Fourier Domain Research Articles

Generating Airy beams through multimode fibres.

Focussing light through a multimode fibre (MMF) is the basis of holographic endoscopes, which currently enable detailed imaging of deep tissue. Achieving high fidelity and purity diffraction-limited foci has been shown to be possible, when fully controlling the amplitude, phase, and two orthogonal polarisation states of the input field. Yet, generating more complex field distributions with similar performance remains to be assessed. Here, we demonstrate the generation of Airy beams through an MMF containing in excess of 90 % of the optical power delivered by the fibre. We discuss two distinct methods for generating optical landscapes: the direct field and the Fourier domain synthesis. Moreover, we showcase the flexibility of the Fourier domain synthesis to modify the generated beam.

Virtual Hall sensor triggered multi-MHz endoscopic OCT imaging for stable real-time visualization.

Circumferential scanning in endoscopic imaging is crucial across various disciplines, and optical coherence tomography (OCT) is often the preferred choice due to its high-speed, high-resolution, and micron-scale imaging capabilities. Moreover, real-time and high-speed 3D endoscopy is a pivotal technology for medical screening and precise surgical guidance, among other applications. However, challenges such as image jitter and non-uniform rotational distortion (NURD) are persistent obstacles that hinder real-time visualization during high-speed OCT procedures. To address this issue, we developed an innovative, low-cost endoscope that employs a brushless DC motor for scanning, and a sensorless technique for triggering and synchronizing OCT imaging with the scanning motor. This sensorless approach uses the motor's electrical feedback (back electromotive force, BEMF) as a virtual Hall sensor to initiate OCT image acquisition and synchronize it with a Fourier Domain Mode-Locked (FDML)-based Megahertz OCT system. Notably, the implementation of BEMF-triggered OCT has led to a substantial reduction in image jitter and NURD (<4 mrad), thereby opening up a new window for real-time visualization capabilities. This approach suggests potential benefits across various applications, aiming to provide a more accurate, deployable, and cost-effective solution. Subsequent studies can explore the adaptability of this system to specific clinical scenarios and its performance under practical endoscopic conditions.

Fourier domain vertical derivative of the nonpotential squared analytical signal of dike and step magnetic anomalies: A case of serendipity

Vertical derivatives of nonpotential fields are, intentionally or not, often performed in the Fourier domain producing nonphysical but interpretable results. Using the dike model, we prove that the vertical derivative of the squared analytic signal amplitude calculated in the Fourier domain does not correspond to the true one. We derive an analytical expression for this pseudovertical derivative, providing a mathematical meaning for it. One significant difference between the pseudo and true vertical derivative is that the former possesses real roots, whereas the latter does not. Taking advantage of this attribute, we find using synthetic and field data that the pseudovertical derivative can be used for qualitative and quantitative interpretation of magnetic data, despite being nonphysical. As an example of the usefulness of this filter in qualitative interpretation, we convert the image of the pseudoderivative to a binary image where the anomalies are treated as discrete objects. This allows us to morphologically enhance, disconnect, classify, and filter them using the tools of shape analysis and mathematical morphology. We also illustrate its usefulness in quantitative interpretation by deriving a formula for estimating the depths of magnetic thin dikes and infinite steps. Our outcomes are also corroborated by the observation of outcrops found by field surveys.

Enhancing medical image analysis with unsupervised domain adaptation approach across microscopes and magnifications

In the domain of medical image analysis, deep learning models are heralding a revolution, especially in detecting complex and nuanced features characteristic of diseases like tumors and cancers. However, the robustness and adaptability of these models across varied imaging conditions and magnifications remain a formidable challenge. This paper introduces the Fourier Adaptive Recognition System (FARS), a pioneering model primarily engineered to address adaptability in malarial parasite recognition. Yet, the foundational principles guiding FARS lend themselves seamlessly to broader applications, including tumor and cancer diagnostics. FARS capitalizes on the untapped potential of transitioning from bounding box labels to richer semantic segmentation labels, enabling a more refined examination of microscopy slides. With the integration of adversarial training and the Color Domain Aware Fourier Domain Adaptation (F2DA), the model ensures consistent feature extraction across diverse microscopy configurations. The further inclusion of category-dependent context attention amplifies FARS’s cross-domain versatility. Evidenced by a substantial elevation in cross-magnification performance from 31.3% mAP to 55.19% mAP and a 15.68% boost in cross-domain adaptability, FARS positions itself as a significant advancement in malarial parasite recognition. Furthermore, the core methodologies of FARS can serve as a blueprint for enhancing precision in other realms of medical image analysis, especially in the complex terrains of tumor and cancer imaging. The code is available at; https://github.com/Mr-TalhaIlyas/FARS.

