Fast, robust total variation-based reconstruction of noisy, blurred images

Vogel, Curtis R.; Oman, Mary Ellen

doi:10.1109/83.679423

Cited by 558 publications

(379 citation statements)

References 24 publications

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“…Here h denotes a known space-invariant blur Top-left: Blurred image with Gaussian noise. Top-right: Restoration using the method of [45]. Bottom-left: Blurred image with salt and pepper noise.…”

Section: Introductionmentioning

confidence: 99%

Image Deblurring in the Presence of Impulsive Noise

Bar

Kiryati

Sochen

2006

Int J Comput Vision

127

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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 main challenge is to deblur the image, recover its discontinuities and at the same time remove the impulse noise. Median-based approaches are inadequate, because at high noise levels they induce nonlinear distortion that hampers the deblurring process. Distinguishing outliers from edge elements is difficult in current gradient-based edge-preserving restoration methods. The suggested approach integrates and extends the robust statistics, line process (half quadratic) and anisotropic diffusion points of view. We present a unified variational approach to image deblurring and impulse noise removal. The objective functional consists of a fidelity term and a regularizer. Data fidelity is quantified using the robust modified L 1 norm, and elements from the Mumford-Shah functional are used for regularization. We show that the Mumford-Shah regularizer can be viewed as an extended line process. It reflects spatial organization properties of the image edges, that do not appear in the common line process or anisotropic diffusion. This allows to distinguish outliers from edges and leads to superior experimental results.

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Section: Introductionmentioning

confidence: 99%

Image Deblurring in the Presence of Impulsive Noise

Bar

Kiryati

Sochen

2006

Int J Comput Vision

127

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“…Let H denote the operator of convolution of different blur PSFs that are pre-estimated. Using the notation of [25]…”

Section: Numerical Experiments and Evaluationmentioning

confidence: 99%

“…To solve the Γ -convergence to the MS functional, we use a discrete scheme called a cell-centered finite difference from [25,9]. Following the way of discretization, Eq.…”

Section: Numerical Experiments and Evaluationmentioning

confidence: 99%

Extended Mumford-Shah Regularization in Bayesian Estimation for Blind Image Deconvolution and Segmentation

Zheng¹,

Hellwich²

2006

Lecture Notes in Computer Science

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Abstract. We present an extended Mumford-Shah regularization for blind image deconvolution and segmentation in the context of Bayesian estimation for blurred, noisy images or video sequences. The MumfordShah functional is extended to have cost terms for the estimation of blur kernels via a newly introduced prior solution space. This functional is minimized using Γ -convergence approximation in an embedded alternating minimization within Neumann conditions. Accurate blur identification is the basis of edge-preserving image restoration in the extended Mumford-Shah regularization. One output of the finite set of curves and object boundaries are grouped and partitioned via a graph theoretical approach for the segmentation of blurred objects. The chosen regularization parameters using the L-curve method is presented. Numerical experiments show that the proposed algorithm is efficiency and robust in that it can handle images that are formed in different environments with different types and amounts of blur and noise.

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“…Traditionally, the L 2 norm is used to measure how well the model structures conform to the imposed constraints, but that is not the only possibility, as demonstrated by Farquharson & Oldenburg (1998), who presented an extensive analysis of the effects of using general measures of misfit (of data, as well as of model adjustment) in the inversion of electromagnetic data. Total Variation regularization, developed in the area of image processing (Rudin et al, 1992;Vogel & Oman, 1998), has been applied in the inversion of geophysical data Lima et al, 2011) to estimate non smooth basement relief in a sedimentary basin from gravity data. The method minimizes the differences between pairs of adjacent parameters in a L 1 norm misfit estimator.…”

Section: Introductionmentioning

confidence: 99%

Delineation of Anisotropic Layers Through 1d Inversion of Marine Csem Data

Régis¹,

Santos²

2017

Rev. Bras. Geof.

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ABSTRACT. This paper describes a method to invert marine CSEM data from anisotropic layered media. The method uses two types of constraints to generate stable solutions that improve the positioning of interfaces in anisotropic layers: applying the L 1 norm equality constraints of the Total Variation method to parameters in adjacent layers, and imposing L 2 norm equality constraints between the different components of the conductivity tensor in each layer. The solutions are compared favorably with those from previously published smoothing methods. The results show that the simultaneous application of the two constraints is able to improve the delineation of the anisotropic layers, including the resistive target commonly sought in the inversion of marine CSEM data. As an example application, the method is applied to real data from an offshore Brazilian basin.Keywords: anisotropic layered media, inversion, CSEM. RESUMO.Este artigo descreve um método para inverter dados do método marinho de fonte controlada CSEM de meios anisotrópicos estratificados. O método usa dois tipos de vínculos para gerar soluções estáveis que melhoram o posicionamento de interfaces entre camadas anisotrópicas: aplicando os vínculos de norma L 1 do método de Variação Total a parâmetros de camadas adjacentes, e impondo vínculos de igualdade de norma L 2 entre as componentes do tensor de impedância em cada camada. As soluções obtidas se mostram melhores que soluções encontradas na literatura com apenas o método de suavidade. Os resultados indicam que a aplicação simultânea dos dois vínculosé capaz de melhorar o delineamento de camadas anisotrópicas, incluindo as camadas-alvo resistivas normalmente buscadas na inversão de dados CSEM. O método foi aplicado a um conjunto de dados reais de uma bacia marinha brasileira.Palavras-chave: meios estratificados anisotrópicos, inversão, CSEM.

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Fast, robust total variation-based reconstruction of noisy, blurred images

Cited by 558 publications

References 24 publications

Image Deblurring in the Presence of Impulsive Noise

Image Deblurring in the Presence of Impulsive Noise

Extended Mumford-Shah Regularization in Bayesian Estimation for Blind Image Deconvolution and Segmentation

Delineation of Anisotropic Layers Through 1d Inversion of Marine Csem Data

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