• Title, Summary, Keyword: total variation regularization

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Regularization Parameter Selection for Total Variation Model Based on Local Spectral Response

  • Zheng, Yuhui;Ma, Kai;Yu, Qiqiong;Zhang, Jianwei;Wang, Jin
    • Journal of Information Processing Systems
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    • v.13 no.5
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    • pp.1168-1182
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    • 2017
  • In the past decades, various image regularization methods have been introduced. Among them, total variation model has drawn much attention for the reason of its low computational complexity and well-understood mathematical behavior. However, regularization parameter estimation of total variation model is still an open problem. To deal with this problem, a novel adaptive regularization parameter selection scheme is proposed in this paper, by means of using the local spectral response, which has the capability of locally selecting the regularization parameters in a content-aware way and therefore adaptively adjusting the weights between the two terms of the total variation model. Experiment results on simulated and real noisy image show the good performance of our proposed method, in visual improvement and peak signal to noise ratio value.

Performance Comparison of Regularization Methods in Electrical Resistance Tomography (전기 저항 단층촬영법에서의 조정기법 성능비교)

  • Kang, Suk-In;Kim, Kyung-Youn
    • Journal of IKEEE
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    • v.20 no.3
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    • pp.226-234
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    • 2016
  • Electrical resistance tomography (ERT) is an imaging technique where the internal resistivity distribution inside an object is reconstructed. The ERT image reconstruction is a highly nonlinear ill-posed problem, so regularization methods are used to achieve desired image. The reconstruction outcome is dependent on the type of regularization method employed such as l2-norm, l1-norm, and total variation regularization method. That is, use of an appropriate regularization method considering the flow characteristics is necessary to attain good reconstruction performance. Therefore, in this paper, regularization methods are tested through numerical simulations with different flow conditions and the performance is compared.

FIXED-POINT-LIKE METHOD FOR A NEW TOTAL VARIATION-BASED IMAGE RESTORATION MODEL

  • WON, YU JIN;YUN, JAE HEON
    • Journal of applied mathematics & informatics
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    • v.38 no.5_6
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    • pp.519-532
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    • 2020
  • In this paper, we first propose a new total variation-based regularization model for image restoration. We next propose a fixed-point-like method for solving the new image restoration model, and then we provide convergence analysis for the fixed-point-like method. To evaluate the feasibility and efficiency of the fixed-point-like method for the new proposed total variation-based regularization model, we provide numerical experiments for several test problems.

Resistivity Image Reconstruction Using Interacting Dual-Mode Regularization (상호작용 이중-모드 조정방법을 이용한 저항률 영상 복원)

  • Kang, Suk-In;Kim, Kyung-Youn
    • Journal of IKEEE
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    • v.20 no.2
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    • pp.152-162
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    • 2016
  • Electrical resistivity tomography (ERT) is a technique to reconstruct the internal resistivity distribution using the measured voltages on the surface electrodes. ERT inverse problem suffers from ill-posedness nature, so regularization methods are used to mitigate ill-posedness. The reconstruction performance varies depending on the type of regularization method. In this paper, an interacting dual-mode regularization method is proposed with two different regularization methods, L1-norm regularization and total variation (TV) regularization, to achieve robust reconstruction performance. The interacting dual-mode regularization method selects the suitable regularization method and combines the regularization methods based on computed mode probabilities depending on the actual conditions. The proposed method is tested with numerical simulations and the results demonstrate an improved reconstruction performance.

MULTIGRID METHOD FOR TOTAL VARIATION IMAGE DENOISING

  • HAN, MUN S.;LEE, JUN S.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.6 no.2
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    • pp.9-24
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    • 2002
  • Total Variation(TV) regularization method is effective for reconstructing "blocky", discontinuous images from contaminated image with noise. But TV is represented by highly nonlinear integro-differential equation that is hard to solve. There have been much effort to obtain stable and fast methods. C. Vogel introduced "the Fixed Point Lagged Diffusivity Iteration", which solves the nonlinear equation by linearizing. In this paper, we apply multigrid(MG) method for cell centered finite difference (CCFD) to solve system arise at each step of this fixed point iteration. In numerical simulation, we test various images varying noises and regularization parameter $\alpha$ and smoothness $\beta$ which appear in TV method. Numerical tests show that the parameter ${\beta}$ does not affect the solution if it is sufficiently small. We compute optimal $\alpha$ that minimizes the error with respect to $L^2$ norm and $H^1$ norm and compare reconstructed images.

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Sparse-View CT Image Recovery Using Two-Step Iterative Shrinkage-Thresholding Algorithm

  • Chae, Byung Gyu;Lee, Sooyeul
    • ETRI Journal
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    • v.37 no.6
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    • pp.1251-1258
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    • 2015
  • We investigate an image recovery method for sparse-view computed tomography (CT) using an iterative shrinkage algorithm based on a second-order approach. The two-step iterative shrinkage-thresholding (TwIST) algorithm including a total variation regularization technique is elucidated to be more robust than other first-order methods; it enables a perfect restoration of an original image even if given only a few projection views of a parallel-beam geometry. We find that the incoherency of a projection system matrix in CT geometry sufficiently satisfies the exact reconstruction principle even when the matrix itself has a large condition number. Image reconstruction from fan-beam CT can be well carried out, but the retrieval performance is very low when compared to a parallel-beam geometry. This is considered to be due to the matrix complexity of the projection geometry. We also evaluate the image retrieval performance of the TwIST algorithm -sing measured projection data.

