FID-Net: an interpretable fourier and image domain convolutional dictionary network for industrial CT metal artifact reduction

Online Continual Learning (OCL) learns from nonindependently and identically distributed streaming data with unknown task boundaries during training and testing. Previous methods suffer from the shortcut feature trap and limited plasticity, leading to two requirements: attribute invariance and structure invariance. The former requires to capture the attributes of objects which maintain invariance during all sessions of OCL, while the latter requires to capture the relation of different attributes during OCL.From the causal invariant representation perspective, we propose Quadruplet Augmentation (QuadAug) by preserving attribute and structure invariance via data and channel augmentation with four types of augmentation strategies. First, we build a fine-grained causal graph of OCL to isolate the session-invariant attributes from confounders. Then, by observing different roles of amplitude and phase components of Fourier domain during knowledge transfer, QuadAug preserves attribute invariance by an Amplitude-Phase augmentation (AP-aug) module via a bidirectional data augmentation strategy, to intervene subtle confounders: the single-session class factor and the class-irrelevant factor. Finally, by decomposing the structure invariance into two necessary conditions: channel independence and channel sufficiency, QuadAug preserves structure invariance by an Independence-Sufficiency augmentation (IS-aug) module, which preserves the channel independence property with an inter-channel discrepancy constraint, and the channel sufficiency property with an adversarial augmentation constraint. QuadAug produces significant improvement on four sequential datasets and three blurry datasets for OCL.

Corrigendum to “Spectrum Analysis for Multirate Sampling of Multiband Signals in the Fractional Fourier Domain” [Digital Signal Processing 171 (2026) 105842/ISSN 1051-2004

A substantial body of evidence demonstrates that measures from mammograms are predictive of breast cancer risk. In this matched case-control study, mammograms acquired near the time of diagnosis were analyzed to investigate bilateral breast asymmetry as measure of short-term risk prediction. Specifically, contralateral breast images were compared with measures derived in the Fourier domain (FD); this technique summarizes power in concentric radial bands that cover the Fourier plane. Equivalently, this approach can be described as a multiscale characterization of the image. The summarized power difference between respective contralateral bands produces an asymmetry measure. Full field digital mammography (FFDM) and synthetic two-dimensional images from digital breast tomosynthesis (DBT) were investigated for women that had both types of mammograms acquired at the same time. Odds ratios (ORs) and the area under the receiver operating curves (Azs) were generated from conditional logistic regression modeling with 95% confidence intervals. Raw unprocessed FFDM images produced significant findings: OR = 1.90 (1.58, 2.29) and Az = 1.72 (0.67, 0.76) per one standard deviation unit. Associations were significant but attenuated for both clinical FFDM and DBT images: OR = 1.31 (1.11, 1.54) and Az = 0.63 (0.58, 0.67); and OR = 1.48 (1.25, 1.76) and Az = 0.65 (0.60, 0.70), respectively. Results suggest that clinical FFDM and DBT images are inferior to raw FFDM images in capturing breast asymmetry with information loss for breast cancer risk prediction. Moreover, these DBT images have lower spatial resolution but produced stronger associations than the clinical FFDM images.

OpenAmp is an open‐source, consistently curated, high‐quality database of earthquake site amplification functions derived from instrumental recordings, accompanied by a comprehensive suite of site metadata, for 1,742 K‐NET and KiK‐net observation sites in Japan. The site metadata introduces several new parameters, including the site‐specific spectral decay parameter ( κ 0 ), the standard deviation of the horizontal‐to‐vertical spectral ratio of earthquake recordings ( σ HV ), and site dimensionality index ( I 1D3D ). A distinctive feature of OpenAmp is the inclusion, for the first time, of a diverse set of vector‐based parameters and proxies, including quarter‐wavelength velocity ( V s,qwl ), and frequency‐ and scale‐dependent topographic metrics, which enable physics‐consistent site parameterization. The (linear) site amplification functions are derived from a large dataset of weak‐motion recordings via a nonparametric generalized inversion technique in the Fourier domain, and their correlations with diverse site parameters are analyzed. OpenAmp is unparalleled in its quality and completeness by any existing site database in the world. It enables a wide range of applications, including optimization of site parameterization, development and benchmarking of site‐specific or geospatial amplification models, and testing of novel ideas. Ultimately, OpenAmp can advance data‐driven approaches for modeling near‐surface effects in seismic hazard assessments. The database and associated resources can be freely accessed via: https://doi.org/10.25398/rd.northumbria.29649008 .

