Regularized image restoration in multiresolution spaces

Stephanakis, Ioannis M.

doi:10.1117/1.601368

Cited by 14 publications

(4 citation statements)

References 12 publications

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“…Zou and Hastie [20] proposed the elastic-net by incorporating the 2 penalty into the 1 penalty, in the hope of retrieving the whole relevant group, and numerically demonstrated its excellent performance for simulation studies and real-data applications. Such multiple/multiscale features appear also in many other applications, e.g., image processing [14,17], electrocardiography [3], and geodesy [19].…”

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confidence: 99%

Multi-parameter Tikhonov regularization

Jin

Takeuchi

2011

Methods and Applications of Analysis

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Abstract. We study multi-parameter Tikhonov regularization, i.e., with multiple penalties. Such models are useful when the sought-for solution exhibits several distinct features simultaneously. Two choice rules, i.e., discrepancy principle and balancing principle, are studied for choosing an appropriate (vector-valued) regularization parameter, and some theoretical results are presented. In particular, the consistency of the discrepancy principle as well as convergence rate are established, and an a posteriori error estimate for the balancing principle is established. Also two fixed point algorithms are proposed for computing the regularization parameter by the latter rule. Numerical results for several nonsmooth multi-parameter models are presented, which show clearly their superior performance over their single-parameter counterparts.

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confidence: 99%

Multi-parameter Tikhonov regularization

Jin

Takeuchi

2011

Methods and Applications of Analysis

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“…In recent years, there has been a growing interest in sophisticated regularization techniques which use multiple constraints as a means of improving the quality of inversion [1,3,4,21]. Examples include the inverse problem of electrocardiography [4] where both temporal and spatial constraints are imposed on the solution, the wavelet domain restoration of blurred images where each subband in the wavelet decomposition of the image is subjected to a different degree of regularization [3], and problems involving depth-varying regularization [19].…”

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confidence: 99%

Efficient determination of multiple regularization parameters in a generalized L-curve framework

2002

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The selection of multiple regularization parameters is considered in a generalized L-curve framework. Multiple-dimensional extensions of the L-curve for selecting multiple regularization parameters are introduced, and a minimum distance function (MDF) is developed for approximating the regularization parameters corresponding to the generalized corner of the L-hypersurface. For the single-parameter (i.e. L-curve) case, it is shown through a model that the regularization parameters minimizing the MDF essentially maximize the curvature of the L-curve. Furthermore, for both the single-and multiple-parameter cases the MDF approach leads to a simple fixed-point iterative algorithm for computing regularization parameters. Examples indicate that the algorithm converges rapidly thereby making the problem of computing parameters according to the generalized corner of the L-hypersurface computationally tractable.

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“…For instance, in [9] the authors proposed a model to preserve both flat and gray regions in natural images by combining TV with Sobolev smooth penalty. We refer interested readers to [17,15] (imaging), [19] (microarray data analysis), [18] (geodesy) and [13] (machine learning) for other interesting applications.…”

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confidence: 99%

Multi-parameter Tikhonov regularization — An augmented approach

Jin

Takeuchi

2014

Chin. Ann. Math. Ser. B

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Abstract. We study multi-parameter regularization (multiple penalties) for solving linear inverse problems to promote simultaneously distinct features of the sought-for objects. We revisit a balancing principle for choosing regularization parameters from the viewpoint of augmented Tikhonov regularization, and derive a new parameter choice strategy called the balanced discrepancy principle. A priori and a posteriori error estimates are provided to theoretically justify the principles, and numerical algorithms for efficiently implementing the principles are also provided. Numerical results on denoising are presented to illustrate the feasibility of the balanced discrepancy principle.

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Regularized image restoration in multiresolution spaces

Cited by 14 publications

References 12 publications

Multi-parameter Tikhonov regularization

Multi-parameter Tikhonov regularization

Efficient determination of multiple regularization parameters in a generalized L-curve framework

Multi-parameter Tikhonov regularization — An augmented approach

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