications

(141 citation statements)

References 44 publications

Supporting

Mentioning

139

Contrasting

Order By: Relevance

“…19. We utilize SPG for the optimization of energy functions since we have previously experienced excellent performance of SPG on restoration of images degraded by Gaussian noise.…”

Section: Optimizationmentioning

confidence: 99%

Restoration of images degraded by signal-dependent noise based on energy minimization: an empirical study

Bajić

Lindblad

Sladoje

2016

J. Electron. Imaging

View full text Add to dashboard Cite

Abstract. Most energy minimization-based restoration methods are developed for signal-independent Gaussian noise. The assumption of Gaussian noise distribution leads to a quadratic data fidelity term, which is appealing in optimization. When an image is acquired with a photon counting device, it contains signal-dependent Poisson or mixed Poisson-Gaussian noise. We quantify the loss in performance that occurs when a restoration method suited for Gaussian noise is utilized for mixed noise. Signal-dependent noise can be treated by methods based on either classical maximum a posteriori (MAP) probability approach or on a variance stabilization approach (VST). We compare performances of these approaches on a large image material and observe that VST-based methods outperform those based on MAP in both quality of restoration and in computational efficiency. We quantify improvement achieved by utilizing Huber regularization instead of classical total variation regularization. The conclusion from our study is a recommendation to utilize a VST-based approach combined with regularization by Huber potential for restoration of images degraded by blur and signal-dependent noise. This combination provides a robust and flexible method with good performance and high speed.

show abstract

“…19. We utilize SPG for the optimization of energy functions since we have previously experienced excellent performance of SPG on restoration of images degraded by Gaussian noise.…”

Section: Optimizationmentioning

confidence: 99%

Restoration of images degraded by signal-dependent noise based on energy minimization: an empirical study

Bajić

Lindblad

Sladoje

2016

J. Electron. Imaging

View full text Add to dashboard Cite

show abstract

“…To enhance the reconstruction efficiency, the graph cuts based methods were organized to conserve computation time due to the gradient-free optimization. 15,16 Although the reconstruction approaches usually work well in some specific and highly controlled situations, no efforts need to be spared in investigating more general cases. 17 In this paper, a parallel iterative shrinkage algorithm has been demonstrated for the dual-modality tomography, i.e., the hybrid optical/μCT imaging.…”

Section: Dmt Not Only Obtains the Functional Changes Ofmentioning

confidence: 99%

Detection of mouse liver cancer via a parallel iterative shrinkage method in hybrid optical/microcomputed tomography imaging

Zhang

et al. 2012

J. Biomed. Opt

View full text Add to dashboard Cite

Abstract. Liver cancer is one of the most common malignant tumors worldwide. In order to enable the noninvasive detection of small liver tumors in mice, we present a parallel iterative shrinkage (PIS) algorithm for dual-modality tomography. It takes advantage of microcomputed tomography and multiview bioluminescence imaging, providing anatomical structure and bioluminescence intensity information to reconstruct the size and location of tumors. By incorporating prior knowledge of signal sparsity, we associate some mathematical strategies including specific smooth convex approximation, an iterative shrinkage operator, and affine subspace with the PIS method, which guarantees the accuracy, efficiency, and reliability for three-dimensional reconstruction. Then an in vivo experiment on the bead-implanted mouse has been performed to validate the feasibility of this method. The findings indicate that a tiny lesion less than 3 mm in diameter can be localized with a position bias no more than 1 mm; the computational efficiency is one to three orders of magnitude faster than the existing algorithms; this approach is robust to the different regularization parameters and the l p norms. Finally, we have applied this algorithm to another in vivo experiment on an HCCLM3 orthotopic xenograft mouse model, which suggests the PIS method holds the promise for practical applications of whole-body cancer detection.

show abstract

“…The penalty term is the composition of a linear operator and the 1 norm. Although the 1 norm stands out as the convex penalty that most effectively induces sparsity [27], non-convex penalties can lead to more accurate estimation of the underlying signal [37], [38], [40], [44], [50].…”

Section: Introductionmentioning

confidence: 99%

Total Variation Denoising Via the Moreau Envelope

Selesnick

2017

IEEE Signal Process. Lett.

102

View full text Add to dashboard Cite

Abstract-Total variation denoising is a nonlinear filtering method well suited for the estimation of piecewise-constant signals observed in additive white Gaussian noise. The method is defined by the minimization of a particular non-differentiable convex cost function. This paper describes a generalization of this cost function that can yield more accurate estimation of piecewise constant signals. The new cost function involves a nonconvex penalty (regularizer) designed to maintain the convexity of the cost function. The new penalty is based on the Moreau envelope. The proposed total variation denoising method can be implemented using forward-backward splitting.

show abstract

Efficient Minimization Method for a Generalized Total Variation Functional

Cited by 210 publications

References 44 publications

Restoration of images degraded by signal-dependent noise based on energy minimization: an empirical study

Restoration of images degraded by signal-dependent noise based on energy minimization: an empirical study

Detection of mouse liver cancer via a parallel iterative shrinkage method in hybrid optical/microcomputed tomography imaging

Total Variation Denoising Via the Moreau Envelope

Contact Info

Product

Resources

About