Full-Matrix Imaging in Fourier Domain towards Ultrasonic Inspection with Wide-Angle Oblique Incidence for Welded Structures

The total focusing method (TFM) has been increasingly applied to weld inspection given its high image quality and defect sensitivity. Oblique incidence is widely used to steer the beam effectively, considering the defect orientation and structural complexity of welded structures. However, the conventional TFM based on the delay-and-sum (DAS) principle is time-consuming, especially for oblique incidence. In this paper, a fast full-matrix imaging algorithm in the Fourier domain is proposed to accelerate the TFM under the condition of oblique incidence. The algorithm adopts the Chebyshev polynomials of the second kind to directly expand the Fourier extrapolator with lateral sound velocity variation. The direct expansion maintains image accuracy and resolution in wide-angle situations, covering both small and large angles, making it highly suitable for weld inspection. Simulations prove that the third-order Chebyshev expansion is required to achieve image accuracy equivalent to the TFM with wide-angle incidence. Experiments verify the algorithm’s performance for weld flaws using the proposed method with the transverse wave and the full-skip mode. The depth deviation is within 0.53 mm, and the sizing error is below 15%. The imaging efficiency is improved by a factor of up to 8 compared to conventional TFM. We conclude that the proposed method is applicable to high-speed weld inspection with various oblique incidence angles.

Spatial–temporal feature-based End-to-end Fourier network for 3D sign language recognition

Most dynamic sign word misclassifications are caused by redundant spatial–temporal (SPT) feature pruning that lacks language semantic and temporal dependencies. SPT feature recognition is one of the important aspects for the evaluation of the misclassification of dynamic sign words. The redundant pruning of SPT feature space influences the language model of sign confusion, model complexity, and SPT feature similarity. The purpose of this article is to develop a new multi-scale SPT feature-based dynamic sign word recognition approach via a low-cost feature selection method (FS) and End-to-end Fourier convolution neural network (EFCNN). Instead of a sensor fusion technique for obtaining frame position alignment, in the EFCNN, new 3D frame position and coordinates are determined using a pixel weighting and alignment function of the first and succeeding 25 spatial intensities of the 3D video changes across hand motion. The new spatial weight and the original spatial coordinates are fused and truncated in the Fourier domain. We generate the temporal dependence of the fused features. A feature selection known as the FS-EFCNN is introduced to select compact features with a preserved language meaning. Five state-of-the-art feature selection methods, namely Infinite FS (InFS), Relief FS, Fisher, MIM, ILFS, and ensemble FS-EFCNN were deployed to guide and optimize the learning performance of EFCNN. The experimental result analysis highlighted the improved results of the FS-EFCNN method with the best accuracy of 99.86%, 99.89%, and 90.69% on 3D American Sign Language, British Sign Language, and Greek Sign Language data sets, respectively.

Towards Faster and Efficient Lightweight Image Super Resolution Using Transformers and Fourier Convolutions

Lightweight Single Image Super Resolution has seen many advances in recent times. Transformer-based methods have achieved great improvements over CNN-based methods. This is mainly driven by the transformer's ability to effectively model long-range dependencies and retain textures in images. However, these transformer-based approaches have many parameters and are computationally expensive during inference. In this work, we propose SWIFT, a hybrid of transformers and Fast Fourier Convolutions (FFC) for Lightweight Single Image Super Resolution. We designed a novel Dual Spectrum Frequency Block (DSFB) that processes features in both the spatial domain and the Fourier domain. DSFB allows us to effectively maintain global context in features and extract high-frequency information. Additionally, to mitigate the frequency erasing nature of transformers, we introduce SwinV2+ transformers that use attention scaling to promote high-frequency information. Experimental results on popular benchmarking datasets show that SWIFT outperforms state-of-the-art transformer-based methods in the realm of lightweight SISR, using 34% fewer parameters and being up to 60% faster during inference.

