High Spatial Frequency Components Research Articles

Denoising low-field MR images with a deep learning algorithm based on simulated data from easily accessible open-source software

In this study, we introduce a denoising method aimed at improving the contrast ratio in low-field MRI (LFMRI) using an advanced 3D deep convolutional residual network model. Our approach employs synthetic brain imaging datasets that closely mimic the contrast and noise characteristics of LFMRI scans, addressing the limitation of available in-vivo LFMRI datasets for training deep learning models. In the simulation data, the Relative Contrast Ratio (RCR) increased, and similar improvements were observed in the in-vivo data across different imaging conditions. Comparative evaluations demonstrate that our model performs better than the widely used non-deep learning method, BM4D, in enhancing RCR and maintaining high spatial frequency components in in-vivo data.

Surface microtopography evolution of monocrystalline silicon in chemical mechanical polishing

Chemical mechanical polishing (CMP) is a widely utilized technique for achieving ultra-smooth surfaces, yet a comprehensive understanding of the surface microtopography evolution remains elusive due to the intricate chemical and mechanical interactions inherent in chemical mechanical polishing. Accordingly, this study explores the evolution law of different spatial frequency features of surface microtopography of monocrystalline silicon by analyzing the changes in the power spectral density (PSD) curve. More importantly, the evolution mechanism of the chemical mechanical polishing surface micromorphology is revealed through the analysis of the power spectral density under different mechanical and chemical conditions. The results emphasize the noticeable impact of both mechanical and chemical actions on the evolution of different spatial frequency features in surface microtopography. The mechanical action of a large particle, less likely to contact the valley region with a small curvature radius, enhances the smoothing speed of high-spatial frequency roughness. Moreover, the mechanical action of polishing pad demonstrates a greater efficiency in smoothing mid-spatial frequency roughness when utilizing a hard pad. This is attributed to the limited impact of pad hardness on the removal depth of single particles within the reaction layer, rendering it less significant for high-spatial frequency roughness. Upon elevating the chemical reaction rate, a notable acceleration in the reduction of roughness in both mid- and high-spatial frequency regions is observed. Furthermore, insights derived from molecular dynamics (MD) simulations of monocrystalline silicon and quartz glass show that the manner of surface atom removal, whether through single atom removal or cluster removal, exerts a significant effect on the final high-spatial frequency components of the power spectral density. This study contributes valuable insights into the intricate formation mechanism of a smooth surface in chemical mechanical polishing.

Deep EEG source localization via EMD-based fMRI high spatial frequency.

Brain imaging with a high-spatiotemporal resolution is crucial for accurate brain-function mapping. Electroencephalography (EEG) and functional Magnetic Resonance Imaging (fMRI) are two popular neuroimaging modalities with complementary features that record brain function with high temporal and spatial resolution, respectively. One popular non-invasive way to obtain data with both high spatial and temporal resolutions is to combine the fMRI activation map and EEG data to improve the spatial resolution of the EEG source localization. However, using the whole fMRI map may cause spurious results for the EEG source localization, especially for deep brain regions. Considering the head's conductivity, deep regions' sources with low activity are unlikely to be detected by the EEG electrodes at the scalp. In this study, we use fMRI's high spatial-frequency component to identify the local high-intensity activations that are most likely to be captured by the EEG. The 3D Empirical Mode Decomposition (3D-EMD), a data-driven method, is used to decompose the fMRI map into its spatial-frequency components. Different validation measurements for EEG source localization show improved performance for the EEG inverse-modeling informed by the fMRI's high-frequency spatial component compared to the fMRI-informed EEG source-localization methods. The level of improvement varies depending on the voxels' intensity and their distribution. Our experimental results also support this conclusion.

Quantum JPEG

The joint photographic expert group algorithm compresses a digital image by filtering its high spatial-frequency components. Similarly, we introduce a quantum algorithm that uses the quantum Fourier transform to discard the high spatial-frequency qubits of an image, downsampling it to a lower resolution. This allows one to capture, compress, and send images even with limited quantum resources for storage and communication. We show under which conditions this protocol is advantageous with respect to its classical counterpart.

Structured illumination contrast transfer function for high resolution quantitative phase imaging.

