Spatial Frequency Domain Research Articles

Computationally-efficient linear scheme for overlap time-gating spatial frequency domain diffuse optical tomography using an analytical diffusion model.

Time-domain (TD) spatial frequency domain (SFD) diffuse optical tomography (DOT) potentially enables laminar tomography of both the absorption and scattering coefficients. Its full time-resolved-data scheme is expected to enhance performances of the image reconstruction but poses heavy computational costs and also susceptible signal-to-noise ratio (SNR) limits, as compared to the featured-data one. We herein propose a computationally-efficient linear scheme of TD-SFD-DOT, where an analytical solution to the TD phasor diffusion equation for semi-infinite geometry is derived and used to formulate the Jacobian matrices with regard to overlap time-gating data of the time-resolved measurement for improved SNR and reduced redundancy. For better contrasting the absorption and scattering and widely adapted to practically-available resources, we develop an algebraic-reconstruction-technique-based two-step linear inversion procedure with support of a balanced memory-speed strategy and multi-core parallel computation. Both simulations and phantom experiments are performed to validate the effectiveness of the proposed TD-SFD-DOT method and show an achieved tomographic reconstruction at a relative depth resolution of ∼4 mm.

Refining Localized Attention Features with Multi-Scale Relationships for Enhanced Deepfake Detection in Spatial-Frequency Domain

The rapid advancement of deep learning and large-scale AI models has simplified the creation and manipulation of deepfake technologies, which generate, edit, and replace faces in images and videos. This gradual ease of use has turned the malicious application of forged faces into a significant threat, complicating the task of deepfake detection. Despite the notable success of current deepfake detection methods, which predominantly employ data-driven CNN classification models, these methods exhibit limited generalization capabilities and insufficient robustness against novel data unseen during training. To tackle these challenges, this paper introduces a novel detection framework, ReLAF-Net. This framework employs a restricted self-attention mechanism that applies self-attention to deep CNN features flexibly, facilitating the learning of local relationships and inter-regional dependencies at both fine-grained and global levels. This attention mechanism has a modular design that can be seamlessly integrated into CNN networks to improve overall detection performance. Additionally, we propose an adaptive local frequency feature extraction algorithm that decomposes RGB images into fine-grained frequency domains in a data-driven manner, effectively isolating fake indicators in the frequency space. Moreover, an attention-based channel fusion strategy is developed to amalgamate RGB and frequency information, achieving a comprehensive facial representation. Tested on the high-quality version of the FaceForensics++ dataset, our method attained a detection accuracy of 97.92%, outperforming other approaches. Cross-dataset validation on Celeb-DF, DFDC, and DFD confirms the robust generalizability, offering a new solution for detecting high-quality deepfake videos.

Extraction of reflected waves from acoustic logging data using variation mode decomposition and curvelet transform

Remote reflection waves, essential for acquiring high-resolution images of geological structures beyond boreholes, often suffer contamination from strong direct mode waves propagating along the borehole. Consequently, the extraction of weak reflected waves becomes pivotal for optimizing migration image quality. This paper introduces a novel approach to extracting reflected waves by sequentially operating in the spatial frequency and curvelet domains. Using variation mode decomposition (VMD), single-channel spatial domain signals within the common offset gather are iteratively decomposed into high-wavenumber and low-wavenumber intrinsic mode functions (IMFs). The low-wavenumber IMF is then subtracted from the overall waveform to attenuate direct mode waves. Subsequently, the curvelet transform is employed to segregate upgoing and downgoing reflected waves within the filtered curvelet domain. As a result, direct mode waves are substantially suppressed, while the integrity of reflected waves is fully preserved. The efficacy of this approach is validated through processing synthetic and field data, underscoring its potential as a robust extraction technique.

CSF-GTNet: A Novel Multi-Dimensional Feature Fusion Network Based on Convnext-GeLU- BiLSTM for EEG-Signals-Enabled Fatigue Driving Detection.