Abstract The 2D Gauss-FFT method, which uses Fourier domain methods, is commonly applied in the large-scale 3D magnetotelluric (MT) forward modelling. However, this method is restricted to staggered regular grids and the computational cost usually becomes unacceptable as the number of Gaussian points increases. To address these limitations, we developed an efficient MT forward modeling based on nonuniform fast Fourier transform (NUFFT), combined with a quasi-sampling theorem (QST) in the Fourier domain. This method allows for non-uniform grid discretization both horizontally and vertically. In addition, we can achieve arbitrary sampling in the Fourier domain according to the changes of wavenumber spectrum, and try to reduce the number of 1D equations to be solved in the Fourier domain while ensuring the calculation accuracy. The novel approach has the advantages of flexible sampling, high computational efficiency, and minimal Fourier transform truncation effect compared to the existing Fourier transform method. We designed a low-resistivity model and verified the correctness of the algorithm proposed in this paper against the integral equation (IE) method. Its performance is further evaluated by comparing our results with the Gauss-FFT method for both low-resistivity and large-scale high-resistivity models, which demonstrates approximately 85 percent of computational time and 91 percent memory are saved.

The nonprewhitening matched filter (NPWMF) is frequently used to assess task-based image quality in computed tomography (CT). However, modern reconstruction algorithms, based on iterative reconstruction (IR) or Deep Learning image reconstruction (DLIR), exhibit properties that undermine Fourier domain approaches. One alternative is to abandon the NPWMF. Here, instead, calculation of the NPWMF in the spatial domain is explored with and without assumption of Gaussian observer response. Model observer predictions of area-under-the-curve were determined for a Revolution CT scanner (GE Healthcare) and a NAEOTOM Alpha scanner (Siemens Healthineers). For the former, the vendor's IR and DLIR were investigated. For the latter, the vendor's IR was used and compared to results from a reader study. Results support the conclusion that Fourier domain calculations can exaggerate benefits of denoising and that spatial domain calculations can provide good agreement with human observers. Assumption of Gaussian observer response did not lead to substantial errors.

Abstract Bedload transport in rivers with mixed grain sizes is challenging to predict, with implications for understanding how rivers form and respond to environmental change. Experimental work shows that collective particle entrainment is an important contributing mechanism of bedload transport, and here collective effects to the transport of a sediment mixture are conceptually explored. Two different time series of experimental sediment particle activity (i.e., a measure of the number of particles in motion) for sediments 4–32 mm in diameter are used to indirectly examine the role of collective entrainment. Particle activity was measured at a fixed position using an imaging light table at a time‐averaged resolution of 1 Hz for a duration of approximately 240 min during periods of topographic steady‐state. The two time series reveal a consistent transport behavior within the Fourier domain: activities for smaller particle size populations have increasing power density for decreasing frequency, whereas activities for larger particle size populations have a near uniform power density across all frequencies. Consequently, the activities of smaller particle sizes dominate the power spectra. A set of coupled transfer functions inspired by a probabilistic birth‐death model are developed to conceptually explore the transport behavior evident in the Fourier domain, with two notable results. The transport of smaller particles includes collective entrainment terms that represent mobilization due to both larger and similar particle sizes, whereas larger particles include collective terms limited to similar sized particles. The size‐dependent collective controls on particle entrainment described here offers a testable explanation for further analysis.

