Fourier Space Research Articles

Small-scale Dynamo with Nonzero Correlation Time

The small-scale dynamo is typically studied by assuming that the correlation time of the velocity field is zero. Some authors have used a smooth renovating flow model to study how the properties of the dynamo are affected by the correlation time being nonzero. Here, we assume the velocity is an incompressible Gaussian random field (which need not be smooth), and derive the lowest-order corrections to the evolution equation for the two-point correlation of the magnetic field in Fourier space. Using this, we obtain the evolution equation for the longitudinal correlation function of the magnetic field (M L ) in nonhelical turbulence, valid for arbitrary Prandtl number. The nonresistive terms of this equation do not contain spatial derivatives of M L of order greater than 2. We further simplify this equation in the limit of high Prandtl number, and find that the growth rate of the magnetic energy is much smaller than previously reported. Nevertheless, the magnetic power spectrum still retains the Kazantsev form at high Prandtl number.

Anisotropic regularization for sparsely sampled and noise-robust Fourier ptychography

Fourier ptychography (FP) is a powerful computational imaging technique that provides super-resolution and quantitative phase imaging capabilities by scanning samples in Fourier space with angle-varying illuminations. However, the image reconstruction in FP is inherently ill-posed, particularly when the measurements are noisy and have insufficient data redundancy in the Fourier space. To improve FP reconstruction in high-throughput imaging scenarios, we propose a regularized FP reconstruction algorithm utilizing anisotropic total variation (TV) and Tikhonov regularizations for the object and pupil functions, respectively. To solve this regularized FP problem, we formulate a reconstruction algorithm using the alternating direction method of multipliers and show that our approach successfully recovers high-quality images with sparsely sampled and/or noisy measurements. The results are quantitatively and qualitatively compared against various FP reconstruction algorithms to analyze the effect of regularization under harsh imaging conditions. In particular, we demonstrate the effectiveness of our method on the real experimental FP microscopy images, where the TV regularizer effectively suppresses the measurement noise while maintaining the edge information in the biological specimen and helps retrieve the correct amplitude and phase images even under insufficient sampling.

Physics-constrained machine learning for electrodynamics without gauge ambiguity based on Fourier transformed Maxwell’s equations

We utilize a Fourier transformation-based representation of Maxwell’s equations to develop physics-constrained neural networks for electrodynamics without gauge ambiguity, which we label the Fourier–Helmholtz–Maxwell neural operator method. In this approach, both of Gauss’s laws and Faraday’s law are built in as hard constraints, as well as the longitudinal component of Ampère–Maxwell in Fourier space, assuming the continuity equation. An encoder–decoder network acts as a solution operator for the transverse components of the Fourier transformed vector potential, A^⊥(k,t)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hat{{\ extbf {A}}}_\\perp ({\ extbf {k}}, t)$$\\end{document}, whose two degrees of freedom are used to predict the electromagnetic fields. This method was tested on two electron beam simulations. Among the models investigated, it was found that a U-Net architecture exhibited the best performance as it trained quicker, was more accurate and generalized better than the other architectures examined. We demonstrate that our approach is useful for solving Maxwell’s equations for the electromagnetic fields generated by intense relativistic charged particle beams and that it generalizes well to unseen test data, while being orders of magnitude quicker than conventional simulations. We show that the model can be re-trained to make highly accurate predictions in as few as 20 epochs on a previously unseen data set.

Fast normalized cross-correlation for template matching with rotations

Normalized cross-correlation is the reference approach to carry out template matching on images. When it is computed in Fourier space, it can handle efficiently template translations but it cannot do so with template rotations. Including rotations requires sampling the whole space of rotations, repeating the computation of the correlation each time.This article develops an alternative mathematical theory to handle efficiently, at the same time, rotations and translations. Our proposal has a reduced computational complexity because it does not require to repeatedly sample the space of rotations. To do so, we integrate the information relative to all rotated versions of the template into a unique symmetric tensor template -which is computed only once per template-. Afterward, we demonstrate that the correlation between the image to be processed with the independent tensor components of the tensorial template contains enough information to recover template instance positions and rotations. Our proposed method has the potential to speed up conventional template matching computations by a factor of several magnitude orders for the case of 3D images.