Electroencephalography (EEG) signal has been recognized as an effective fatigue detection method, which can intuitively reflect the drivers' mental state. However, the research on multi-dimensional features in existing work could be much better. The instability and complexity of EEG signals will increase the difficulty of extracting data features. More importantly, most current work only treats deep learning models as classifiers. They ignored the features of different subjects learned by the model. Aiming at the above problems, this paper proposes a novel multi-dimensional feature fusion network, CSF-GTNet, based on time and space-frequency domains for fatigue detection. Specifically, it comprises Gaussian Time Domain Network (GTNet) and Pure Convolutional Spatial Frequency Domain Network (CSFNet). The experimental results show that the proposed method effectively distinguishes between alert and fatigue states. The accuracy rates are 85.16% and 81.48% on the self-made and SEED-VIG datasets, respectively, which are higher than the state-of-the-art methods. Moreover, we analyze the contribution of each brain region for fatigue detection through the brain topology map. In addition, we explore the changing trend of each frequency band and the significance between different subjects in the alert state and fatigue state through the heat map. Our research can provide new ideas in brain fatigue research and play a specific role in promoting the development of this field.

Band-amplified angle spectrum method for the phase hologram design to achieve high-quality holographic imaging in long distance

The angular spectrum method (ASM) is widely used in the design of computer-generated holograms (CGH) due to its strict adherence to the Helmholtz equations and the potential for accelerated computation using fast Fourier transform (FFT). However, when dealing with long distance propagation conditions, the reduction of effective spectral components and spectral aliasing will introduce significant computation errors, leading to a substantial degradation in holographic imaging quality. To achieve high-quality holographic imaging design in long distance, we introduce a novel angular spectrum computation method, the calculation process is divided into two steps: (1) First propagate a longer distance from the CGH plane to an intermediate plane. (2) Then continue to propagate to the observation plane after incorporating a spread spectrum phase factor to amplify the effective non-aliased bandwidth in the intermediate plane and eliminating the aliasing artifacts. Furthermore, the non-uniform fast Fourier transform (NUFFT) algorithm is adopted which allows for the flexible adjustments of the sampling interval and quantity in the spatial frequency domain, all while maintaining compliance with the Nyquist sampling theorem even in the context of bandwidth amplification. Both simulations and optical experiments are conducted to validate the feasibility and effectiveness of our proposed method.

An efficient ultrasonic full-matrix imaging method for industrial curved-surface components defect detection

Curved-surface components are ubiquitous in various industries. However, defects inside the components badly degenerate the mechanical properties and lead to premature failure. Ultrasonic full-matrix imaging is a prominent method in nondestructive testing, but there is still a lack of efficient imaging methods for cases with curved interfaces. To amend this problem, this article proposes an efficient ultrasonic full-matrix imaging method to detect the defects in the industrial curved-surface components. The wavefield extrapolation for full matrix capture (FMC) dataset is taken as the combined effect of the downward migration of the source and receiver wavefields in the wavenumber-frequency domain. Compensation terms corresponding to the source and receiver wavefields act on the wavefield of FMC in the spatial-frequency domain to make up for lateral variations of the sound speed. After the wavefield reconstruction, an efficient imaging condition is implemented to transform the wavefield into the defect image. The best compensation term is determined and the influence factors is investigated in the simulation experiments. Laboratory experiments furtherly validate the superiority of the proposed method over the existing methods, especially for the imaging efficiency which is twice of the phase shift migration (PSM) based method.

Multi-frequency spatial frequency domain imaging: a depth-resolved optical scattering model to isolate scattering contrast in thin layers of skin.

