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   https://doi.org/10.21468/SciPostPhysCodeb.19  

   Nogaki, Kosuke; Fei, Jiani; Gull, Emanuel; Shinaoka, Hiroshi (November 2023, SciPost Physics Codebases)

   We introduce a Julia implementation of the recently proposed Nevanlinna analytic continuation method. The method is based on Nevanlinna interpolants and inherently preserves the causality of a response function due to its construction. For theoretical calculations without statistical noise, this continuation method is a powerful tool to extract real-frequency information from numerical input data on the Matsubara axis. This method has been applied to first-principles calculations of correlated materials. This paper presents its efficient and full-featured open-source implementation of the method including the Hamburger moment problem and smoothing. 

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2. Imaging of 3D objects with experimental data using orthogonality sampling methods

   https://doi.org/10.1088/1361-6420/ac3d85  

   Le, Thu; Nguyen, Dinh-Liem; Schmidt, Hayden; Truong, Trung (December 2021, Inverse Problems)

   Abstract This paper is concerned with imaging of 3D scattering objects with experimental data from the Fresnel database. The first goal of the paper is to investigate a modified version of the orthogonality sampling method (OSM) by Harris and Nguyen [2020 SIAM J. Sci. Comput. 42 B72–737] for the imaging problem. The advantage of the modified OSM over its original version lies in its applicability to more types of polarization vectors associated with the electromagnetic scattering data. We analyze the modified OSM using the factorization analysis for the far field operator and the Funk–Hecke formula. The second goal is to verify the performance of the modified OSM, the OSM, and the classical factorization method for the 3D Fresnel database. The modified OSM we propose is able to invert the sparse and limited-aperture real data in a fast, simple, and efficient way. It is also shown in the real data verification that the modified OSM performs better than its original version and the factorization method. 

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3. Variational Surface Reconstruction Using Natural Neighbors

   https://doi.org/10.1145/3731191  

   Xia, Jianjun; Ju, Tao (August 2025, ACM Transactions on Graphics)

   Surface reconstruction from points is a fundamental problem in computer graphics. While numerous methods have been proposed, it remains challenging to reconstruct from sparse and non-uniform point distributions, particularly when normals are absent. We present a robust and scalable method for reconstructing an implicit surface from points without normals. By exploring the locality of natural neighborhoods, we propose local reformulations of a previous global method, known for its ability to surface sparse points but high computational cost, thereby significantly improving its scalability while retaining its robustness. Experiments show that our method achieves comparable speed to existing reconstruction methods on large inputs while producing fewer artifacts in under-sampled regions. 

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4. A new framework of designing iterative techniques for image deblurring

   https://doi.org/10.1016/j.patcog.2021.108463  

   Zhang, Min; Young, Geoffrey S.; Tie, Yanmei; Gu, Xianfeng; Xu, Xiaoyin (April 2022, Pattern Recognition)

   In this work we present a framework of designing iterative techniques for image deblurring in inverse problem. The new framework is based on two observations about existing methods. We used Landweber method as the basis to develop and present the new framework but note that the framework is applicable to other iterative techniques. First, we observed that the iterative steps of Landweber method consist of a constant term, which is a low-pass filtered version of the already blurry observation. We proposed a modification to use the observed image directly. Second, we observed that Landweber method uses an estimate of the true image as the starting point. This estimate, however, does not get updated over iterations. We proposed a modification that updates this estimate as the iterative process progresses. We integrated the two modifications into one framework of iteratively deblurring images. Finally, we tested the new method and compared its performance with several existing techniques, including Landweber method, Van Cittert method, GMRES (generalized minimal residual method), and LSQR (least square), to demonstrate its superior performance in image deblurring. 

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5. EXPLANATION BY PROGRESSIVE EXAGGERATION

   Sumedha Singla, Brian Pollack (January 2020, The International Conference on Learning Representations)

   null (Ed.)

   As machine learning methods see greater adoption and implementation in high-stakes applications such as medical image diagnosis, the need for model interpretability and explanation has become more critical. Classical approaches that assess feature importance (e.g., saliency maps) do not explain how and why a particular region of an image is relevant to the prediction. We propose a method that explains the outcome of a classification black-box by gradually exaggerating the semantic effect of a given class. Given a query input to a classifier, our method produces a progressive set of plausible variations of that query, which gradually changes the posterior probability from its original class to its negation. These counter-factually generated samples preserve features unrelated to the classification decision, such that a user can employ our method as a “tuning knob” to traverse a data manifold while crossing the decision boundary. Our method is model agnostic and only requires the output value and gradient of the predictor with respect to its input. 

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