CAS3D: 3D quantitative morphometry on Second Harmonic Generation image volumes from single skeletal muscle fibers

The CAS3D image processing method intuitively applies a combination of Fourier space and real space 3D analysis algorithms to volumetric images of single skeletal muscle fiber Myosin II Second Harmonic Generation (SHG) XYZ image data. Our developed tool automatically quantifies the myofibrillar orientation in muscle samples by determining the cosine angle sum of intensity gradients in 3D (CAS3D) while determining the mean sarcomere length (SL) and sample orientation. The expected CAS3D values could be reproduced from ideal artificial data sets. Applied random noise in artificial images lowers the detected CAS3D value, and for noise levels below 20%, the correlation can be approximated by a linear function with a slope of −0.006 CAS3D/noise%. The deviations in SL and orientation detection were determined on ideal and noisy artificial data sets and were statistically indistinguishable from 0 (null hypothesis t-test P > 0.1). The software was applied to a previously published data set of single skeletal muscle fiber volumetric SHG image data from a rat intensive care unit (ICU) model of ventilator-induced diaphragm dysfunction (VIDD) with treatment regimens involving the small anti-inflammatory molecules BGP-15, vamorolone, or prednisolone. Our method reliably reproduced the results of the previous work and improved the standard deviation of the cosine angle sum detection in all sample groups from a mean of 0.03 to 0.008. This improvement is achieved by applying analysis algorithms to the whole volumetric images in 3D in contrast to the previously common method of slice-wise XY analysis.

The Uchuu-glam BOSS and eBOSS LRG lightcones: exploring clustering and covariance errors

ABSTRACT This study investigates the clustering and bias of Luminous Red Galaxies (LRG) in the BOSS-LOWZ, -CMASS, -COMB, and eBOSS samples, using two types of simulated lightcones: (i) high-fidelity lightcones from UchuuN-body simulation, employing SHAM technique to assign LRG to (sub)haloes, and (ii) 16 000 covariance lightcones from GLAM-UchuuN-body simulations, including LRG using HOD data from Uchuu. Our results indicate that Uchuu and glam lightcones closely replicate BOSS/eBOSS data, reproducing correlation function and power spectrum across scales from redshifts 0.2 to 1.0, from 2 to $150 \,h^{-1}\,\mathrm{Mpc}$ in configuration space, from 0.005 to $0.7\, h\,\mathrm{Mpc}^{-1}$ in Fourier space, and across different LRG stellar masses. Furthermore, comparing with existing MD-Patchy and EZmock BOSS/eBOSS lightcones based on approximate methods, our GLAM-Uchuu lightcones provide more precise clustering estimates. We identify significant deviations from observations within $20 \,h^{-1}\,\mathrm{Mpc}$ scales in MD-Patchy and EZmock, with our covariance matrices indicating that these methods underestimate errors by between 10 per cent and 60 per cent. Lastly, we explore the impact of cosmology on galaxy clustering. Our findings suggest that, given the current level of uncertainties in BOSS/eBOSS data, distinguishing models with and without massive neutrino effects on large-scale structure (LSS) is challenging. This paper highlights the Uchuu and GLAM-Uchuu simulations’ robustness in verifying the accuracy of Planck cosmological parameters, providing a strong foundation for enhancing lightcone construction in future LSS surveys. We also demonstrate that generating thousands of galaxy lightcones is feasible using N-body simulations with adequate mass and force resolution.

Frequency-Oriented Transformer for Remote Sensing Image Dehazing.

Remote sensing images are inevitably affected by the degradation of haze with complex appearance and non-uniform distribution, which remarkably affects the effectiveness of downstream remote sensing visual tasks. However, most current methods principally operate in the original pixel space of the image, which hinders the exploration of the frequency characteristics of remote sensing images, resulting in these models failing to fully exploit their representation ability to produce high-quality images. This paper proposes a frequency-oriented remote sensing dehazing Transformer named FOTformer, to explore information in the frequency domain to eliminate disturbances caused by haze in remote sensing images. It contains three components. Specifically, we developed a frequency-prompt attention evaluator to estimate the self-correlation of features in the frequency domain rather than the spatial domain, improving the image restoration performance. We propose a content reconstruction feed-forward network that captures information between different scales in features and integrates and processes global frequency domain information and local multi-scale spatial information in Fourier space to reconstruct the global content under the guidance of the amplitude spectrum. We designed a spatial-frequency aggregation block to exchange and fuse features from the frequency domain and spatial domain of the encoder and decoder to facilitate the propagation of features from the encoder stream to the decoder and alleviate the problem of information loss in the network. The experimental results show that the FOTformer achieved a more competitive performance against other remote sensing dehazing methods on commonly used benchmark datasets.