We report a sub-diffraction resolution imaging of non-fluorescent samples through quantitative phase imaging. This is achieved through a novel application of structured illumination microscopy (SIM), a super-resolution imaging technique established primarily for fluorescence microscopy. Utilizing our contrast transfer function formalism with SIM, we extract the high spatial frequency components of the phase profile from the defocused intensity images, enabling the reconstruction of a quantitative phase image with a frequency spectrum that surpasses the diffraction limit imposed by the imaging system. Our approach offers several advantages including a deterministic, phase-unwrapping-free algorithm and an easily implementable, non-interferometric setup. We validate the proposed technique for high-resolution phase imaging through both simulation and experimental results, demonstrating a two-fold enhancement in resolution. A lateral resolution of 0.814 µm is achieved for the phase imaging of human cheek cells using a 0.42 NA objective lens and an illumination wavelength of 660 nm, highlighting the efficacy of our approach for high-resolution quantitative phase imaging.

Spatial modulation of scalable nanostructures by combining maskless plasmonic lithography and grayscale-patterned strategy.

Nanolithography techniques providing good scalability and feature size controllability are of great importance for the fabrication of integrated circuits (IC), MEMS/NEMS, optical devices, nanophotonics, etc. Herein, a cost-effective, easy access, and high-fidelity patterning strategy that combines the high-resolution capability of maskless plasmonic lithography with the spatial morphology controllability of grayscale lithography is proposed to generate the customized pattern profile from microscale to nanoscale. Notably, the scaling effect of gap size in plasmonic lithography with a contact bowtie-shaped nanoaperture (BNA) is found to be essential to the rapid decay characteristics of an evanescent field, which leads to a wide energy bandwidth of the required optimal dose to record pattern in per unit volume, and hence, achieves the volumetrically scalable control of the photon energy deposition in the space more precisely. Based on the proper calibration and cooperation of pattern width and depth, a grayscale-patterned map is designed to compensate for the dose difference caused by the loss of the high spatial frequency component of the evanescent field. A Lena nanostructure with varying feature sizes by spatially modulating the exposure dose distribution was successfully demonstrated, and besides, we also successfully generated a microlens array (MLA) with high uniformity. The practical patterning method makes plasmonic lithography significant in the fabrication of functional nanostructures with high performance, including metasurfaces, plasmonics, and optical imaging systems.

Speckle Noise-Free Interconnective Holographic Projection

Generally, speckle noise is regarded as unavoidable in holographic projection, and it results from unexpected high spatial frequency components of diffracted light at the sharp edge of pixel openings in a spatial light modulator. Speckle noise typically reduces image contrast and degrades the image quality of the holographic projection. In this study, we propose a novel holographic optical interconnection method free of speckle noise in holographic projection. This optical interconnection is achieved by using a holographic optical element (HOE). The HOE is designed to reconstruct Gaussian beams with low divergence. These Gaussian beams become points which form target images at desired depths. Since the Gaussian beam from the HOE does not share the same position with other Gaussian beams, there is no interference at the projection image. Therefore, the image is composed of the points from the Gaussian beams and there is no reason for unexpected high spatial frequency noise to appear on the image. In this paper, we fabricate the HOE, produced with our specially manufactured hologram printer, where the directions of two Gaussian beams with low divergence are controlled by goniometers. We experimentally demonstrated a speckle noise-free interconnective holographic projection. Two images are successfully formed at different depths by optically connecting two points in pairs.

Angular dependence of spatial frequency modulation in diffusion media

An optical field will undergo coherent diffusion when it is mapped into thermal-motioned atoms, e.g., in a slow or storage light process. As was demonstrated before, such diffusion effect is equivalent to a spatial low-pass filter attenuating the high spatial frequency (SF) components of the optical field. Here, employing electromagnetically induced transparency (EIT) based light storage in hot atomic vapor, we demonstrate that the angular deviation between the control and probe beams could be utilized as a degree of freedom to modulate the SF of the probe beam. The principle is to change the diffusion-induced low-pass filter into a band-pass filter, whose SF response can be tuned by varying the direction and magnitude of the angular deviation. Transverse multimode light fields, such as optical images and Laguerre-Gaussian modes are utilized to study such SF modulation. Our findings could be broadly applied to the fields of quantum information processing, all-optical image manipulation and imaging through diffusive media.

Constrained deconvolution from wavefront sensing using the frozen flow hypothesis and complex wavelet regularization.

