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SIAM Journal on Imaging Sciences
Journal Prestige (SJR): 1.371

Citation Impact (citeScore): 3
Number of Followers: 7

Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1936-4954
Published by Society for Industrial and Applied Mathematics

[17 journals]

Convergence Results for Primal-Dual Algorithms in the Presence of Adjoint
Mismatch
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  Authors: Emilie Chouzenoux, Andrés Contreras, Jean-Christophe Pesquet, Marion Savanier
  Pages: 1 - 34
  Abstract: SIAM Journal on Imaging Sciences, Volume 16, Issue 1, Page 1-34, March 2023.
  Abstract. Most optimization problems arising in imaging science involve high-dimensional linear operators and their adjoints. In the implementations of these operators, changes may be introduced for various practical considerations (e.g., memory limitation, computational cost, convergence speed), leading to an adjoint mismatch. This occurs for the X-ray tomographic inverse problems found in computed tomography (CT), where a surrogate operator often replaces the adjoint of the measurement operator (called the projector). The resulting adjoint mismatch can jeopardize the convergence properties of iterative schemes used for image recovery. In this paper, we study the theoretical behavior of a panel of primal-dual proximal algorithms, which rely on forward-backward-(forward) splitting schemes when an adjoint mismatch occurs. We analyze these algorithms by focusing on the resolution of possibly nonsmooth convex penalized minimization problems in an infinite-dimensional setting. Using tools from fixed point theory, we show that they can solve monotone inclusions beyond minimization problems. Such findings indicate that these algorithms can be seen as a generalization of classical primal-dual formulations. The applicability of our findings is also demonstrated through two numerical experiments in the context of CT image reconstruction.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2023-01-19T08:00:00Z
  DOI: 10.1137/22M1490223
  Issue No: Vol. 16, No. 1 (2023)
Convexification Numerical Method for a Coefficient Inverse Problem for the
Radiative Transport Equation
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  Authors: Michael V. Klibanov, Jingzhi Li, Loc H. Nguyen, Zhipeng Yang
  Pages: 35 - 63
  Abstract: SIAM Journal on Imaging Sciences, Volume 16, Issue 1, Page 35-63, March 2023.
  Abstract. An [math]-D coefficient inverse problem for the stationary radiative transport equation is considered for the first time. A globally convergent so-called convexification numerical method is developed and its convergence analysis is provided. The analysis is based on a Carleman estimate. Extensive numerical studies in the two-dimensional case are presented.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2023-01-19T08:00:00Z
  DOI: 10.1137/22M1509837
  Issue No: Vol. 16, No. 1 (2023)
Asymptotic Links between Signal Processing, Acoustic Metamaterials, and
Biology
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  Authors: Habib Ammari, Bryn Davies
  Pages: 64 - 88
  Abstract: SIAM Journal on Imaging Sciences, Volume 16, Issue 1, Page 64-88, March 2023.
  Abstract. Biomimicry is a powerful science that takes inspiration from nature’s innovative solutions to challenging problems. In this work, we use asymptotic methods to develop the mathematical foundations for the exchange of design inspiration and features between biological hearing systems, signal processing algorithms, and acoustic metamaterials. Our starting point is a concise asymptotic analysis of high-contrast acoustic metamaterials. We are able to fine tune this graded structure to mimic the biomechanical properties of the cochlea, at the same scale. We then turn our attention to developing a biomimetic signal processing algorithm. We use the response of the cochlea-like metamaterial as an initial filtering layer and then add additional biomimetic processing stages, designed to mimic the human auditory system’s ability to recognize the global properties of natural sounds. This demonstrates the three-way exchange of ideas that, thanks to our analysis, is possible between signal processing, metamaterials and biology.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2023-01-24T08:00:00Z
  DOI: 10.1137/22M1510352
  Issue No: Vol. 16, No. 1 (2023)
Utilizing Variational Autoencoders in the Bayesian Inverse Problem of
Photoacoustic Tomography
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  Authors: Teemu Sahlström, Tanja Tarvainen
  Pages: 89 - 110
  Abstract: SIAM Journal on Imaging Sciences, Volume 16, Issue 1, Page 89-110, March 2023.