Real-Time Synthetic Aperture Radar Imaging with Random Sampling Employing Scattered Power Mapping.

A novel image-reconstruction method is proposed for the processing of data acquired at random spatial positions. The images are reconstructed and updated in real time concurrently with the measurements to produce an evolving image, the quality of which is continuously improving and converging as the number of data points increases with the stream of additional measurements. It is shown that the images converge to those obtained with data acquired on a uniformly sampled surface, where the sampling density satisfies the Nyquist limit. The image reconstruction employs a new formulation of the method of scattered power mapping (SPM), which first maps the data into a three-dimensional (3D) preliminary image of the target on a uniform spatial grid, followed by fast Fourier space image deconvolution that provides the high-quality 3D image.

A multitracer analysis for the eBOSS galaxy sample based on the effective field theory of large-scale structure

ABSTRACT We perform a multitracer full-shape analysis in Fourier space based on the effective field theory of large-scale structure (EFTofLSS) using the complete Sloan Digital Sky Survey IV (SDSS-IV) extended Baryon Oscillation Spectroscopic Survey (eBOSS) DR16 luminous red galaxy (LRG) and emission line galaxy (ELG) samples. We study in detail the impact of the volume projection effect and different prior choices when doing the full-shape analysis based on the EFTofLSS model. We show that adopting a combination of Jeffreys prior and Gaussian prior can mitigate the volume effect and avoid exploring unphysical regions in the parameter space at the same time, which is crucial when jointly analysing the eBOSS LRG and ELG samples. We validate our pipeline using 1000 eBOSS EZmocks. By performing a multitracer analysis on mocks with comparable footprints, we find that cosmological constraints can be improved by $\sim 10-35~{{\ \rm per\ cent}}$ depending on whether we assume zero stochastic terms in the cross power spectrum, which breaks the degeneracy and boosts the constraints on the standard deviation of matter density fluctuation σ8. Combining with the Big Bang Nucleosynthesis (BBN) prior and fixing the spectral tilt ns to Planck value, our multitracer full-shape analysis measures H0 = 70.0 ± 2.3 km s−1Mpc−1, $\Omega _m=0.317^{+0.017}_{-0.021}$, $\sigma _8=0.787_{-0.062}^{+0.055}$, and $S_8=0.809_{-0.078}^{+0.064}$, consistent with the Planck 2018 results. In particular, the constraint on σ8 is improved beyond that obtained from the single tracer analysis by 18 per cent, or by 27 per cent when assuming zero stochastic terms in the cross power spectrum.

Linear analytical model for the seismic response of a straight‐jointed shield tunnel

AbstractIn this study, the segment joint and ring joint of the lining of the straight‐jointed tunnel are simplified as an equivalent open cylindrical shell with a small central angle and an equivalent closed cylindrical shell with a small width, and the lining of the straight‐jointed tunnel is thus simplified as an equivalent continuous periodic shell (ECPS) described by the cylindrical shell theory. Since the ECPS lining is periodic along the longitudinal direction, the tunnel‐soil system can thus be treated as a periodic system, which is referred to as the periodic tunnel‐soil system (PTSS) in this study. Based on the proposed ECPS lining model, an analytical method for the tunnel with the ECPS lining (ECPS tunnel) under seismic waves is established in this study. By employing the periodicity condition for the PTSS as well as the wave function expansion method, the representation for the wave field in the soil is established. With the aforementioned cylindrical shell theory and Fourier series expansion method, the convolution type constitutive relation for the ECPS lining and the Fourier space equations of motion are derived. By using the soil‐lining continuity condition and aforementioned formulations for the ECPS lining and soil, the coupled Fourier space equations of motion for the PTSS are established, with which the response of the ECPS lining and scattered waves in the soil can be determined.

Dynamo action driven by precessional turbulence.