Current methods for wound healing assessment rely on visual inspection, which gives qualitative information. Optical methods allow for quantitative non-invasive measurements of optical properties relevant to wound healing. Spatial frequency domain imaging (SFDI) measures the absorption and reduced scattering coefficients of tissue. Typically, SFDI assumes homogeneous tissue; however, layered structures are present in skin. We evaluate a multi-frequency approach to process SFDI data that estimates depth-specific scattering over differing penetration depths. Multi-layer phantoms were manufactured to mimic wound healing scattering contrast in depth. An SFDI device imaged these phantoms and data were processed according to our multi-frequency approach. The depth sensitive data were then compared with a two-layer scattering model based on light fluence. The measured scattering from the phantoms changed with spatial frequency as our two-layer model predicted. The performance of two models solutions for SFDI was consistently better than the standard diffusion approximation. We presented an approach to process SFDI data that returns depth-resolved scattering contrast. This method allows for the implementation of layered optical models that more accurately represent physiologic parameters in thin tissue structures as in wound healing.

Highly-accelerated CEST MRI using frequency-offset-dependent k-space sampling and deep-learning reconstruction.

To develop a highly accelerated CEST Z-spectral acquisition method using a specifically-designed k-space sampling pattern and corresponding deep-learning-based reconstruction. For k-space down-sampling, a customized pattern was proposed for CEST, with the randomized probability following a frequency-offset-dependent (FOD) function in the direction of saturation offset. For reconstruction, the convolution network (CNN) was enhanced with a Partially Separable (PS) function to optimize the spatial domain and frequency domain separately. Retrospective experiments on a self-acquired human brain dataset (13 healthy adults and 15 brain tumor patients) were conducted using k-space resampling. The prospective performance was also assessed on six healthy subjects. In retrospective experiments, the combination of FOD sampling and PS network (FOD + PSN) showed the best quantitative metrics for reconstruction, outperforming three other combinations of conventional sampling with varying density and a regular CNN (nMSE and SSIM, p < 0.001 for healthy subjects). Across all acceleration factors from 4 to 14, the FOD + PSN approach consistently outperformed the comparative methods in four contrast maps including MTRasym, MTRrex, as well as the Lorentzian Difference maps of amide and nuclear Overhauser effect (NOE). In the subspace replacement experiment, the error distribution demonstrated the denoising benefits achieved in the spatial subspace. Finally, our prospective results obtained from healthy adults and brain tumor patients (14×) exhibited the initial feasibility of our method, albeit with less accurate reconstruction than retrospective ones. The combination of FOD sampling and PSN reconstruction enabled highly accelerated CEST MRI acquisition, which may facilitate CEST metabolic MRI for brain tumor patients.

Use of nonlinear pulsed magnetic fields for spatial encoding in magnetic resonance imaging

This study examines the use of nonlinear magnetic field coils for spatial encoding in magnetic resonance imaging. Existing theories on imaging with such coils share a complex reconstruction process that originates from a suboptimal signal interpretation in the spatial-frequency domain (k-space). In this study, a new solution to this problem is proposed, namely a two-step reconstruction process, in which in the first step, the image signal is converted into a frequency spectrum, and in the second step, the spectrum, which represents the distorted image, is geometrically and intensity corrected to obtain an undistorted image. This theory has been verified by numerical simulations and experimentally using a straight wire as a coil model for an extremely nonlinear magnetic field. The results of this study facilitate the use of simple encoding coil designs that can feature low inductance, allowing for much faster switching times and higher magnetic field gradients.

Dual-Channel in Spatial-Frequency Domain CycleGAN for perceptual enhancement of transcranial cortical vascular structure and function

Observing cortical vascular structures and functions using laser speckle contrast imaging (LSCI) at high resolution plays a crucial role in understanding cerebral pathologies. Usually, open-skull window techniques have been applied to reduce scattering of skull and enhance image quality. However, craniotomy surgeries inevitably induce inflammation, which may obstruct observations in certain scenarios. In contrast, image enhancement algorithms provide popular tools for improving the signal-to-noise ratio (SNR) of LSCI. The current methods were less than satisfactory through intact skulls because the transcranial cortical images were of poor quality. Moreover, existing algorithms do not guarantee the accuracy of dynamic blood flow mappings. In this study, we develop an unsupervised deep learning method, named Dual-Channel in Spatial-Frequency Domain CycleGAN (SF-CycleGAN), to enhance the perceptual quality of cortical blood flow imaging by LSCI. SF-CycleGAN enabled convenient, non-invasive, and effective cortical vascular structure observation and accurate dynamic blood flow mappings without craniotomy surgeries to visualize biodynamics in an undisturbed biological environment. Our experimental results showed that SF-CycleGAN achieved a SNR at least 4.13 dB higher than that of other unsupervised methods, imaged the complete vascular morphology, and enabled the functional observation of small cortical vessels. Additionally, the proposed method showed remarkable robustness and could be generalized to various imaging configurations and image modalities, including fluorescence images, without retraining.