  Abstract. There has been an increasing interest in utilizing machine learning methods in inverse problems and imaging. Most of the work has, however, concentrated on image reconstruction problems, and the number of studies regarding the full solution of the inverse problem is limited. In this work, we study a machine learning–based approach for the Bayesian inverse problem of photoacoustic tomography. We develop an approach for estimating the posterior distribution in photoacoustic tomography using an approach based on the variational autoencoder. The approach is evaluated with numerical simulations and compared to the solution of the inverse problem using a Bayesian approach.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2023-01-24T08:00:00Z
  DOI: 10.1137/22M1489897
  Issue No: Vol. 16, No. 1 (2023)
High-Frequency Limit of the Inverse Scattering Problem: Asymptotic
Convergence from Inverse Helmholtz to Inverse Liouville
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  Authors: Shi Chen, Zhiyan Ding, Qin Li, Leonardo Zepeda-Núñez
  Pages: 111 - 143
  Abstract: SIAM Journal on Imaging Sciences, Volume 16, Issue 1, Page 111-143, March 2023.
  Abstract. We investigate the asymptotic relation between the inverse problems relying on the Helmholtz equation and the radiative transfer equation (RTE) as physical models in the high-frequency limit. In particular, we evaluate the asymptotic convergence of a generalized version of the inverse scattering problem based on the Helmholtz equation, to the inverse scattering problem of the Liouville equation (a simplified version of RTE). The two inverse problems are connected through the Wigner transform that translates the wave-type description on the physical space to the kinetic-type description on the phase space, and the Husimi transform that models data localized both in location and direction. The finding suggests that impinging tightly concentrated monochromatic beams can indeed provide stable reconstruction of the medium, asymptotically in the high-frequency regime. This fact stands in contrast with the unstable reconstruction for the classical inverse scattering problem when the probing signals are plane waves.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2023-01-27T08:00:00Z
  DOI: 10.1137/22M147075X
  Issue No: Vol. 16, No. 1 (2023)
Gaussian Patch Mixture Model Guided Low-Rank Covariance Matrix
Minimization for Image Denoising
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  Authors: Jing Guo, Yu Guo, Qiyu Jin, Michael Kwok-Po Ng, Shuping Wang
  Pages: 1601 - 1622
  Abstract: SIAM Journal on Imaging Sciences, Volume 15, Issue 4, Page 1601-1622, December 2022.
  Image denoising is one of the most important tasks in image processing. In this paper, we study image denoising methods by using similar patches which have low-rank covariance matrices to recover an underlying image which is corrupted by additive Gaussian noise. In order to enhance global patch-matching results, we make use of a Gaussian mixture model with an auxiliary image to determine different groups of patches. The auxiliary image is an output of BM3D. The noisy version of covariance matrix is formed by each group of patches from the given noisy image. Its low-rank version can be estimated by using covariance matrix nuclear norm minimization, and the resulting denoised image can be obtained. Experimental results are reported to show that the proposed method outperforms the state-of-the-art denoising methods, including testing deep learning methods, in the peak signal-to-noise ratio, structural similarity values, and visual quality.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2022-10-06T07:00:00Z
  DOI: 10.1137/21M1454262
  Issue No: Vol. 15, No. 4 (2022)
Image Warp Preserving Content Intensity
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  Authors: Enrico Segre
  Pages: 1623 - 1645
  Abstract: SIAM Journal on Imaging Sciences, Volume 15, Issue 4, Page 1623-1645, December 2022.
  An accurate method for warping images is presented. Different from most commonly used techniques, this method guarantees the conservation of the intensity of the transformed image, evaluated as the sum of its pixel values over the whole image or over corresponding transformed subregions of it. Such property is mandatory for quantitative analysis, as, for instance, when deformed images are used to assess radiances, to measure optical fluxes from light sources, or to characterize material optical densities. The proposed method enforces area resampling by decomposing each rectangular pixel into two triangles, and projecting the pixel intensity onto half pixels of the transformed image, with weights proportional to the area of overlap of the triangular half-pixels. The result is quantitatively exact, as long as the original pixel value is assumed to represent a constant image density within the pixel area, and as long as the coordinate transformation is diffeomorphic. Implementation details and possible variations of the method are discussed.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2022-10-06T07:00:00Z
  DOI: 10.1137/21M1452688
  Issue No: Vol. 15, No. 4 (2022)
Optimality Conditions for Bilevel Imaging Learning Problems with Total
Variation Regularization
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  Authors: Juan Carlos De los Reyes, David Villacís
  Pages: 1646 - 1689
  Abstract: SIAM Journal on Imaging Sciences, Volume 15, Issue 4, Page 1646-1689, December 2022.