Spectrum analysis for multirate sampling of multiband signals in the fractional fourier domain

Temporal graph representation learning seeks to capture the intrinsic evolution of nodes in temporal graphs for various applications. While existing models primarily learn node representations by aggregating temporal information from historical interactions of nodes, they often overlook the critical structural impacts arising from these interactions. To address this issue, we propose a Structure-aware model for Temporal Graph representation learning (STG), a framework that explicitly incorporates the impacts of evolving structural roles to enhance the learned node representations. Specifically, STG encodes distinct structural roles of nodes by extracting both single-unit and multi-unit interaction patterns. These roles are then transformed into the Fourier domain for a deeper analysis of the complex structural dynamics. To capture the structural impacts on future node interactions, we design a dynamic filter to process these roles. The filter is equipped with a personalized weight coefficient generator to perform the interaction-specific analysis. Finally, we employ a mixer to collaboratively aggregate the temporal and structural information to obtain structure-aware temporal node representations. Extensive experiments conducted on several real-world temporal graph datasets demonstrate the superior performance of our model in dynamic link prediction tasks under both transductive and inductive settings.

Image denoising is a crucial preprocessing step in medical imaging. While deep learning methods offer state-of-the-art performance, their computational complexity and data requirements can be prohibitive. Traditional transform-domain methods, particularly wavelet transforms, remain widely used due to their efficiency and interpretability. However, a comprehensive comparison of wavelet families and thresholding techniques for diverse medical noise types is lacking, and the relative performance of wavelet versus localized Fourier methods is not well established. Here, we conduct a two-part investigation. First, we evaluate eight wavelet families combined with twelve thresholding functions and four threshold selection rules on a CT image corrupted with Gaussian, Uniform, Poisson, and Salt-and-Pepper noise. Second, we compare the best wavelet configurations against a block-based Discrete Fourier Cosine Transform (DFCT) approach using overlapping blocks. Among wavelet methods, Biorthogonal Spline and Daubechies wavelets with adaptive thresholding (Smooth Garrote, SURE) performed best. However, the block-based DFCT method consistently outperformed all global DWT configurations across all noise types. DFCT achieved PSNR dB-values of [Formula: see text] (Gaussian), [Formula: see text] (uniform), [Formula: see text] (Poisson), and [Formula: see text] (salt-and-pepper), representing improvements of 4.63, 4.57, 6.25, and 5.07 dB respectively over the best wavelet results. In contrast to the common assumption that wavelet transforms are superior due to multi-resolution analysis, our results demonstrate that a block-based DFCT approach provides significantly better denoising performance across diverse noise types. These findings emphasize the importance of algorithmic selection based on processing methodology rather than solely on transform properties.

This Letter investigates the phase noise estimation (PNE) problem in probabilistic shaping (PS) dual-polarization continuous spectrum nonlinear frequency division multiplexing (DP-CS-NFDM) systems. Firstly, a rigorous phase noise model in the nonlinear Fourier domain establishes the structure of intra-burst impairment, consisting of a common phase rotation on the ideal nonlinear Fourier coefficient plus an additive signal-coupled perturbation. This finding motivates a low-complexity per-burst PNE scheme. Secondly, we propose a QPSK-partitioning and decision-aided (QP-DA) scheme, which integrates QPSK-partitioning with a decision-aided mechanism to counteract the performance degradation of conventional PNE induced by PS. Finally, the experimental validations on a 40 GHz PS DP-CS-NFDM system demonstrate that the proposed QP-DA scheme achieves a 187-km extension in transmission reach and a 475-kHz improvement in laser linewidth tolerance over the blind phase search (BPS) benchmark, yielding a computational complexity of merely 8.4% relative to BPS.