Analysis and implementation of volume reflection gratings in photorefractive lithium niobate for edge enhancement.

Diffraction from volume reflection gratings written in bulk photorefractive lithium niobate is modeled for the case of longitudinally varying index modulation depths. Numerical solutions to the Helmholtz equation are found in the spatial frequency domain, leading to transfer functions for the volume reflection grating. These transfer functions are then used to show the spatial frequency filtering effect of the volume reflection grating on input light fields containing 2D spatial information. It is shown, first through simulations and then by experiment, that the 0th order transmitted beam undergoes a 2D edge enhancement.

SG-Transunet: A segmentation-guided Transformer U-Net model for KRAS gene mutation status identification in colorectal cancer

Accurately identifying the Kirsten rat sarcoma virus (KRAS) gene mutation status in colorectal cancer (CRC) patients can assist doctors in deciding whether to use specific targeted drugs for treatment. Although deep learning methods are popular, they are often affected by redundant features from non-lesion areas. Moreover, existing methods commonly extract spatial features from imaging data, which neglect important frequency domain features and may degrade the performance of KRAS gene mutation status identification. To address this deficiency, we propose a segmentation-guided Transformer U-Net (SG-Transunet) model for KRAS gene mutation status identification in CRC. Integrating the strength of convolutional neural networks (CNNs) and Transformers, SG-Transunet offers a unique approach for both lesion segmentation and KRAS mutation status identification. Specifically, for precise lesion localization, we employ an encoder–decoder to obtain segmentation results and guide the KRAS gene mutation status identification task. Subsequently, a frequency domain supplement block is designed to capture frequency domain features, integrating it with high-level spatial features extracted in the encoding path to derive advanced spatial-frequency domain features. Furthermore, we introduce a pre-trained Xception block to mitigate the risk of overfitting associated with small-scale datasets. Following this, an aggregate attention module is devised to consolidate spatial-frequency domain features with global information extracted by the Transformer at shallow and deep levels, thereby enhancing feature discriminability. Finally, we propose a mutual-constrained loss function that simultaneously constrains the segmentation mask acquisition and gene status identification process. Experimental results demonstrate the superior performance of SG-Transunet over state-of-the-art methods in discriminating KRAS gene mutation status.

MicroRNA-155 mediates multiple gene regulations pertinent to the role of human adipose-derived mesenchymal stem cells in skin regeneration.

Introduction: The role of Adipose-derived mesenchymal stem cells (AD-MSCs) in skin wound healing remains to be fully characterized. This study aims to evaluate the regenerative potential of autologous AD-MSCs in a non-healing porcine wound model, in addition to elucidate key miRNA-mediated epigenetic regulations that underlie the regenerative potential of AD-MSCs in wounds. Methods: The regenerative potential of autologous AD-MSCs was evaluated in porcine model using histopathology and spatial frequency domain imaging. Then, the correlations between miRNAs and proteins of AD-MSCs were evaluated using an integration analysis in primary human AD-MSCs in comparison to primary human keratinocytes. Transfection study of AD-MSCs was conducted to validate the bioinformatics data. Results: Autologous porcine AD-MSCs improved wound epithelialization and skin properties in comparison to control wounds. We identified 26 proteins upregulated in human AD-MSCs, including growth and angiogenic factors, chemokines and inflammatory cytokines. Pathway enrichment analysis highlighted cell signalling-associated pathways and immunomodulatory pathways. miRNA-target modelling revealed regulations related to genes encoding for 16 upregulated proteins. miR-155-5p was predicted to regulate Fibroblast growth factor 2 and 7, C-C motif chemokine ligand 2 and Vascular cell adhesion molecule 1. Transfecting human AD-MSCs cell line with anti-miR-155 showed transient gene silencing of the four proteins at 24h post-transfection. Discussion: This study proposes a positive miR-155-mediated gene regulation of key factors involved in wound healing. The study represents a promising approach for miRNA-based and cell-free regenerative treatment for difficult-to-heal wounds. The therapeutic potential of miR-155 and its identified targets should be further explored in-vivo.