Real‐world image deblurring using data synthesis and feature complementary network

AbstractMany learning‐based approaches to image deblurring have received increasing attention in recent years. However, the models trained on existing synthetic datasets do not generalize well to real‐world blur, resulting in undesirable artifacts and residual blur. This work attempts to address this problem from two aspects: training data synthesis and network architecture. To narrow the domain gap between synthetic and real domains, a realistic blur synthesis pipeline to generate high‐quality blurred data is proposed. Since the blur is non‐uniform and has different scales and degrees, a parallel feature complementary module to fully exploit the local and non‐local information, which improves the feature representation and helps the network to perceive the non‐uniform blur, is developed. In addition, a spatial Fourier reconstruction block to facilitate correct detail recovery in the spatial and Fourier domains is introduced. Based on these two designs, an effective encoder–decoder network for deblurring is designed. Extensive experiments demonstrate the validity and superiority of the proposed blur synthesis method and deblurring network. In particular, the proposed deblurring network can achieve superior or comparable performance to Restormer, while saving 70% of network parameters and 53% of floating point operations (FLOPs).

Multi-modal brain tumor segmentation via conditional synthesis with Fourier domain adaptation

Accurate brain tumor segmentation is critical for diagnosis and treatment planning, whereby multi-modal magnetic resonance imaging (MRI) is typically used for analysis. However, obtaining all required sequences and expertly labeled data for training is challenging and can result in decreased quality of segmentation models developed through automated algorithms.In this work, we examine the possibility of employing a conditional generative adversarial network (GAN) approach for synthesizing multi-modal images to train deep learning-based neural networks aimed at high-grade glioma (HGG) segmentation. The proposed GAN is conditioned on auxiliary brain tissue and tumor segmentation masks, allowing us to attain better accuracy and control of tissue appearance during synthesis. To reduce the domain shift between synthetic and real MR images, we additionally adapt the low-frequency Fourier space components of synthetic data, reflecting the style of the image, to those of real data. We demonstrate the impact of Fourier domain adaptation (FDA) on the training of 3D segmentation networks and attain significant improvements in both the segmentation performance and prediction confidence. Similar outcomes are seen when such data is used as a training augmentation alongside the available real images. In fact, experiments on the BraTS2020 dataset reveal that models trained solely with synthetic data exhibit an improvement of up to 4% in Dice score when using FDA, while training with both real and FDA-processed synthetic data through augmentation results in an improvement of up to 5% in Dice compared to using real data alone. This study highlights the importance of considering image frequency in generative approaches for medical image synthesis and offers a promising approach to address data scarcity in medical imaging segmentation.

Estimation of scalar field distribution in the Fourier domain

In this paper we consider the problem of estimation of scalar field distribution (e.g. pollutant, moisture, temperature) from noisy measurements collected by unmanned autonomous vehicles such as UAVs. The field is modelled as a sum of Fourier components/modes, where the number of modes retained and estimated determines in a natural way the approximation quality. An algorithm for estimating the modes using an online optimisation approach is presented, under the assumption that the noisy measurements are quantized. The algorithm can also be used to estimate time-varying fields. Simulation studies demonstrate the effectiveness of the proposed approach.

Semi-Analytical Approach and Green's Function Method: A Comparison in the Analysis of the Interaction of a Moving Mass on an Infinite Beam on a Three-Layer Viscoelastic Foundation at the Stability Limit-The Effect of Damping of Foundation Materials.

In this paper, the interaction of a mass moving uniformly on an infinite beam on a three-layer viscoelastic foundation is analyzed with the objective of determining the lowest velocity at the stability limit, called, in this context, the critical velocity. This issue is important for rail transport and, in particular, for the high-speed train, because the moving mass is the basic model of a vehicle, and the infinite beam on a three-layer viscoelastic foundation is the usual mechanical representation of the railway track. In addition to this, the advantages and disadvantages of the two implemented methods, namely, the semi-analytical approach and the Green's function method, are summarized in terms of computational time, the precision of the obtained results, limitations, and the feasibility of implementation. All results are presented in a dimensionless form to cover a wide range of possible scenarios. Some results may be considered academic, however, results related to a particular railway track are also included. Particular attention is paid to the influence of the damping of materials in the foundation upon the critical velocity of the moving mass. Regarding the semi-analytical approach, it is demonstrated that the critical velocities can be obtained in an exact manner by tracing the branches of the so-called instability lines in the velocity-moving-mass plane. This analysis can be maintained within the real domain. As for the time series, they can be determined by a numerical inverse Laplace transform. Moreover, thanks to the analytical form of the final result in the Fourier domain, each value corresponding to a specific time instant can be obtained directly, that is, without the previous time history. Regarding the Green's function method, this is used to verify a few points delimiting the stable and unstable regions of the moving mass with the help of the D-decomposition approach. Additionally, a numerical algorithm based on the Green's function and convolution integral written for dimensionless quantities is used to calculate the time series of the moving mass. In addition to identifying the critical velocity of the moving mass, its connection with the critical velocity of the moving force is emphasized, and the possibility of validating the results on long finite beams using modal expansion is presented and described.

