A New Augmented Lagrangian Approach for L1-mean Curvature Image Denoising
Myllykoski, M., Glowinski, R., Kärkkäinen, T., & Rossi, T. (2015). A New Augmented Lagrangian Approach for L1-mean Curvature Image Denoising. SIAM Journal on Imaging Sciences, 8(1), 95-125. https://doi.org/10.1137/140962164
Published inSIAM Journal on Imaging Sciences
© 2015 Society for Industrial and Applied Mathematics. Published in this repository with the kind permission of the publisher.
Variational methods are commonly used to solve noise removal problems. In this paper, we present an augmented Lagrangian-based approach that uses a discrete form of the L1-norm of the mean curvature of the graph of the image as a regularizer, discretization being achieved via a finite element method. When a particular alternating direction method of multipliers is applied to the solution of the resulting saddle-point problem, this solution reduces to an iterative sequential solution of four subproblems. These subproblems are solved using Newton’s method, the conjugate gradient method, and a partial solution variant of the cyclic reduction method. The approach considered here differs from existing augmented Lagrangian approaches for the solution of the same problem; indeed, the augmented Lagrangian functional we use here contains three Lagrange multipliers “only,” and the associated augmentation terms are all quadratic. In addition to the description of the solution algorithm, this paper contains the results of numerical experiments demonstrating the performance of the novel method discussed here. ...
PublisherSociety for Industrial and Applied Mathematics
ISSN Search the Publication Forum1936-4954
Publication in research information system
MetadataShow full item record
Showing items with similar title or keywords.
On GPU-accelerated fast direct solvers and their applications in image denoising Myllykoski, Mirko (University of Jyväskylä, 2015)
A GPU-Accelerated Augmented Lagrangian Based L1-mean Curvature Image Denoising Algorithm Implementation Myllykoski, Mirko; Glowinski, Roland; Kärkkäinen, Tommi; Rossi, Tuomo (Union Agency, 2015)This paper presents a graphics processing unit (GPU) implementation of a recently published augmented Lagrangian based L1-mean curvature image denoising algorithm. The algorithm uses a particular alternating direction ...
Analysis of microtomographic images of porous heterogeneous materials Turpeinen, Tuomas (University of Jyväskylä, 2015)In this work, we study the phases of image processing chain of microtomographic imag- ing in order to obtain reliable results while optimizing the time spent on denoising and segmentation. We consider that the decisions ...
Density-Functional Tight-Binding Simulations of Curvature-Controlled Layer Decoupling and Band-Gap Tuning in Bilayer MoS2 Koskinen, Pekka; Fampiou, Ioanna; Ramasubramaniam, Ashwin (American Physical Society, 2014)Monolayer transition-metal dichalcogenides (TMDCs) display valley-selective circular dichroism due to the presence of time-reversal symmetry and the absence of inversion symmetry, making them promising candidates for ...
Image inpainting using directional wavelet packets originating from polynomial splines Averbuch, Amir; Neittaanmäki, Pekka; Zheludev, Valery; Salhov, Moshe; Hauser, Jonathan (Elsevier, 2021)The paper presents a new algorithm for the image inpainting problem. The algorithm uses a recently designed versatile library of quasi-analytic complex-valued wavelet packets (qWPs) which originate from polynomial splines ...