Deconvolution from wavefront sensing (DWFS) is a high-performance image restoration technique designed to compensate for atmospheric turbulence-induced wavefront distortions. It uses simultaneously recorded short-exposure images of the object and high cadence wavefront sensor (WFS) data to estimate both the wavefronts and the object. Conventional DWFS takes no account of the temporal correlations in WFS data, which limits the reconstruction of high-spatial frequency components of wavefront distortion and then the recovery of the object. This paper takes the frozen flow hypothesis (FFH) to model the temporal evolution of atmospheric turbulence. Under this assumption, a joint estimation is performed in a Bayesian framework to simultaneously estimate the object and the turbulence phases with strict constraints imposed by WFS data and the FFH. It takes into account the temporal correlations in WFS data as well as the available a priori knowledge about the object and turbulence phases. Taking advantage of the sparse analysis prior of the object in the wavelet domain, a sparse regularization of the object based on the 2D dual-tree complex wavelet transform is proposed. Numerical experiments show that the proposed method is robust and effective for high-resolution image restoration in different seeing conditions.

Evaluation of Noise Properties at Nonuniformity Area and Resolution Properties of CT Image Using Iterative Reconstruction Method

The purpose of this study was to investigate the resolution property and the noise properties at the nonuniformity area in the slice plane of iterative reconstruction (IR)-CT image. CT images of a phantom with nonuniformity areas including multiple contrast (medium, high, and ultra-high contrast) signals were acquired at various scan dose conditions and reconstructed with different iterative intensity levels. The noise properties at the nonuniformity and the uniformity areas were evaluated by measuring normalized noise power spectra (nNPSs) using subtracted images from sequential scanning data under the same scan conditions. We investigated the relationship between the noise properties and the resolution properties evaluated by measuring task transfer function (TTF) using multiple contrast signals before the subtraction. There was a correlation between the nNPS at the nonuniformity area and the TTF because the nNPS values at high spatial frequency were increased with superior TTF (higher dose, mild iterative intensity, and higher contrast level). The differences in the high spatial frequency component of the nNPSs among each task were decreased with the inferior TTF tasks. We conclude that the noise properties in the slice plane at the nonuniformity area and resolution properties of the IR-CT image were correlated similar to image quality properties of the linear imaging system due to the dependence of the nNPSs curve on the TTF value under each task.

Three-Dimensional Transfer Functions of Interference Microscopes

Three-dimensional transfer functions (3D TFs) are generally assumed to fully describe the transfer behavior of optical topography measuring instruments such as coherence scanning interferometers in the spatial frequency domain. Therefore, 3D TFs are supposed to be independent of the surface under investigation resulting in a clear separation of surface properties and transfer characteristics. In this paper, we show that the 3D TF of an interference microscope differs depending on whether the object is specularly reflecting or consists of point scatterers. In addition to the 3D TF of a point scatterer, we will derive an analytical expression for the 3D TF corresponding to specular surfaces and demonstrate this as being most relevant in practical applications of coherence scanning interferometry (CSI). We additionally study the effects of temporal coherence and disclose that in conventional CSI temporal coherence effects dominate. However, narrowband light sources are advantageous if high spatial frequency components of weak phase objects are to be resolved, whereas, for low-frequency phase objects of higher amplitude, the temporal coherence is less affecting. Finally, we present an approach that explains the different transfer characteristics of coherence peak and phase detection in CSI signal analysis.

Investigation of the morphological and fractal behavior at nanoscale of patterning lines by scratching in an atomic force microscope.

In this work, the topographical effect of the scratching trajectory and the feed direction on the formation of lithographed lines on the (001) InP surface was investigated using an atomic force microscope (AFM) tip-based nanomachining approach. Nanoscratching tests were carried out using the sharp face of a diamond AFM tip in contact mode. From the topographic maps obtained by AFM, several morphological and fractal parameters were obtained and analyzed. Surface morphology presented a surface smoothing for surfaces with scratches produced in [011] and [001] directions. The height parameters confirmed this behavior because scratches in [001] direction exhibited lower roughness. Moreover, this scratch direction promoted the height distribution most symmetrical and platykurtic. The other morphological parameters revealed that this direction provided a more irregular surface (smaller Smc and Sxp ), peak distribution, denser and pointed, smaller portion of material in the core, less deep furrows, higher spatial frequency components, and high isotropy. Fractal parameters revealed that FRE90 has the highest spatial complexity, it is dominated by higher spatial frequencies, and has the lowest surface percolation. Furthermore, all samples exhibited high topographic uniformity.

