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An analytical description of arbitrary strongly aberrated axially symmetric focusing is developed. This is done by matching the solution of geometrical optics with a wave pattern which is universal for the underlying ray structure. The…
Finite differences, as a subclass of direct methods in the calculus of variations, consist in discretizing the objective functional using appropriate approximations for derivatives that appear in the problem. This article generalizes the…
Practitioners often face the challenge of deploying prediction models in new environments with shifted distributions of covariates and responses. With observational data, such shifts are often driven by unobserved confounding, and can in…
The Fast Multipole Method (FMM) for the Poisson equation is extended to the case of non-axisymmetric problems in an axisymmetric domain, described by cylindrical coordinates. The method is based on a Fourier decomposition of the source into…
In partial differential equations-based (PDE-based) inverse problems with many measurements, many large-scale discretized PDEs must be solved for each evaluation of the misfit or objective function. In the nonlinear case, evaluating the…
To improve the generalization of detectors, for domain adaptive object detection (DAOD), recent advances mainly explore aligning feature-level distributions between the source and single-target domain, which may neglect the impact of…
Diffusion models have shown significant progress in image translation tasks recently. However, due to their stochastic nature, there's often a trade-off between style transformation and content preservation. Current strategies aim to…
Many existing translation averaging algorithms are either sensitive to disparate camera baselines and have to rely on extensive preprocessing to improve the observed Epipolar Geometry graph, or if they are robust against disparate camera…
To address the issue of feature descriptors being ineffective in representing grayscale feature information when images undergo high affine transformations, leading to a rapid decline in feature matching accuracy, this paper proposes a…
A novel general framework is proposed in this paper for dimension reduction in regression to fill the gap between linear and fully nonlinear dimension reduction. The main idea is to transform first each of the raw predictors monotonically,…
The recent development of scintillation crystals combined with $\gamma$-rays sources opens the way to an imaging concept based on Compton scattering, namely Compton scattering tomography (CST). The associated inverse problem rises many…
A systematic mismatch exists between mathematically ideal and effective activation updates during gradient descent. As intended, parameters update in their direction of steepest descent. However, activations are argued to constitute a more…
In optical imaging, light propagation is affected by the inhomogeneities of the medium. Sample-induced aberrations and multiple scattering can strongly degrade the image resolution and contrast. Based on a dynamic correction of the incident…
Anomaly detection, the technique of identifying abnormal samples using only normal samples, has attracted widespread interest in industry. Existing one-model-per-category methods often struggle with limited generalization capabilities due…
Diffusion models have emerged as a dominant framework for generative modeling, but their mathematical foundations are often presented separately through diffusion probabilistic models, score-based modeling, stochastic differential…
Regression evaluation has been performed for decades. Some metrics have been identified to be robust against shifting and scaling of the data but considering the different distributions of data is much more difficult to address (imbalance…
Multi-focus image fusion (MFF) is a popular technique to generate an all-in-focus image, where all objects in the scene are sharp. However, existing methods pay little attention to defocus spread effects of the real-world multi-focus…
Distribution shift is an important concern in deep image classification, produced either by corruption of the source images, or a complete change, with the solution involving domain adaptation. While the primary goal is to improve accuracy…
This work sets the statistical affine shape theory in the context of real normed division algebras. The general densities apply for every field: real, complex, quaternion, octonion, and for any noncentral and non-isotropic elliptical…
Domain shift degrades the performance of object detection models in practical applications. To alleviate the influence of domain shift, plenty of previous work try to decouple and learn the domain-invariant (common) features from source…