  We address the problem of optimal scale-dependent parameter learning in total variation image denoising. Such problems are formulated as bilevel optimization instances with total variation denoising problems as lower-level constraints. For the bilevel problem, we are able to derive M-stationarity conditions, after characterizing the corresponding Mordukhovich generalized normal cone and verifying suitable constraint qualification conditions. We also derive B-stationarity conditions, after investigating the Lipschitz continuity and directional differentiability of the lower-level solution operator. A characterization of the Bouligand subdifferential of the solution mapping, by means of a properly defined linear system, is provided as well. Based on this characterization, we propose a two-phase nonsmooth trust-region algorithm for the numerical solution of the bilevel problem and test it computationally for two particular experimental settings.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2022-10-10T07:00:00Z
  DOI: 10.1137/21M143412X
  Issue No: Vol. 15, No. 4 (2022)
Bilevel Training Schemes in Imaging for Total Variation--Type Functionals
with Convex Integrands
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  Authors: Valerio Pagliari, Kostas Papafitsoros, Bogdan Raib̧tă, Andreas Vikelis
  Pages: 1690 - 1728
  Abstract: SIAM Journal on Imaging Sciences, Volume 15, Issue 4, Page 1690-1728, December 2022.
  In the context of image processing, we study a class of integral regularizers defined in terms of spatially inhomogeneous integrands that depend on general linear differential operators. Particularly, the spatial dependence is assumed to be only measurable. The setting is made rigorous by means of the theory of Radon measures and of suitable function spaces modeled on functions of bounded variation. We prove the lower semicontinuity of the functionals at stake and existence of minimizers for the corresponding variational problems. Then, we embed the latter into a bilevel scheme in order to automatically compute the regularization parameters. These parameters are considered to be spatially varying, thus allowing for good flexibility and preservation of details in the reconstructed image. After identifying a series of spatially inhomogeneous regularization functionals commonly used in image processing that are included in our framework, we substantiate its feasibility by performing numerical denoising examples in which the spatial dependence of the integrand is measurable. Specifically, we use Huber versions of the first and second order total variation (and their sum) with both the Huber and the regularization parameter being spatially varying. Notably, the spatially varying version of second order total variation produces high quality reconstructions when compared to regularizations of similar type, and the introduction of the low regularity spatially dependent Huber parameter leads to a further enhancement of the image details. We expect that our theoretical investigations and our numerical feasibility study will support future work on setting up schemes where general differential operators with spatially dependent coefficients will also be part of the optimization scheme.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2022-10-10T07:00:00Z
  DOI: 10.1137/21M1467328
  Issue No: Vol. 15, No. 4 (2022)
Deep Learning--Based Dictionary Learning and Tomographic Image
Reconstruction
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  Authors: Jevgenija Rudzusika, Thomas Koehler, Ozan Oktem
  Pages: 1729 - 1764
  Abstract: SIAM Journal on Imaging Sciences, Volume 15, Issue 4, Page 1729-1764, December 2022.
  This work presents an approach for image reconstruction in clinical low-dose tomography that combines principles from sparse signal processing with ideas from deep learning. First, we describe sparse signal representation in terms of dictionaries from a statistical perspective and interpret dictionary learning as a process of aligning the distribution that arises from a generative model with the empirical distribution of true signals. As a result, we can see that sparse coding with learned dictionaries resembles a specific variational autoencoder, where the encoder is a sparse coding algorithm and the decoder is a linear function. Next, we show that dictionary learning can also benefit from computational advancements introduced in the context of deep learning, such as parallelism and stochastic optimization. Finally, we show that regularization by dictionaries achieves competitive performance in computed tomography reconstruction compared to state-of-the-art model-based and data-driven approaches, while being unsupervised with respect to tomographic data.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2022-10-13T07:00:00Z
  DOI: 10.1137/21M1445697
  Issue No: Vol. 15, No. 4 (2022)
Parallelizable Global Quasi-Conformal Parameterization of Multiply
Connected Surfaces via Partial Welding
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  Authors: Zhipeng Zhu, Gary P. T. Choi, Lok Ming Lui
  Pages: 1765 - 1807
  Abstract: SIAM Journal on Imaging Sciences, Volume 15, Issue 4, Page 1765-1807, December 2022.