Blind Super-Resolution Approach for Exploiting Illumination Variety in Optical-Lattice Illumination Microscopy

Optical-lattice illumination patterns help in pushing high spatial frequency components of the sample into the optical transfer function of a collection microscope. However, exploiting these high-frequency components require precise knowledge of illumination if reconstruction approaches similar to structured illumination microscopy are employed. Here, we present an alternate blind reconstruction approach that can provide super-resolution without the requirement of extra frames. For this, the property of exploiting temporal fluctuations in the sample emissions using “multiple signal classification algorithm” is extended aptly toward using spatial fluctuation of phase-modulated lattice illuminations for super-resolution. The super-resolution ability is shown for sinusoidal and multiperiodic lattice with approximately 3- and 6-fold resolution enhancements, respectively, over the diffraction limit.

Complex wavelet filter improves FLIM phasors for photon starved imaging experiments.

Fluorescence lifetime imaging microscopy (FLIM) with phasor analysis provides easy visualization and analysis of fluorophores' lifetimes which is valuable for multiple applications including metabolic imaging, STED imaging, FRET imaging and functional imaging. However, FLIM imaging typically suffers from low photon budgets, leading to unfavorable signal to noise ratios which in many cases prevent extraction of information from the data. Traditionally, median filters are applied in phasor analysis to tackle this problem. This unfortunately degrades high spatial frequency FLIM information in the phasor analysis. These high spatial frequency components are typically edges of features and puncta, which applies to membranes, mitochondria, granules and small organelles in a biological sample. To tackle this problem, we propose a filtering strategy with complex wavelet filtering and Anscombe transform for FLIM phasor analysis. This filtering strategy preserves fine structures and reports accurate lifetimes in photon starved FLIM imaging. Moreover, this filter outperforms median filters and makes FLIM imaging with lower laser power and faster imaging possible.

Spatial Frequency Effective for Increasing Perceived Glossiness by Contrast Enhancement.

It has been suggested that luminance edges in retinal images are potential cues for glossiness perception, particularly when the perception relies on low-luminance specular regions. However, a previous study has shown only statistical correlations between luminance edges and perceived glossiness, not their causal relations. Additionally, although specular components should be embedded at various spatial frequencies depending on the micro-roughness on the object surface, it is not well understood what spatial frequencies are essential for glossiness perception on objects with different micro-roughness. To address these issues, we examined the impact of a sub-band contrast enhancement on the perceived glossiness in the two conditions of stimuli: the Full condition where the stimulus had natural specular components and the Dark condition where it had specular components only in dark regions. Object images with various degrees of surface roughness were generated as stimuli, and their contrast was increased in various spatial-frequency sub-bands. The results indicate that the enhancement of the sub-band contrast can significantly increase perceived glossiness as expected. Furthermore, the effectiveness of each spatial frequency band depends on the surface roughness in the Full condition. However, effective spatial frequencies are constant at a middle spatial frequency regardless of the stimulus surface roughness in the Dark condition. These results suggest that, for glossiness perception, our visual system depends on specular-related information embedded in high spatial frequency components but may change the dependency on spatial frequency based on the surface luminance to be judged.

Nanoflare Theory Revisited

Abstract At any scale l in the turbulent inertial range, the magnetic field can be divided up into a large-scale component and a small-scale, high spatial frequency component which undergoes magnetic reversals. Such local reconnections, i.e., on any inertial scale l, seem to be an inseparable part of magnetohydrodynamic (MHD) turbulence, whose collective outcome can lead to global reconnection with a rate independent of the small-scale physics dominant at dissipative scales. We show that this picture, known as stochastic reconnection, is intimately related to nanoflare theory, proposed long ago to explain solar coronal heating. We argue that, due to stochastic flux freezing, a generalized version of magnetic flux freezing in turbulence, the field follows the flow in a statistical sense. Turbulence bends and stretches the field, increasing its spatial complexity. Strong magnetic shears associated with such a highly tangled field can trigger local reversals and field annihilations on a wide range of inertial scales which convert magnetic energy into kinetic and thermal energy. The former may efficiently enhance turbulence and the latter heat generation. We support this theoretical picture using scaling laws of MHD turbulence and also recent analytical and numerical studies which suggest a statistical correlation between magnetic spatial complexity and energy dissipation. Finally, using an MHD numerical simulation, we show that the time evolution of the magnetic complexity is statistically correlated with the rate of kinetic energy injection and/or magnetic-to-thermal energy conversion, in agreement with our proposed theoretical picture.