We reveal and analyze an efficient magnetic dynamo action due to precession-driven hydrodynamic turbulence in the local model of a precessional flow, focusing on the kinematic stage of this dynamo. The growth rate of the magnetic field monotonically increases with the Poincaré number Po, characterizing precession strength, and the magnetic Prandtl number Pm, equal to the ratio of viscosity to resistivity, for the considered ranges of these parameters. The critical Po_{c} for the dynamo onset decreases with increasing Pm. To understand the scale-by-scale evolution (growth) of the precession dynamo and its driving processes, we perform spectral analysis by calculating the spectra of magnetic energy and of different terms in the induction equationin Fourier space. To this end, we decompose the velocity field of precession-driven turbulence into two-dimensional (2D) vortical and three-dimensional (3D) inertial wave modes. It is shown that the dynamo operates across a broad range of scales and exhibits a remarkable transition from a primarily vortex-driven regime at lower Po to a more complex regime at higher Po where it is driven jointly by vortices, inertial waves, and the shear of the background precessional flow. Vortices and shear drive the dynamo mostly at large scales comparable to the flow system size, and at intermediate scales, while at smaller scales it is mainly driven by inertial waves. This study can be important not only for understanding the magnetic dynamo action in precession-driven flows, but also in a general context of flows where vortices emerge and govern the flow dynamics and evolution.

Suppression of lift-up effect in the 3D Boussinesq equations around a stably stratified Couette flow

In this paper, we establish linear enhanced dissipation results for the three-dimensional Boussinesq equations around a stably stratified Couette flow, in the viscous and thermally diffusive setting. The dissipation rates are faster compared to those observed in the homogeneous Navier-Stokes equations, in light of the interplay between velocity and temperature, driven by buoyant forces. Our approach involves introducing a change of variables grounded in a Fourier space symmetrization framework. This change elucidates the energy structure inherent in the system. Specifically, we handle non-streaks modes through an augmented energy functional, while streaks modes are amenable to explicit solutions. This explicit treatment reveals the oscillatory nature of shear modes, providing the elimination of the well-known three-dimensional instability mechanism known as the “lift-up effect”.

Pillar data-acquisition strategies for cryo-electron tomography of beam-sensitive biological samples.

For cryo-electron tomography (cryo-ET) of beam-sensitive biological specimens, a planar sample geometry is typically used. As the sample is tilted, the effective thickness of the sample along the direction of the electron beam increases and the signal-to-noise ratio concomitantly decreases, limiting the transfer of information at high tilt angles. In addition, the tilt range where data can be collected is limited by a combination of various sample-environment constraints, including the limited space in the objective lens pole piece and the possible use of fixed conductive braids to cool the specimen. Consequently, most tilt series are limited to a maximum of ±70°, leading to the presence of a missing wedge in Fourier space. The acquisition of cryo-ET data without a missing wedge, for example using a cylindrical sample geometry, is hence attractive for volumetric analysis of low-symmetry structures such as organelles or vesicles, lysis events, pore formation or filaments for which the missing information cannot be compensated by averaging techniques. Irrespective of the geometry, electron-beam damage to the specimen is an issue and the first images acquired will transfer more high-resolution information than those acquired last. There isalso an inherent trade-off between higher sampling in Fourier space and avoiding beam damage to the sample. Finally, the necessity of using a sufficient electron fluence to align the tilt images means that this fluence needs to be fractionated across a small number of images; therefore, the order of data acquisition is also a factor to consider. Here, an n-helix tilt scheme is described and simulated which uses overlapping and interleaved tilt series to maximize the use of a pillar geometry, allowing the entire pillar volume to be reconstructed asa single unit. Three related tilt schemes are also evaluated that extend the continuous and classic dose-symmetric tilt schemes for cryo-ET to pillar samples to enable the collection of isotropic information across all spatial frequencies. Afourfold dose-symmetric scheme is proposed which provides a practical compromise between uniform information transfer and complexity of data acquisition.

Vector wave dark matter and terrestrial quantum sensors

(Ultra)light spin-1 particles — dark photons — can constitute all of dark matter (DM) and have beyond Standard Model couplings. This can lead to a coherent, oscillatory signature in terrestrial detectors that depends on the coupling strength. We provide a signal analysis and statistical framework for inferring the properties of such DM by taking into account (i) the stochastic and (ii) the vector nature of the underlying field, along with (iii) the effects due to the Earth's rotation. Owing to equipartition, on time scales shorter than the coherence time the DM field vector typically traces out a fixed ellipse. Taking this ellipse and the rotation of the Earth into account, we highlight a distinctive three-peak signal in Fourier space that can be used to constrain DM coupling strengths. Accounting for all three peaks, we derive latitude-independent constraints on such DM couplings, unlike those stemming from single-peak studies. We apply our framework to the search for ultralight B - L DM using optomechanical sensors, demonstrating the ability to delve into previously unprobed regions of this DM candidate's parameter space.