Voice Vista

Blind image restoration involves leveraging prior information within an image to restore the sharpness of edges. De-blurring, on the other hand, aims to eliminate blurring artifacts caused by factors like defocus aberration or motion blur, which manifests as apparent streaking in still images of rapidly moving objects. Gaussian blur results from applying a Gaussian function to blur an image. Recent advancements in single-image methods owe their success in part to the utilization of various sparse priors for either latent images or motion blur kernels. KSR introduces an efficient kernel matrix approximation to accelerate blurring processes and achieve notable de-blur performance on digital datasets. License plate recognition serves as a critical tool for identifying over-speed vehicles or those involved in hit-and-run incidents. However, surveillance camera snapshots of speeding vehicles often suffer from motion blur, rendering them unrecognizable to the human eye and presenting a challenge to existing blind deblurring techniques. To address this, we propose a novel sparse representation-based scheme for identifying motion blur kernels. By analyzing sparse representation coefficients of the recovered image, we determine the kernel angle, and estimate the length of the motion kernel using Radon transform in Fourier domain. Our approach effectively handles large motion blur, even when license plates are unidentifiable by humans. Experimental evaluations on real-world images demonstrate the superiority of our method over several state-of-the-art blind image de-blurring algorithms.

Lightweight Prompt Learning Implicit Degradation Estimation Network for Blind Super Resolution.

Blind image super-resolution (SR) aims to recover a high-resolution (HR) image from its low-resolution (LR) counterpart under the assumption of unknown degradations. Many existing blind SR methods rely on supervising ground-truth kernels referred to as explicit degradation estimators. However, it is very challenging to obtain the ground-truths for different degradations kernels. Moreover, most of these methods rely on heavy backbone networks, which demand extensive computational resources. Implicit degradation estimators do not require the availability of ground truth kernels, but they see a significant performance gap with the explicit degradation estimators due to such missing information. We present a novel approach that significantly narrows such a gap by means of a lightweight architecture that implicitly learns the degradation kernel with the help of a novel loss component. The kernel is exploited by a learnable Wiener filter that performs efficient deconvolution in the Fourier domain by deriving a closed-form solution. Inspired by prompt-based learning, we also propose a novel degradation-conditioned prompt layer that exploits the estimated kernel to drive the focus on the discriminative contextual information that guides the reconstruction process in recovering the latent HR image. Extensive experiments under different degradation settings demonstrate that our model, named PL-IDENet, yields PSNR and SSIM improvements of more than 0.4dB and 1.3%, and 1.4dB and 4.8% to the best implicit and explicit blind-SR method, respectively. These results are achieved while maintaining a substantially lower number of parameters/FLOPs (i.e., 25% and 68% fewer parameters than best implicit and explicit methods, respectively).

Double Discrete Cosine Transform-Oriented Multi-View Subspace Clustering.

Low-rank tensor representation with the tensor nuclear norm has been rising in popularity in multi-view subspace clustering (MVSC), in which the tensor nuclear norm is commonly implemented using discrete Fourier transform (DFT). Unfortunately, existing DFT-oriented MVSC methods may provide unsatisfactory results since (1) DFT exploits complex arithmetic in the Fourier domain, usually resulting in high tubal tensor rank, and (2) local structural information is rarely considered. To solve these problems, in this paper, we propose a novel double discrete cosine transform (DCT)-oriented multi-view subspace clustering (D2CTMSC) method, in which the first DCT aims to derive the tensor nuclear norm without complex arithmetic while the second DCT aims to explore the local structure of the self-representation tensor, such that the essential low-rankness and sparsity embedding in multi-view features can be thoroughly exploited. Moreover, we design an effective alternating iteration strategy to solve the proposed model. Experimental results on four types of multi-view datasets (News stories, Face images, Scene images, and Generic objects) demonstrate the superiority of the D2CTMSC method compared with DFT-based methods and other state-of-the-art clustering methods.

Tensor Robust Kernel PCA for Multidimensional Data.

