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This paper proposes a novel parameter selection strategy for kernel-based gradient descent (KGD) algorithms, integrating bias-variance analysis with the splitting method. We introduce the concept of empirical effective dimension to quantify…

Machine Learning · Statistics 2026-03-05 Xiaotong Liu , Yunwen Lei , Xiangyu Chang , Shao-Bo Lin

In the last five decades, iterative phase retrieval methods draw large amount of interest across the research community as a non-interferometric approach to recover quantitative phase distributions from one (or more) intensity measurement.…

Optics · Physics 2020-07-21 Nathaniel Hai , Joseph Rosen

In modern electronic manufacturing, defect detection on Printed Circuit Boards (PCBs) plays a critical role in ensuring product yield and maintaining the reliability of downstream assembly processes. However, existing methods often suffer…

Computer Vision and Pattern Recognition · Computer Science 2025-07-08 Jiangzhong Cao , Huanqi Wu , Xu Zhang , Lianghong Tan , Huan Zhang

Phase retrieval is a well known ill-posed inverse problem where one tries to recover images given only the magnitude values of their Fourier transform as input. In recent years, new algorithms based on deep learning have been proposed,…

Image and Video Processing · Electrical Eng. & Systems 2022-04-21 Leon Gugel , Shai Dekel

Phase retrieval, a long-established challenge for recovering a complex-valued signal from its Fourier intensity measurements, has attracted significant interest because of its far-flung applications in optical imaging. To enhance accuracy,…

Signal Processing · Electrical Eng. & Systems 2023-05-16 Qiuliang Ye , Bingo Wing-Kuen Ling , Li-Wen Wang , Daniel Pak-Kong Lun

Spectral deferred corrections (SDC) is an iterative approach for constructing higher- order accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of…

Computational Engineering, Finance, and Science · Computer Science 2017-06-14 R. W. Grout , H. Kolla , M. L. Minion , J. B. Bell

Coherent surface scattering imaging (CSSI) is an emerging experimental technique uniquely suited to probing the structure of thin nanostructures. In these experiments, a specimen is placed on a substrate, and a series of X-ray diffraction…

Computational Physics · Physics 2026-04-22 Jeffrey J. Donatelli , Miaoqi Chu , Zixi Hu , Zhang Jiang , Nicholas Schwarz , Jin Wang , James A. Sethian

Stochastic Gradient Descent (SGD) is a known stochastic iterative method popular for large-scale convex optimization problems due to its simple implementation and scalability. Some objectives, such as those found in complex-valued neural…

Machine Learning · Computer Science 2026-05-26 Natanael Alpay , Emeric Battaglia

Coherent diffractive imaging (CDI) provides new opportunities for high resolution X-ray imaging with simultaneous amplitude and phase contrast. Extensions to CDI broaden the scope of the technique for use in a wide variety of experimental…

Optics · Physics 2016-01-20 Matthew H. Seaberg , Alexandre d'Aspremont , Joshua J. Turner

We leverage 3D Gaussian Splatting (3DGS) as a scene representation and propose a novel test-time camera pose refinement (CPR) framework, GS-CPR. This framework enhances the localization accuracy of state-of-the-art absolute pose regression…

Computer Vision and Pattern Recognition · Computer Science 2025-03-04 Changkun Liu , Shuai Chen , Yash Bhalgat , Siyan Hu , Ming Cheng , Zirui Wang , Victor Adrian Prisacariu , Tristan Braud

Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…

Numerical Analysis · Mathematics 2025-10-20 Veit Elser

This paper proposes a transformer-based lossless crossover method, termed Resonant Transformer Router (RTR), which achieves frequency separation while ensuring perfect phase alignment between low-frequency (LF) and high-frequency (HF)…

Signal Processing · Electrical Eng. & Systems 2025-10-07 Xiangying Li , Jiankuan Li , Yong Tang

If the phase retrieval problem can be solved by a method similar to that of solving a system of linear equations under the context of FFT, the time complexity of computer based phase retrieval algorithm would be reduced. Here I present such…

Numerical Analysis · Mathematics 2013-05-20 Yuan Sun

In the phase retrieval problem, the aim is the recovery of an unknown image from intensity-only measurements such as Fourier intensity. Although there are several solution approaches, solving this problem is challenging due to its nonlinear…

Image and Video Processing · Electrical Eng. & Systems 2025-01-20 Cagatay Isil , Figen S. Oktem

Knowledge of longitudinal electron bunch profiles is vital to optimize the performance of plasma wakefield accelerators and x-ray free electron laser linacs. Because of their importance to these novel applications, noninvasive frequency…

Accelerator Physics · Physics 2021-09-20 Bricker Ostler , Nikolai Yampolsky , Quinn Marksteiner

Retrieving molecular structures from tandem mass spectra is a crucial step in rapid compound identification. Existing retrieval methods, such as traditional mass spectral library matching, suffer from limited spectral library coverage,…

Machine Learning · Computer Science 2025-11-11 Yiwen Zhang , Keyan Ding , Yihang Wu , Xiang Zhuang , Yi Yang , Qiang Zhang , Huajun Chen

The simulation of crack initiation and propagation in an elastic material is difficult, as crack paths with complex topologies have to be resolved. Phase-field approach allows to simulate crack behavior by circumventing the need to…

Numerical Analysis · Mathematics 2020-02-19 Alena Kopaničáková , Rolf Krause

High order modulation formats constitute the most prominent way for increasing spectral efficiency in transmission systems. Coherent transceivers that support such higher order formats require heavy digital signal processing (DSP), which…

We present a convex relaxation-based algorithm for large-scale general phase retrieval problems. General phase retrieval problems include i.a. the estimation of the phase of the optical field in the pupil plane based on intensity…

Optimization and Control · Mathematics 2018-08-15 Reinier Doelman , H. Thao Nguyen , Michel Verhaegen

The high-precision solution of the radial Dirac equation is fundamental to relativistic quantum chemistry, essential for reliable pseudopotential generation and all-electron electronic structure methods. However, standard basis-set…

Numerical Analysis · Mathematics 2026-04-14 Sheng Chen , Sihong Shao , Shuai Wu