Phase-space entropy cascade and irreversibility of stochastic heating in nearly collisionless plasma turbulence.

We consider a nearly collisionless plasma consisting of a species of "test particles" in one spatial and one velocity dimension, stirred by an externally imposed stochastic electric field-a kinetic analog of the Kraichnan model of passive advection. The mean effect on the particle distribution function is turbulent diffusion in velocity space-known as stochastic heating. Accompanying this heating is the generation of fine-scale structure in the distribution function, which we characterize with the collisionless (Casimir) invariant C_{2}∝∫∫dxdv〈f^{2}〉-a quantity that here plays the role of (negative) entropy of the distribution function. We find that C_{2} is transferred from large scales to small scales in both position and velocity space via a phase-space cascade enabled by both particle streaming and nonlinear interactions between particles and the stochastic electric field. We compute the steady-state fluxes and spectrum of C_{2} in Fourier space, with k and s denoting spatial and velocity wave numbers, respectively. In our model, the nonlinearity in the evolution equationfor the spectrum turns into a fractional Laplacian operator in k space, leading to anomalous diffusion. Whereas even the linear phase mixing alone would lead to a constant flux of C_{2} to high s (towards the collisional dissipation range) at every k, the nonlinearity accelerates this cascade by intertwining velocity and position space so that the flux of C_{2} is to both high k and high s simultaneously. Integrating over velocity (spatial) wave numbers, the k-space (s-space) flux of C_{2} is constant down to a dissipation length (velocity) scale that tends to zero as the collision frequency does, even though the rate of collisional dissipation remains finite. The resulting spectrum in the inertial range is a self-similar function in the (k,s) plane, with power-law asymptotics at large k and s. Our model is fully analytically solvable, but the asymptotic scalings of the spectrum can also be found via a simple phenomenological theory whose key assumption is that the cascade is governed by a "critical balance" in phase space between the linear and nonlinear timescales. We argue that stochastic heating is made irreversible by this entropy cascade and that, while collisional dissipation accessed via phase mixing occurs only at small spatial scales rather than at every scale as it would in a linear system, the cascade makes phase mixing even more effective overall in the nonlinear regime than in the linear one.

Reduced Geostatistical Approach With a Fourier Neural Operator Surrogate Model for Inverse Modeling of Hydraulic Tomography

AbstractIn this study, we propose a new approach for inverse modeling of hydraulic tomography (HT) using the Fourier neural operator (FNO) as a surrogate forward model. FNO is a deep learning model that directly parameterizes the integral kernel in Fourier space to learn solution operators for parametric partial differential equations (PDEs). We trained a highly accurate FNO to learn the solution operators of PDEs in HT, which can efficiently generate multiple channels of hydraulic head fields corresponding to specific pumping tests in new parameter fields through a single forward pass. The trained FNO surrogate model is integrated with the reduced geostatistical approach (RGA) to provide a powerful tool, named RGA‐FNO, for inverse modeling of Gaussian random fields. RGA utilizes principal components to effectively reduce problem dimensions and encode geostatistical information. FNO benefits from deep learning automatic differentiation, enabling efficient backpropagation of gradients during inverse modeling. Our results show that RGA‐FNO can efficiently produce satisfactory estimations for random transmissivity fields with an exponential covariance function, which is non‐differentiable and visually non‐smooth. The RGA‐FNO application on steady‐state multi‐well HT is better than the single‐well transient pumping test for inverse modeling. The data required for inverse modeling applications of RGA‐FNO increases with the variance of the random transmissivity fields. FNO and other neural operator models have the potential to play an important role in groundwater modeling, especially in inverse modeling and experimental design, which often requires a large number of forward simulations.

All-dielectric super-lattice metasurfaces with fivefold spatial resolution enhancement for structured illumination microscopy.