We consider the kinetics of spinodal decomposition in a mixture of oppositely charged ionic species A- and C+ with a short-range Flory-Huggins incompatibility, χ > 0, between them. This represents the minimal model of systems with short-range attractions and long-range repulsions. In contrast to nonionic blends undergoing macroscopic phase separation, ionic mixtures at equilibrium form periodic phases of finite-size domains or clusters-a phenomenon known as electrostatically stabilized microphase separation. A dynamical (time-dependent Ginzburg-Landau) field theory is developed, classified as Model B plus long-range Coulomb interactions. Electrostatics generates an extra term in the resulting Cahn-Hilliard equation, which slows spinodal decomposition. Analysis of the amplification factor R(q) in the Fourier domain shows that electrostatic interactions (i) do not affect the optimal wavevector qm; (ii) slow down the optimal growth; (iii) reduce the window of positive growth, R(q) > 0, by suppressing long-wavelength modes due to the high Coulomb cost of large charged domains; and (iv) lead to a new critical scaling of the optimal growth rate with quench depth, Ropt ∼ δχ1, contrasting the exponent 2 for nonionic systems. Extension to polymer blends shows that monomer connectivity and Rouse dynamics shift qm to lower values and further decelerate growth. In dimensionless form, R(q/qm) depends on two parameters: the reduced electrostatic strength, linear in the Bjerrum length, and the reduced chain length. After rapid spinodal decay, clusters slowly coarsen to their equilibrium finite size, which exceeds the spinodal pattern scale. These results advance the understanding of the dynamics of biocondensate formation in living cells, where Coulomb interactions are ubiquitous.

Single frame complex Fourier domain approach for simultaneous film surface profiling and thickness measurement in spectrally resolved white light interferometry

High-resolution imaging in the terahertz (THz) spectral range remains fundamentally constrained by the limited numerical apertures of currently existing state-of-the-art imagers, which restricts its applicability across many fields, such as imaging in complex media or non-destructive testing. To address this challenge, we introduce a proof-of-concept implementation of THz Fourier ptychographic imaging to enhance spatial resolution without requiring extensive hardware modifications. Our method employs a motorized kinematic mirror to generate a sequence of controlled, multi-angle plane-wave illuminations, with each resulting oblique-illumination intensity image encoding a limited portion of the spatial-frequency content of the target imaging sample. These measurements are combined in the Fourier domain using an aberration-corrected iterative phase-retrieval algorithm integrated with an efficient illumination calibration scheme, which enables the reconstruction of resolution-enhanced amplitude and phase images through the synthetic expansion of the effective numerical aperture. Our work establishes a robust framework for high-resolution THz imaging and paves the way for a wide array of applications in materials characterization, spectroscopy, and non-destructive evaluation.

Abstract This study presents an integrated geophysical investigation of the Zeyve Höyük archaeological site, combining magnetic data analysis and electrical resistivity tomography (ERT) to delineate buried structural features. Magnetic anomalies were processed using a discrete wavelet transform (DWT) with the Haar mother wavelet at decomposition level 2, enabling the extraction of horizontal, vertical, and diagonal detail coefficients. The HVDM operator was applied to these coefficients for edge enhancement and was compared with the conventional balanced horizontal derivative (BHD) method in the Fourier domain. Results demonstrated that HVDM not only captured maxima-based lineaments but also identified significant structural minima, enhancing the detection of weakly magnetic archaeological features. ERT sections revealed high-resistivity zones extending to ∼4 m depth, which closely corresponded to magnetic anomalies, supporting the structural interpretation. Quantitative evaluation showed that HVDM achieved a higher signal-to-noise ratio (SNR: 3.35 dB vs. 1.57 dB for BHD) and produced distinct structural boundaries not detected by BHD, as indicated by a low Dice similarity coefficient (0.215). These findings demonstrate the advantages of wavelet-based edge detection in resolving small-scale archaeological targets. The proposed methodology provides a reliable, non-destructive framework to guide excavation strategies and refine geophysical interpretations in complex settlement contexts.