Recently, the tensor nuclear norm (TNN)-based tensor robust principle component analysis (TRPCA) has achieved impressive performance in multidimensional data processing. The underlying assumption in TNN is the low-rankness of frontal slices of the tensor in the transformed domain (e.g., Fourier domain). However, the low-rankness assumption is usually violative for real-world multidimensional data (e.g., video and image) due to their intrinsically nonlinear structure. How to effectively and efficiently exploit the intrinsic structure of multidimensional data remains a challenge. In this article, we first suggest a kernelized TNN (KTNN) by leveraging the nonlinear kernel mapping in the transform domain, which faithfully captures the intrinsic structure (i.e., implicit low-rankness) of multidimensional data and is computed at a lower cost by introducing kernel trick. Armed with KTNN, we propose a tensor robust kernel PCA (TRKPCA) model for handling multidimensional data, which decomposes the observed tensor into an implicit low-rank component and a sparse component. To tackle the nonlinear and nonconvex model, we develop an efficient alternating direction method of multipliers (ADMM)-based algorithm. Extensive experiments on real-world applications collectively verify that TRKPCA achieves superiority over the state-of-the-art RPCA methods.

Neuro-BERT: Rethinking Masked Autoencoding for Self-Supervised Neurological Pretraining.

Deep learning associated with neurological signals is poised to drive major advancements in diverse fields such as medical diagnostics, neurorehabilitation, and brain-computer interfaces. The challenge in harnessing the full potential of these signals lies in the dependency on extensive, high-quality annotated data, which is often scarce and expensive to acquire, requiring specialized infrastructure and domain expertise. To address the appetite for data in deep learning, we present Neuro-BERT, a self-supervised pre-training framework of neurological signals based on masked autoencoding in the Fourier domain. The intuition behind our approach is simple: frequency and phase distribution of neurological signals can reveal intricate neurological activities. We propose a novel pre-training task dubbed Fourier Inversion Prediction (FIP), which randomly masks out a portion of the input signal and then predicts the missing information using the Fourier inversion theorem. Pre-trained models can be potentially used for various downstream tasks such as sleep stage classification and gesture recognition. Unlike contrastive-based methods, which strongly rely on carefully hand-crafted augmentations and siamese structure, our approach works reasonably well with a simple transformer encoder with no augmentation requirements. By evaluating our method on several benchmark datasets, we show that Neuro-BERT improves downstream neurological-related tasks by a large margin.

Improved Fourier Domain Model and Adaptive Controller Design for Handling Double Resonance Impact on Performance of Current-Fed Isolated DC/DC Converter

Improved Fourier Domain Model and Adaptive Controller Design for Handling Double Resonance Impact on Performance of Current-Fed Isolated DC/DC Converter

Curriculum-Based Augmented Fourier Domain Adaptation for Robust Medical Image Segmentation

Curriculum-Based Augmented Fourier Domain Adaptation for Robust Medical Image Segmentation

Efficient calculation of the three-dimensional sound pressure field around a slab track

The wavenumber domain Boundary Element (2.5D BE) method is well suited to calculate the acoustic sound field around structures with a constant cross-section along one dimension, such as noise barriers or railway track. By expressing the sound field along this dimension in wavenumber domain, the numerical model is reduced from a 3D model to 2D model at each wavenumber. A consequence of the required discrete Fourier domain representation is that the sound field is represented by periodically repeating sections, of which only one section is physically meaningful. The resolution and the number of required wavenumbers increases with the desired length and spatial discretisation of this section. Describing the sound field adequately to auralise the sound without disturbing artefacts requires a large number of wavenumbers (and thus 2D BE computations), which is not feasible for large geometries. Here, a method is introduced that allows the calculation of the 3D sound field by solving a single 2D BE problem for a dense frequency spectrum and interpolating at higher wavenumbers. The calculation efficiency is further increased by precalculating the acoustic transfer functions between each BE surface element and receiver positions. Combining these two methods allows for efficient calculation of the 3D sound field around acoustically rigid structures such as slab tracks. The numerical approach is validated by comparison with a standard 2.5D BEM calculation and an analytical solution. Precalculated transfer functions to calculate the sound radiation from railway track, which are made available online, are illustrated. An example application is presented.

Superpixels meet essential spectra for fast Raman hyperspectral microimaging.

In the context of spectral unmixing, essential information corresponds to the most linearly dissimilar rows and/or columns of a two-way data matrix which are indispensable to reproduce the full data matrix in a convex linear way. Essential information has recently been shown accessible on-the-fly via a decomposition of the measured spectra in the Fourier domain and has opened new perspectives for fast Raman hyperspectral microimaging. In addition, when some spatial prior is available about the sample, such as the existence of homogeneous objects in the image, further acceleration for the data acquisition procedure can be achieved by using superpixels. The expected gain in acquisition time is shown to be around three order of magnitude on simulated and real data with very limited distortions of the estimated spectrum of each object composing the images.