Graduated adaptive image denoising: local compromise between total variation and isotropic diffusion

Bollt, Erik M.; Chartrand, Rick; Esedoḡlu, Selim; Schultz, Pete; Vixie, Kevin R.

doi:10.1007/s10444-008-9082-7

Cited by 83 publications

(53 citation statements)

References 10 publications

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“…The drawback of the approach is that the introduced smoothness of the higher-order derivatives may cause image features to be oversmoothed. Other relevant extensions of the TV model to include additional smoothness constraints are, e.g., [12,23,13].…”

Section: Variational Methodsmentioning

confidence: 99%

Mapping-Based Image Diffusion

2016

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In this work, we introduce a novel tensorbased functional for targeted image enhancement and denoising. Via explicit regularization, our formulation incorporates application dependent and contextual information using first principles. Few works in literature treat variational models that describe both application dependent information and contextual knowledge of the denoising problem. We prove the existence of a minimizer and present results on tensor symmetry constraints, convexity, and geometric interpretation of the proposed functional. We show that our framework excels in applications where nonlinear functions are present such as in gamma correction and targeted value range filtering. We also study general denoising performance where we show comparable results to dedicated PDE-based state of the art methods.

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Section: Variational Methodsmentioning

confidence: 99%

Mapping-Based Image Diffusion

2016

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“…For complex structured noise, the TV type method could oversmooth the structure and create the staircasing effect. 26 For small, subtle signals, the TV method was the worst in terms of CNR for both phantom and real calcifications. At p Ͻ 1, the TpV method is nonconvex and can enhance even some lowcontrast features.…”

Section: Discussionmentioning

confidence: 99%

Selective‐diffusion regularization for enhancement of microcalcifications in digital breast tomosynthesis reconstruction

Chan

Wei

et al. 2010

Medical Physics

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Purpose: Digital breast tomosynthesis ͑DBT͒ has been shown to improve mass detection. Detection of microcalcifications is more challenging because of the large breast volume to be searched for subtle signals. The simultaneous algebraic reconstruction technique ͑SART͒ was found to provide good image quality for DBT, but the image noise is amplified with an increasing number of iterations. In this study, the authors developed a selective-diffusion ͑SD͒ method for noise regularization with SART to improve the contrast-to-noise ratio ͑CNR͒ of microcalcifications in the DBT slices for human or machine detection. Methods:The SD method regularizes SART reconstruction during updating with each projection view. Potential microcalcifications are differentiated from the noisy background by estimating the local gradient information. Different degrees of regularization are applied to the signal or noise classes, such that the microcalcifications will be enhanced while the noise is suppressed. The new SD method was compared to several current methods, including the quadratic Laplacian ͑QL͒ method, the total variation ͑TV͒ method, and the nonconvex total p-variation ͑TpV͒ method for noise regularization with SART. A GE GEN2 prototype DBT system with a stationary digital detector was used for the acquisition of DBT scans at 21 angles in 3°increments over a Ϯ30°r ange. The reconstruction image quality without regularization and that with the different regularization methods were compared using the DBT scans of an American College of Radiology phantom and a human subject. The CNR and the full width at half maximum ͑FWHM͒ of the line profiles of microcalcifications within the in-focus DBT slices were used as image quality measures. Results: For the comparison of large microcalcifications in the DBT data of the subject, the SD method resulted in comparable CNR to the nonconvex TpV method. Both of them performed better than the other two methods. For subtle microcalcifications, the SD method was superior to other methods in terms of CNR. In both the subject and phantom DBT data, for large microcalcifications, the FWHM of the SD method was comparable to that without regularization, which was wider than that of the TV type methods. For subtle microcalcifications, the SD method had comparable FWHM values to the TV type methods. All three regularization methods were superior to the QL method in terms of FWHM. Conclusions: The SART regularized by the selective-diffusion method enhanced the CNR and preserved the sharpness of microcalcifications. In comparison with three existing regularization methods, the selective-diffusion regularization was superior to the other methods for subtle microcalcifications.

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“…Bollt ve ark. veya norm terimiyle bu problemin [8]'de bir minimumlaştırıcıya sahip olduğunu kanıtladı. Sonra Chen ve arkadaşları [11]'de yer alan aşağıdaki modeli önerdi; bir sabit ve için…”

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