A new variant of L-curve for Tikhonov regularization

Rezghi, Mansoor; Hosseini, Seyed Mohammad

doi:10.1016/j.cam.2009.05.016

Cited by 77 publications

(28 citation statements)

References 9 publications

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“…This approach leads to a constrained optimization problem and its efficiency is dependent on tuning some parameters manually. To overcome these limitations, here, we introduce a geometrical view point to solve this problem based on L-curve method (Hansen, 2001;Rezghi & Hosseini, 2009). This new approach leads to an unconstrained optimization and does not need any manual tuning.…”

Section: L-curve Methods To Adjust Watermark Strength Factormentioning

confidence: 99%

A novel robust scaling image watermarking scheme based on Gaussian Mixture Model

Amirmazlaghani

Rezghi

Amindavar

2015

Expert Systems with Applications

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Section: L-curve Methods To Adjust Watermark Strength Factormentioning

confidence: 99%

A novel robust scaling image watermarking scheme based on Gaussian Mixture Model

Amirmazlaghani

Rezghi

Amindavar

2015

Expert Systems with Applications

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“…It represents a canonical example of a linear discrete ill-posed problem whose meaningful solution can be obtained by replacing the "original" linear system (18) and (19) by a nearby system that is less sensitive to perturbations of the right-hand side of the system, and considers the solution of this new system as a good approximation of the original one. This operation is known as regularization and can be performed using truncated singular value decomposition (TSVD) [30], Tikhonov regularization [31], maximum entropy principle [32]. TSVD practically consists in decomposing the matrix B with SVD and truncating (putting to zeros) the small singular values, in such a way that they do not dominate the solution leading to spurious oscillations.…”

Section: Generation Ofmentioning

confidence: 99%

“…for a suitable value of the regularization parameter α, which can effectively be found using (for instance) L-curve method [31]. The goal of L-curve is to search for a regularization parameter α for which the solution has an optimal balance between the minimization of residual norm…”

Section: Generation Ofmentioning

confidence: 99%

Generation of Earth’s Surface Three-Dimensional (3-D) Displacement Time-Series by Multiple-Platform SAR Data

Pepe¹

2018

Time Series Analysis and Applications

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In this chapter, the recent advancements of differential synthetic aperture radar interferometry (DInSAR) technique are presented, with the focus on the DInSAR-based approaches leading to the generation of three-dimensional time-series of Earth's surface deformation, based on the combination of multi-platform line-of-sight (LOS)-projected time-series of deformation. Use of pixel-offset (PO) measurements for the retrieval of North-South deformation components, which are difficult to be extracted from DInSAR data, only, is also discussed. A review of the principal techniques based on the exploitation of amplitude and phase signatures of sequences of SAR images will be first provided, by emphasizing the limitations and strength of each single approach. Then, the interest will be concentrated on the recently proposed multi-track InSAR combination algorithm, referred as minimum acceleration InSAR combination (MinA) approach. The algorithm assumes the availability of two (or more) sets of SAR images acquired from complementary tracks. SAR data are pre-processed through one of currently available multi-temporal DInSAR toolboxes, and the LOS-projected surface deformation timeseries are computed. An under-determined system of linear equations is then solved, based on imposing that the 3-D displacement time-series have minimum acceleration (MA). The presented results demonstrate the validity of the MinA algorithm.

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“…Most researches based on L-curve focus on three aspects: one is some intuitive analysis or theoretical justification for the curve [13][14]; one is how to compute the global corner or its nearby points automatically to select the proper regularization parameter [15][16][17][18][19]; and the last is about some variants of Lcurve to determine a proper regularization parameter in a new angle [20][21].…”

Section: Introductionmentioning

confidence: 99%

A modified L-curve method for choosing regularization parameter in electrical resistance tomography

Yang

Dong

2015

2015 IEEE International Conference on Imaging Systems and Techniques (IST)

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Regularization methods are widely used in dealing with the ill-posed inverse problem of electrical resistance tomography (ERT), especially the Tikhonov method. A proper choice of regularization parameter is crucial to produce an efficient regularization solution. As a regularization parameter choice method, L-curve method is popular for its simpleness and intuition. However there is no guarantee that the method can always determine a proper parameter for all situations of ERT. The investigation on those failed situations shows that a new corner point often appears on the curve and the parameter corresponding to the new corner point can obtain a better solution than the one corresponding to the traditional global corner point. Therefore a modified L-curve method is proposed based on the new corner point. Moreover two strategies are provided to implement the modified method: one computes the new corner point by means of the second-order differential of Lcurve, and another computes the new corner point with the help of the curvature of L-curve. The modified L-curve method is verified by numerical simulations of some typical distributions in ERT. And the results indicate that the modified method can achieve an efficient solution and implement the image reconstruction where the traditional L-curve method cannot. The modified L-curve method extends the application of L-curve in the field of choosing regularization parameter and can also be applied in other kinds of tomography.

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A new variant of L-curve for Tikhonov regularization

Cited by 77 publications

References 9 publications

A novel robust scaling image watermarking scheme based on Gaussian Mixture Model

A novel robust scaling image watermarking scheme based on Gaussian Mixture Model

Generation of Earth’s Surface Three-Dimensional (3-D) Displacement Time-Series by Multiple-Platform SAR Data

A modified L-curve method for choosing regularization parameter in electrical resistance tomography

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