  Conformal and quasi-conformal mappings have widespread applications in imaging science, computer vision, and computer graphics and can be used in surface registration, segmentation, remeshing, and texture map compression. While various conformal and quasi-conformal parameterization methods for simply connected surfaces have been proposed, efficient parameterization algorithms for multiply connected surfaces have been less explored. In this paper, we propose a novel parallelizable algorithm for computing the global conformal and quasi-conformal parameterizations of multiply connected surfaces onto a 2D circular domain using variants of the partial welding method and the Koebe's iteration. The main idea is to first partition a multiply connected surface into several subdomains and compute the free-boundary conformal and quasi-conformal parameterizations of them, respectively, and then apply a variant of the partial welding algorithm to reconstruct the global mapping. We apply the Koebe's iteration, together with the geodesic algorithm, to the boundary points and welding paths before and after the global welding to transform all the boundaries into circles conformally. After getting all the updated boundary conditions, we obtain the global parameterization of the multiply connected surface by solving the Laplace equation for each subdomain. Using this divide-and-conquer approach, the global conformal and quasi-conformal parameterizations of surfaces can be efficiently computed. Experimental results are presented to demonstrate the effectiveness of our proposed algorithm. More broadly, the proposed shift in perspective from solving a global quasi-conformal mapping problem to solving multiple local mapping problems paves a new way for computational quasi-conformal geometry.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2022-10-27T07:00:00Z
  DOI: 10.1137/21M1466323
  Issue No: Vol. 15, No. 4 (2022)
An Algorithm to Compute Any Simple $k$-gon of a Maximum Area or Perimeter
Inscribed in a Region of Interest
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  Authors: Rubén Molano, Mar Ávila, José Carlos Sancho, Pablo G. Rodríguez, Andres Caro
  Pages: 1808 - 1832
  Abstract: SIAM Journal on Imaging Sciences, Volume 15, Issue 4, Page 1808-1832, December 2022.
  Computational and mathematical models are research subjects for solving engineering, computer science, and computer vision problems. Image preprocessing usually needs to efficiently compute polygons related to some previously delimited region of interest. Most of the solved problems are limited to the search for some type of polygon with $k$ sides (triangles, rectangles, squares, etc.) with maximum area, maximum perimeter, or similar. This paper presents a generic algorithm that computes in $O(n^5 k)$ computational time the polygon of any number of sides (any simple $k$-gon) inscribed in a region of interest (in any closed contour without restrictions). The polygon obtained fulfills the requirements specified by the user: maximum area or perimeter or minimum area or perimeter. No previous work has been proposed to obtain any $k$-gon inscribed in any unconstrained contour. The algorithms and mathematical models are presented and explained, and the source code is available in a GitHub repository for research purposes.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2022-11-14T08:00:00Z
  DOI: 10.1137/22M1482676
  Issue No: Vol. 15, No. 4 (2022)
Bioinspired Random Projections for Robust, Sparse Classification
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  Authors: Nina Dekoninck Bruhin, Bryn Davies
  Pages: 1833 - 1850
  Abstract: SIAM Journal on Imaging Sciences, Volume 15, Issue 4, Page 1833-1850, December 2022.