Compressive Sensing Recovery of Natural Images Using Smooth Residual Error Regularization (평활 잔차 오류 정규화를 통한 자연 영상의 압축센싱 복원)

  • Trinh, Chien Van;Dinh, Khanh Quoc;Nguyen, Viet Anh;Park, Younghyeon;Jeon, Byeungwoo
    • Journal of the Institute of Electronics and Information Engineers
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    • v.51 no.6
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    • pp.209-220
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    • 2014
  • Compressive Sensing (CS) is a new signal acquisition paradigm which enables sampling under Nyquist rate for a special kind of signal called sparse signal. There are plenty of CS recovery methods but their performance are still challenging, especially at a low sub-rate. For CS recovery of natural images, regularizations exploiting some prior information can be used in order to enhance CS performance. In this context, this paper addresses improving quality of reconstructed natural images based on Dantzig selector and smooth filters (i.e., Gaussian filter and nonlocal means filter) to generate a new regularization called smooth residual error regularization. Moreover, total variation has been proved for its success in preserving edge objects and boundary of reconstructed images. Therefore, effectiveness of the proposed regularization is verified by experimenting it using augmented Lagrangian total variation minimization. This framework is considered as a new CS recovery seeking smoothness in residual images. Experimental results demonstrate significant improvement of the proposed framework over some other CS recoveries both in subjective and objective qualities. In the best case, our algorithm gains up to 9.14 dB compared with the CS recovery using Bayesian framework.

Multi-Frame Super-Resolution of High Frequency with Spatially Weighted Bilateral Total Variance Regularization

  • Lee, Oh-Young;Park, Sae-Jin;Kim, Jae-Woo;Kim, Jong-Ok
    • IEIE Transactions on Smart Processing and Computing
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    • v.3 no.5
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    • pp.271-274
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    • 2014
  • Bayesian based Multi-Frame Super-Resolution (MF-SR) has been used as a popular and effective SR model. On the other hand, the texture region is not reconstructed sufficiently because it works on the spatial domain. In this study, the MF-SR method was extended to operate on the frequency domain to improve HF information as much as possible. For this, a spatially weighted bilateral total variation model was proposed as a regularization term for a Bayesian estimation. The experimental results showed that the proposed method can recover the texture region more realistically with reduced noise, compared to conventional methods.

Spatio-Temporal Video De-interlacing Algorithm Based on MAP Estimation (MAP 예측기 기반의 시공간 동영상 순차주사화 알고리즘)

  • Lee, Ho-Taek;Song, Byung-Cheol
    • Journal of the Institute of Electronics Engineers of Korea SP
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    • v.49 no.2
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    • pp.69-75
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    • 2012
  • This paper presents a novel de-interlacing algorithm that can make up motion compensation errors by using maximum a posteriori (MAP) estimator. First, a proper registration is performed between a current field and its adjacent fields, and the progressive frame corresponding to the current field is found via MAP estimator based on the computed registration information. Here, in order to obtain a stable solution, well-known bilateral total variation (BTV)-based regularization is employed. Next, so-called feathering artifacts are detected on a block basis effectively. So, edge-directional interpolation is applied to the pixels where feathering artifact may happen, instead of the above-mentioned temporal de-interlacing. Experimental results show that the PSNR of the proposed algorithm is on average 4dB higher than that of previous studies and provides the better subjective quality than the previous works.

Regularized Multichannel Blind Deconvolution Using Alternating Minimization

  • James, Soniya;Maik, Vivek;Karibassappa, K.;Paik, Joonki
    • IEIE Transactions on Smart Processing and Computing
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    • v.4 no.6
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    • pp.413-421
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    • 2015
  • Regularized Blind Deconvolution is a problem applicable in degraded images in order to bring the original image out of blur. Multichannel blind Deconvolution considered as an optimization problem. Each step in the optimization is considered as variable splitting problem using an algorithm called Alternating Minimization Algorithm. Each Step in the Variable splitting undergoes Augmented Lagrangian method (ALM) / Bregman Iterative method. Regularization is used where an ill posed problem converted into a well posed problem. Two well known regularizers are Tikhonov class and Total Variation (TV) / L2 model. TV can be isotropic and anisotropic, where isotropic for L2 norm and anisotropic for L1 norm. Based on many probabilistic model and Fourier Transforms Image deblurring can be solved. Here in this paper to improve the performance, we have used an adaptive regularization filtering and isotropic TV model Lp norm. Image deblurring is applicable in the areas such as medical image sensing, astrophotography, traffic signal monitoring, remote sensors, case investigation and even images that are taken using a digital camera / mobile cameras.