Structured illumination microscopy (SIM) is a promising imaging technique for high-resolution imaging with a wide field of view. Although a periodic nanostructure is a versatile platform for engineering the spatial frequency of structured illumination patterns in SIM, challenges remain, including artifacts from Fourier space gaps. We designed an all-dielectric super-lattice metasurface (ADSLM) to generate structured illumination patterns with enhanced spatial frequency and broadened spatial frequency coverage with no intermediate frequency gaps. Our numerical simulations reveal that ADSLM-based image reconstruction is capable of producing high-contrast, artifact-free images, resulting in enhanced spatial resolution up to 5.7-fold for coherent SIM at 450 nm. Our results show that the ADSLM-SIM technique may facilitate high-resolution imaging using CMOS-compatible substrates, offering potential for compact miniaturized imaging applications.

On the Cauchy problem for acoustic waves in hereditary fluids: Decay properties and inviscid limits

This paper considers the viscous/inviscid Moore–Gibson–Thompson (MGT) equations with memory of type I in the whole space . For one thing, associating with a new condition on initial data, we derive the optimal estimates and the optimal leading term of the acoustic velocity potential for large time, where we analyze different contributions from viscous, thermally relaxing, as well as hereditary fluids on large time asymptotic behavior for the acoustic waves models. For another, by using the multiscale analysis and energy methods in the Fourier space, we demonstrate the inviscid limits (i.e., as the diffusivity of sound tends to zero), which match our Wentzel‐Kramers‐Brillouin (WKB) expansion of the solution. Finally, we give a further application of our results on large time behavior for the nonlinear Jordan‐MGT equation in viscous hereditary fluids.

Internal waves generated from asymmetric topographies

Previous experimental and theoretical research on tidally generated internal waves over oceanic topography has often used symmetric topographic profiles. However, due to the complex nature of real ocean topography, the effect of asymmetry cannot be overlooked. Studies have shown that topographic complexities, including asymmetry, can have a significant impact on internal wave generation, but topographic asymmetry has not yet been explored in a systematic manner. This work presents a comparison of tidally generated internal waves from nine different two-dimensional asymmetric topographies, consisting of a steeper Gaussian curve on one side, and a wider Gaussian curve on the other. The amplitude of the wider curve varies from 60% of the steeper curve to its equivalent. Two oscillation frequencies are tested. Kinetic energy density in tidally generated internal waves on each side of the topography is compared qualitatively and quantitatively, in both physical and Fourier space. When compared to similar symmetric topographies, waves generated by the asymmetric topographies varied distinctly in both magnitude and wavenumber distribution of kinetic energy density. Waves on the relatively steep side of the topography contain up to 50% more kinetic energy than on the wider side. However, there is very little kinetic energy at the higher wavenumbers associated with the steeper topography. Instead, the internal wavefield is dominated by lower wavenumbers, 50%–90% of the kinetic energy density is contained in wavelengths corresponding to the wider side of the topography. Decreasing the amplitude of the wider curve does not make an appreciable difference in the kinetic energy density spectrum. Thus, the differences quantified here are due solely to changing slope and show the effect which relatively slight asymmetry has on internal wave generation.

A Novel Energy-Efficient Coding Based on Coordinated Group Signal Transformation for Image Compression in Energy-Starved Systems

This paper introduces a new method for compressing images in energy-starved systems, like satellites, unmanned aerial vehicles, and Internet of Things nodes, which is based on coordinated group signal transformation (CGST). The transformation algorithm is a type of difference coding and may be classified as a non-transform-based image-compression method. CGST simplifies the difference signal conversion scheme using a single group codec for all signals. It considers color channels as correlated signals of a multi-channel communication system. The performance of CGST was evaluated using a dataset of 128 × 128 pixel images from satellite remote sensing systems. To adapt CGST to image compression, some modifications were introduced to the algorithm, such as fixing the procedure of the difference signals calculation to prevent any “zeroing” of brightness and supplementing the group codec with a neural network to improve the quality of restored images. The following types of neural networks were considered: fully connected, recurrent, convolution, and convolution in the Fourier space. Based on the simulation results, fully connected neural networks are recommended if the goal is to minimize processing delay time. These networks have a response time of 13 ms. Conversely, suppose the priority is to improve quality in cases where delays are not critical. In that case, convolution neural networks in the Fourier space should be used, providing an image compression ratio of 4.8 with better minimum square error and Mikowsky norm values than JPEG with the same compression ratio.