The graph Hilbert transform (GHT) is a key tool in constructing analytic signals and extracting envelope and phase information in graph signal processing. However, its utility is limited by confinement to the graph Fourier domain, a fixed phase shift, information loss for real-valued spectral components, and the absence of tunable parameters. The graph fractional Fourier transform introduces domain flexibility through a fractional order parameter α but does not resolve the issues of phase rigidity and information loss. Inspired by the dual-parameter fractional Hilbert transform (FRHT) in classical signal processing, we propose the graph FRHT (GFRHT). The GFRHT incorporates a dual-parameter framework: the fractional order α enables analysis across arbitrary fractional domains, interpolating between vertex and spectral spaces, while the angle parameter β provides adjustable phase shifts and a non-zero real-valued response (cosβ) for real eigenvalues, thereby eliminating information loss. We formally define the GFRHT, establish its core properties, and design a method for graph analytic signal construction, enabling precise envelope extraction and demodulation. Experiments on anomaly identification, speech classification and edge detection demonstrate that GFRHT outperforms GHT, offering greater flexibility and superior performance in graph signal processing.

Abstract The geomagnetic field, as observed at the Earth’s surface or LEO satellite altitudes (between 300 km and 800 km), is the combination of signals generated by various internal and external sources. The internal sources are mainly associated with the liquid outer core flow, magnetized rocks in the lithosphere and induced electric currents in the crust and mantle. External sources are electric currents flowing in the ionosphere and magnetosphere. We focus on the contributions from the magnetospheric fields and describe a modeling approach in Spherical Harmonics (SH) based on magnetic observatory vector field measurements. The aim of this study is to model the magnetospheric field contributions observed during geomagnetically quiet time up to SH degree 6, with a 1-h temporal resolution for the period covering years 1996.0–2024.8. The adopted modeling approach is based on the Kalman filter and the correlation-based technique, which leads to series of hourly snapshot models together with robust error estimates. The series of models in time compare well with the global magnetospheric Ring Current index (RC). We observed and described various magnetospheric field structures, including local time asymmetries and contributions from ring and magnetotail currents. We also examined annual, semi-annual, monthly and daily variations in magnetospheric field Gauss coefficients in the Fourier domain. Graphical Abstract

Abstract We investigate identifying differential equations in the frequency domain. Fourier analysis is an important tool in theoretical analysis and numerical solvers of differential equations, yet there is limited work in exploring this connection in the identification of differential equations. This paper aims to identify the underlying differential equation in the frequency domain, from a given single realization of the differential equation perturbed by noise. Such setting imposes difficulties which are different from other identification methods where computation is carried out in the physical domain. We propose several ways to mitigate the challenges arising from noise in data and large differences in the magnitudes of frequency responses. The main takeaways are that identifying differential equations solely in the frequency domain is challenging, the method we propose is based on a form of domain partitions in the frequency domain, and this method shows benefits for complex data even with high level of noise. We introduce a Fourier feature denoising, and define the meaningful data region and the core regions of features to reduce the effect of noise in the frequency domain and to enhance the accuracy in coefficient identification. The proposed method is tested on various differential equations with linear, nonlinear, and high-order derivative feature terms, and shows advantages on complex data with many frequency modes, even under high level of noise.

Semantic segmentation of laparoscopic images requires costly pixel-level annotations, which are often unavailable for real surgical data. This gives rise to an unsupervised domain adaptation scenario, where labeled synthetic images serve as the source domain and unlabeled real images as the target. We propose a frequency-aware unsupervised domain adaptation framework to mitigate the domain gap between simulated and real laparoscopic images. Specifically, we introduce a Radial Frequency Masking module that selectively masks frequency components of real images, and employ a Mean Teacher framework to enforce consistency between high- and low-frequency representations. In addition, we propose a module called Fourier Domain Adaptation-Blend, a style transfer strategy based on low-frequency blending, and apply entropy minimization to enhance prediction confidence on the target domain. Experiments are conducted on public datasets by jointly training on simulated and real laparoscopic images. Our method consistently outperforms representative baselines. These results demonstrate the effectiveness of frequency-aware adaptation in surgical image segmentation without relying on manual annotations from the target domain.