  Inspired by the use of random projections in biological sensing systems, we present a new algorithm for processing data in classification problems. This is based on observations of the human brain and the fruit fly's olfactory system and involves randomly projecting data into a space of greatly increased dimension before applying a cap operation to truncate the smaller entries. This leads to a simple algorithm that is very computationally efficient and can be used to either give a sparse representation with minimal loss in classification accuracy or give improved robustness, in the sense that classification accuracy is improved when noise is added to the data. This is demonstrated with numerical experiments, which supplement theoretical results demonstrating that the resulting signal transform is continuous and invertible, in an appropriate sense.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2022-11-14T08:00:00Z
  DOI: 10.1137/22M1503579
  Issue No: Vol. 15, No. 4 (2022)
Harmonic Beltrami Signature: A Novel 2D Shape Representation for Object
Classification
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  Authors: Chenran Lin, Lok Ming Lui
  Pages: 1851 - 1893
  Abstract: SIAM Journal on Imaging Sciences, Volume 15, Issue 4, Page 1851-1893, December 2022.
  There has been a growing interest in shape analysis in recent years. We present a novel shape signature for 2D Jordan domains. The proposed signature is based on Sharon's conformal welding signature [E. Sharon and D. Mumford, Internat. J. Comput. Vis., 70 (2006), pp. 55--75], which is one of the main building blocks of our proposed shape signature. The conformal welding signature is a well-known shape signature used to represent 2D shapes. Nevertheless, it is not invariant under rotation. It is also sensitive to the choice of particular feature points and shape perturbations. Motivated by this, we propose in this paper an invariant shape signature under rigid transformations and scaling. The proposed signature does not require the delineation of feature points and is robust under shape perturbations. More specifically, the proposed signature is a Beltrami coefficient of the harmonic extension of the conformal welding. We show that there is a one-to-one correspondence between a quotient space of Beltrami coefficients and the space of 2D Jordan domains up to a translation, rotation, and scaling. With a suitable normalization, each equivalence class in the quotient space is associated with a unique representative named the Harmonic Beltrami Signature (HBS). As such, each shape is associated with a unique HBS. Conversely, the associated shape of an HBS can be reconstructed based on quasiconformal Teichmüller theories, which are uniquely determined up to a translation, rotation, and scaling. The HBS is thus an effective fingerprint to represent a 2D shape. The robustness of the HBS is studied both theoretically and experimentally. With the HBS, simple metrics, such as $L^2$, can measure geometric dissimilarity between shapes. Experiments have been carried out to classify shapes into different classes using HBS. Results show good classification performance, which demonstrates the efficacy of our proposed shape signature.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2022-11-15T08:00:00Z
  DOI: 10.1137/22M1470852
  Issue No: Vol. 15, No. 4 (2022)
Single Pixel X-ray Transform and Related Inverse Problems
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  Authors: Ru-Yu Lai, Gunther Uhlmann, Jian Zhai, Hanming Zhou
  Pages: 1894 - 1909
  Abstract: SIAM Journal on Imaging Sciences, Volume 15, Issue 4, Page 1894-1909, December 2022.
  In this paper, we analyze the nonlinear single pixel X-ray transform $K$ and study the reconstruction of $f$ from the measurement $Kf$. Different from the well-known X-ray transform, the transform $K$ is a nonlinear operator and uses a single detector that integrates all rays in the space. We derive stability estimates and an inversion of the linearization at zero. We also consider the case where we integrate along geodesics of a Riemannian metric. Moreover, we conduct several numerical experiments to corroborate the theoretical results.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2022-11-21T08:00:00Z
  DOI: 10.1137/21M1468103
  Issue No: Vol. 15, No. 4 (2022)
Recovery of Piecewise Smooth Density and Lamé Parameters from High
Frequency Exterior Cauchy Data
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  Authors: Sombuddha Bhattacharyya, Maarten V. de Hoop, Vitaly Katsnelson, Gunther Uhlmann
  Pages: 1910 - 1943
  Abstract: SIAM Journal on Imaging Sciences, Volume 15, Issue 4, Page 1910-1943, December 2022.