DBL-Net: A dual-branch learning network with information from spatial and frequency domains for tumor segmentation and classification in breast ultrasound image

Breast cancer is a common malignancy, ranking as one of the most prevalent cancers among women globally. Improving treatment success rates for breast cancer are crucially dependent on early detection and accurate diagnosis. Ultrasound imaging, as a non-invasive and low-radiation imaging technique, plays a significant role in early breast cancer detection. However, due to the characteristics of fuzzy tumor boundaries and irregular shapes of the tumor, accurate breast tumor classification and segmentation remain challenging tasks. This paper introduces a novel approach for breast ultrasound image segmentation and classification tasks. Firstly, we study the potential value of frequency domain information in breast image analysis and propose the DBL-Net, a multi-task learning network for simultaneous tumor segmentation and tumor classification. Secondly, we customize a Spatial-Frequency Domain Feature Encoding module (S-FEM) to better encode and fuse spatial and frequency domain features of breast ultrasound images. Furthermore, we design a Representational Perception Enhancer (RPE) to improve the feature representation capabilities and prediction accuracy of the model. Finally, We have carried out a comprehensive series of tests on the BUS dataset, and the findings clearly indicate that our method outperforms the current state-of-the-art methods.

Spatial frequency domain imaging combining profile correction enables accurate real-time quantitative mapping of optical properties of apples

Spatial frequency domain imaging technology enables non-contact, wide-field quantitative analysis of optical properties in strong turbid media, thereby enhancing bruise detection in fruits based on changes in optical property values. However, precise and real-time measurement of the optical properties of curved biological materials is challenging due to the significant influence of tissue contours. This paper primarily presents a research study on real-time correction method based on the property that DC component diffuse reflectance (Rd_DC) and AC component diffuse reflectance (Rd_AC) are influenced by the contour trend of the tissue in a similar manner. The aim of this method is to eliminate the significant impact of sample contour angle on demodulation and enhance the detection of apple bruise. Sinusoidal illumination at a spatial frequency of 0.2 mm−1 was projected at 730 nm, with the experiments carried out on standard reflector, polytetrafluoroethylene sphere, and non-bruised and bruised apples. The results showed that, the relative error of the planar standard reflector decreased from the maximum value of 52.85–4.74%. The median of the Rd_AC for the polytetrafluoroethylene spherical standard, which fluctuated between 0.6 and 0.8, was corrected to the theoretical value of 1. For normal apples, the maximum fluctuation in the standard deviation of Rd_AC, after median filtering, reduced from 172.94% at 300×300 pixels to 18.69%. The boxplot of Rd_AC for bruised apples became smaller, with the lower fence being corrected from nearly 0–0.1750, which closely matched the theoretical value of 0.17. Additionally, the correlation of reduced scattering coefficient (μs′) in the ideal region of interest (100×100 pixels) remained at 0.9785 before and after correction, while other areas were corrected, making the bruising more pronounced. The correction method did not require additional experiments, with the consumed time in millisecond level.