Power spectral analysis of surface microtopography formed in CW Laser surface texturing

Laser surface texturing (LST) has shown immense promise in modifying the physical as well as interactive properties of the surfaces. Understanding the surface microtopography generated during LST provides key knowledge on developing desirable surfaces for different technologies. The work focuses on determining the range of frequency components present in the microtopography when processed at different parameters, such as beam diameter (BD), scanning speed (SS), and beam overlap (BO). Power spectral density (PSD) is utilized to evaluate the intensity of each spatial frequency and fitting models are applied to quantify their contribution to the overall microtopography. The experiments were performed on titanium alloy Ti6Al4V using a continuous watt fiber laser at constant power. The surface microtopography differs when processed under different conditions. The microtopography contains low and high spatial frequency components distributed along both the scan and overlap direction. The PSD analysis reveals the increase in high spatial frequency features when BD and SS are increased. Conversely, the growth of spatial features is observed with an increase in BO reducing the dominance of high spatial frequencies. With the increase in BD, the energy density decreases which reduces the growth of spatial features inducing increased contribution of high spatial frequency content noticeable by upward curvature in the PSD. An increase in SS causes rapid laser motion to affect the microtopography along the scan direction. The increase in BO leads to the enhanced overlapping between successive passes causing remelting and growth of previously formed microtopography and increasing the contribution of low spatial frequency content in the microtopography. The fitting model parameters from ABC at low spatial frequency and Fractal at high frequency provide the quantitative reasoning for the observed trend. Power spectral analysis reveals significant information about the surface microtopography formed during LST and accurate quantification of the PSD may help numerical models to fine-tune the surface features according to the desired functionality.

Inferring Point Cloud Quality via Graph Similarity.

Objective quality estimation of media content plays a vital role in a wide range of applications. Though numerous metrics exist for 2D images and videos, similar metrics are missing for 3D point clouds with unstructured and non-uniformly distributed points. In this paper, we propose [Formula: see text]-a metric to accurately and quantitatively predict the human perception of point cloud with superimposed geometry and color impairments. Human vision system is more sensitive to the high spatial-frequency components (e.g., contours and edges), and weighs local structural variations more than individual point intensities. Motivated by this fact, we use graph signal gradient as a quality index to evaluate point cloud distortions. Specifically, we first extract geometric keypoints by resampling the reference point cloud geometry information to form an object skeleton. Then, we construct local graphs centered at these keypoints for both reference and distorted point clouds. Next, we compute three moments of color gradients between centered keypoint and all other points in the same local graph for local significance similarity feature. Finally, we obtain similarity index by pooling the local graph significance across all color channels and averaging across all graphs. We evaluate [Formula: see text] on two large and independent point cloud assessment datasets that involve a wide range of impairments (e.g., re-sampling, compression, and additive noise). [Formula: see text] provides state-of-the-art performance for all distortions with noticeable gains in predicting the subjective mean opinion score (MOS) in comparison with point-wise distance-based metrics adopted in standardized reference software. Ablation studies further show that [Formula: see text] can be generalized to various scenarios with consistent performance by adjusting its key modules and parameters. Models and associated materials will be made available at https://njuvision.github.io/GraphSIM or http://smt.sjtu.edu.cn/papers/GraphSIM.

Do Laguerre–Gaussian beams recover their spatial properties after all obstacles?

It has been known for some time that Bessel–Gaussian beams and their associated families self-heal after encountering obstacles. Recently, it has been shown theoretically and experimentally that radial mode Laguerre–Gaussian (LG) beams would likewise self-heal. In this work, we show that the self-healing occurs after opaque disks but not after circular apertures. We put forward arguments to explain this and perform key experiments, assessing the impact of obstructions on the usual intensity reconstruction, as well as the focal shift effect and the beam propagation factor, $$M^2$$ . In addition, these results are supported by a physical interpretation based on the Abbe experiment of spatial frequency filtering, highlighting that the self-healing process requires a high-spatial frequency component to the field, i.e., LG beams self-heal when modulated by a low spatial frequency filter (opaque disk) but not when modulated by a high-spatial frequency filter (circular aperture). We believe that this work will contribute significantly to the field of laser beam propagation through obstacles.

Manipulation of glossiness perception by contrast enhancement of high spatial frequency components

Manipulation of glossiness perception by contrast enhancement of high spatial frequency components