  We consider an isotropic elastic medium occupying a bounded domain $\Omega \subset {\mathbb R}^3$ whose density and Lamé parameters are piecewise smooth. In the elastic wave initial value inverse problem, we are given the solution operator for the elastic wave equation, but only outside $\Omega$ and only for initial data supported outside $\Omega$, and we study the recovery of the density and Lamé parameters. For known density, results have recently been obtained using the scattering control method to recover wave speeds. Here, we extend this result to include the recovery of the density in addition to the Lamé parameters under certain geometric conditions using techniques from microlocal analysis and a connection to local tensor tomography.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2022-11-21T08:00:00Z
  DOI: 10.1137/22M1480951
  Issue No: Vol. 15, No. 4 (2022)
A Quantum Information-Based Refoundation of Color Perception Concepts
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  Authors: Michel Berthier, Nicoletta Prencipe, Edoardo Provenzi
  Pages: 1944 - 1976
  Abstract: SIAM Journal on Imaging Sciences, Volume 15, Issue 4, Page 1944-1976, December 2022.
  In this paper we deal with the problem of overcoming the intuitive definition of several color perception attributes by replacing them with novel mathematically rigorous ones. Our framework is a quantum-like color perception theory recently developed, which constitutes a radical change of view with respect to the classical Commission Interntional de l'Éclairage models and their color appearance counterparts. We show how quantum information concepts, (e.g., effects, generalized states, postmeasurement transformations, and relative entropy) provide tools that seem to be perfectly fit to model color perception attributes such as brightness, lightness, colorfulness, chroma, saturation, and hue. An illustration of the efficiency of these novel definitions is provided by the rigorous derivation of the so-called lightness constancy phenomenon.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2022-11-21T08:00:00Z
  DOI: 10.1137/22M1476071
  Issue No: Vol. 15, No. 4 (2022)
Convergence Results in Image Interpolation With the Continuous SSIM
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  Authors: Francesco Marchetti, Gabriele Santin
  Pages: 1977 - 1999
  Abstract: SIAM Journal on Imaging Sciences, Volume 15, Issue 4, Page 1977-1999, December 2022.
  Assessing the similarity of two images is a complex task that attracts significant efforts in the image processing community. The widely used structural similarity index measure (SSIM) addresses this problem by quantifying a perceptual structural similarity. In this paper we consider a recently introduced continuous SSIM (cSSIM), which allows one to analyze sequences of images of increasingly fine resolutions, and further extend the definition of the index to encompass the locally weighted version that is used in practice. For both the local and the global versions, we prove that the continuous index includes the classical SSIM as a special case, and we provide a precise connection between image similarity measured by the cSSIM and by the $L_2$ norm. Using this connection, we derive bounds on the cSSIM by means of bounds on the $L_2$ error, and we even prove that the two error measures are equivalent in certain circumstances. We exploit these results to obtain precise rates of convergence with respect to the cSSIM for several concrete image interpolation methods, and we further validate these findings by different numerical experiments. This newly established connection paves the way to obtain novel insights into the features and limitations of the SSIM, including on the effect of the local weighted window on the index performances.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2022-11-21T08:00:00Z
  DOI: 10.1137/22M147637X
  Issue No: Vol. 15, No. 4 (2022)
Adaptive and Implicit Regularization for Matrix Completion
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  Authors: Zhemin Li, Tao Sun, Hongxia Wang, Bao Wang
  Pages: 2000 - 2022
  Abstract: SIAM Journal on Imaging Sciences, Volume 15, Issue 4, Page 2000-2022, December 2022.
  The explicit low-rank regularization, e.g., nuclear norm regularization, has been widely used in imaging sciences. However, it has been found that implicit regularization outperforms explicit ones in various image processing tasks. Another issue is that the fixed explicit regularization limits the applicability to broad images since different images favor different features captured by different explicit regularizations. As such, this paper proposes a new adaptive and implicit low-rank regularization that captures the low-rank prior dynamically from the training data. The core of our new adaptive and implicit low-rank regularization is parameterizing the Laplacian matrix in the Dirichlet energy-based regularization, which we call the adaptive and implicit regularization (AIR). Theoretically, we show that the adaptive regularization of AIR enhances the implicit regularization and vanishes at the end of training. We validate AIR's effectiveness on various benchmark tasks, indicating that the AIR is particularly favorable for the scenarios when the missing entries are nonuniform. The code can be found at https://github.com/lizhemin15/AIR-Net.
  Citation: SIAM Journal on Imaging Sciences
  PubDate: 2022-11-22T08:00:00Z
  DOI: 10.1137/22M1489228
  Issue No: Vol. 15, No. 4 (2022)