Optical encryption by dynamically modulating the spatial frequency of light fields

Optical encryption has received increasing attention recently as information security is playing a crucial role in the modern information society. Particularly, the intensive investigation and rapid development of metasurfaces have significantly facilitated the research of optical encryption with enhanced security and increased capacity for information. Nevertheless, most metasurface encryption schemes still suffer from the challenge of dynamic modulation. Here, we demonstrate a novel dynamic optical encryption scheme in which information can be encrypted in light fields in a reconfigurable manner. Specifically, the spatial frequencies of optical images are utilized as information carriers and dynamically modulated for encrypting information. With the developed reconfigurable Fourier optics technique, various kinds of messages can be directly embedded in the spatial frequency domain of the ciphertext images and maintained with high fidelity. Importantly, information security and capacity can benefit from high-speed dynamic modulation with advanced coding techniques, an example of which has been demonstrated via exploiting the position, profile, and time degrees of freedom of spatial frequency. The proposed novel optical encryption scheme may pave the way for realizing high-performance information encryption systems.

Deep-learning approach to stratified reconstructions of tissue absorption and scattering in time-domain spatial frequency domain imaging.

The conventional optical properties (OPs) reconstruction in spatial frequency domain (SFD) imaging, like the lookup table (LUT) method, causes OPs aliasing and yields only average OPs without depth resolution. Integrating SFD imaging with time-resolved (TR) measurements enhances space-TR information, enabling improved reconstruction of absorption () and reduced scattering () coefficients at various depths. To achieve the stratified reconstruction of OPs and the separation between and , using deep learning workflow based on the temporal and spatial information provided by time-domain SFD imaging technique, while enhancing the reconstruction accuracy. Two data processing methods are employed for the OPs reconstruction with TR-SFD imaging, one is full TR data, and the other is the featured data extracted from the full TR data (, continuous-wave component, , mean time of flight). We compared their performance using a series of simulation and phantom validations. Compared to the LUT approach, utilizing full TR, and datasets yield high-resolution OPs reconstruction results. Among the three datasets employed, full TR demonstrates the optimal accuracy. Utilizing the data obtained from SFD and TR measurement techniques allows for achieving high-resolution separation reconstruction of and at different depths within 5mm.

Application of Multimedia Watermarking Technology in the Field of Information Security

This paper aims at comprehensively discussing the principle, methods, applications, challenges and future development of multimedia watermarking technology. In order to achieve this goal, this paper first introduces the basic concept and classification of multimedia watermarking technology, and then expounds in detail the core principles of spatial domain, frequency domain and mixed domain watermarking technology and the methods of watermark embedding and extraction. In terms of methods, this paper reveals their technical differences in robustness, invisibility and capacity through in-depth analysis of the characteristics of watermarking technology in different domains. In terms of application, the article shows the extensive application of multimedia watermarking technology in copyright protection, content authentication, covert communication and multimedia data integrity and authenticity verification through specific case analysis, highlighting its important value in the field of information security. Generally speaking, this paper systematically analyzes the principle, method and application of multimedia watermarking technology, which provides an important theoretical basis and practical guidance for further research and development in this field.

Mainlobe deceptive jammer suppression with DEPC-MIMO radar with joint transmit–receive design

This paper investigates the problem of mainlobe deceptive jammer suppression via joint transmit–receive design in a multiple-input multiple-output (MIMO) radar. At the design stage, a discrete element-pulse coding (DEPC) phase is implemented in both the slow-time pulses and transmit array antennas. After decoding and compensation of the delayed pulses, the true and false targets can be identified in the joint transmit–receive (JTR) spatial frequency domain. Furthermore, to eliminate the false targets, a data-dependent beamforming technique is adopted, where an optimization problem is constructed to maximize the output signal-to-interference-plus-noise ratio (SINR) by optimizing the DEPC coefficients and the weight vector of the receive filter in an alternating way. Specifically, two methods, including the Single Jammer Suppression (SJS)-Alternating Direction Method of Multipliers (ADMM) and Multiple Jammers Suppression (MJS)-Gradient Descent (GD) methods are developed for the cases of a single jammer and multiple jammers, respectively. A series of numerical results are utilized to verify the effectiveness of the proposed methods for mainlobe deceptive jammer suppression.

Extended Kalman filtering for enhancing a cyclic pattern-updating scheme of single-pixel dynamic fluorescence spatial frequency domain imaging: publisher's note.

This publisher's note contains a correction to Opt. Lett.48, 5443 (2023)10.1364/OL.495099.