Filtering In Fourier Domain Research Articles

High-speed spatially re-modulated structured illumination microscopy.

Structured illumination microscopy (SIM) allows non-invasive visualization of nanoscale subcellular structures. However, image acquisition and reconstruction become the bottleneck to further improve the imaging speed. Here, we propose a method to accelerate SIM imaging by combining the spatial re-modulation principle with Fourier domain filtering and using measured illumination patterns. This approach enables high-speed, high-quality imaging of dense subcellular structures using a conventional nine-frame SIM modality without phase estimation of the patterns. In addition, seven-frame SIM reconstruction and additional hardware acceleration further improve the imaging speed using our method. Furthermore, our method is also applicable to other spatially uncorrelated illumination patterns, such as distorted sinusoidal, multifocal, and speckle patterns.

Weighted convolutions in the quadratic-phase Fourier domains: Product theorems and applications

Convolution and product operations play a pivotal role in different aspects of signal and image processing, including quantum mechanics, sampling, filter designing and so on. In this article, we formulate two types of novel weighted convolutions, Type-I and Type-II, in the framework of the quadratic-phase Fourier transforms. Besides presenting the efficacy of the weighted convolutions of Type-I via the well-known Wigner distribution, we also show that a variant of novel weighted convolution of Type-II is convenient to implement in constructing computationally reliable multiplicative filters in the quadratic-phase Fourier domain.

Application of geometrical irregularities identification using the cubic phase masks

The geometrical analysis of the healthy and the deformed biological cells is a very helpful aide to the generally more expensive and complicated pathological methods for disease detection. The methods demonstrated in this paper have successfully identified the healthy and the distorted cells using the cubic phase masks as the Fourier domain filters and a 4-f setup architecture of the Fourier Optics principles and the orientation wise weighted tuning of the edges of the cell. For two orthogonal arrangements of the mask, two images are generated. For the healthy and regular shaped cells, the maximum intensity values of these two images are the same whereas they are different for a distorted cell – for example, an ellipse or a sickle cell. Moreover, the maximum intensity values of the two halves of an image frame for a particular arrangement of the mask will be different for a tear-drop cell. These maximum brightness values are automatically read and the appropriate marking of these recognized cells has been done in an automated process.

Emission spectroscopy with coded apertures for enhanced dimensionality

A coded aperture is used to demonstrate emission spectroscopy from multiple one-dimensional measurement locations simultaneously with a single camera. The coded aperture mask has several columns of periodic apertures, each with a unique spatial frequency. Light transmitted through all mask columns is detected through an imaging spectrometer. Dispersed light from the various mask columns overlaps on the spectrometer camera but is separated using Fourier-domain filtering using the known spatial frequencies of the mask. As the coded aperture is placed at an image plane, each Fourier-filtered spectrogram comes from a unique one-dimensional measurement location. This technique represents a significant increase in the amount of spatially and spectrally resolved emission data available using a single emission spectrometer and camera at the expense of some spatial resolution due to the Fourier filtering. This instrument is particularly useful for studying transient, non-repeating events. Megahertz-rate emission spectroscopy from five one-dimensional measurement locations is demonstrated with explosive fireballs using a single camera. Optical design parameters and instrument performance characteristics are discussed.

Sparse grid-based adaptive noise reduction strategy for particle-in-cell schemes

We propose a sparse grid-based adaptive noise reduction strategy for electrostatic particle-in-cell (PIC) simulations. By projecting the charge density onto sparse grids we reduce the high-frequency particle noise. Thus, we exploit the ability of sparse grids to act as a multidimensional low-pass filter in our approach. Thanks to the truncated combination technique [1–3], we can reduce the larger grid-based error of the standard sparse grid approach for non-aligned and non-smooth functions. The truncated approach also provides a natural framework for minimizing the sum of grid-based and particle-based errors in the charge density. We show that our approach is, in fact, a filtering perspective for the noise reduction obtained with the sparse PIC schemes first introduced in [4]. This enables us to propose a heuristic based on the formal error analysis in [4] for selecting the optimal truncation parameter that minimizes the total error in charge density at each time step. Hence, unlike the physical and Fourier domain filters typically used in PIC codes for noise reduction, our approach automatically adapts to the mesh size, number of particles per cell, smoothness of the density profile and the initial sampling technique. It can also be easily integrated into high performance large-scale PIC code bases, because we only use sparse grids for filtering the charge density. All other operations remain on the regular grid, as in typical PIC codes. We demonstrate the efficiency and performance of our approach with two test cases: the diocotron instability in two dimensions and the three-dimensional electron dynamics in a Penning trap. Our run-time performance studies indicate that our approach can provide significant speedup and memory reduction to PIC simulations for achieving comparable accuracy in the charge density.

Computationally Efficient Wildfire Detection Method Using a Deep Convolutional Network Pruned via Fourier Analysis.

In this paper, we propose a deep convolutional neural network for camera based wildfire detection. We train the neural network via transfer learning and use window based analysis strategy to increase the fire detection rate. To achieve computational efficiency, we calculate frequency response of the kernels in convolutional and dense layers and eliminate those filters with low energy impulse response. Moreover, to reduce the storage for edge devices, we compare the convolutional kernels in Fourier domain and discard similar filters using the cosine similarity measure in the frequency domain. We test the performance of the neural network with a variety of wildfire video clips and the pruned system performs as good as the regular network in daytime wild fire detection, and it also works well on some night wild fire video clips.

Single-Point Detection Architecture via Liquid Crystal Modulation for Hyperspectral Imaging Systems

Hyperspectral imaging (HSI) architectures can acquire one-dimension of spatial information and one-dimension of spectral information on a two-dimensional image sensor for an image, such as in the traditional line-scan HSI architecture. However, development of HSI architectures for multiple spatial dimensions is challenging as there is not a third dimension on a two-dimensional image sensor on which to store spectral information. The presented work introduces a snapshot HSI architecture to alleviate this issue. The snapshot HSI architecture incorporates single-point detection via liquid crystal modulation and a single photodiode. Mixing of hyperspectral data is expressed as intermodulation frequency products within the Fourier-domain. Spatial information can be recorded through spatial frequencies and spectral information can be recorded through spectral frequencies. Such modulation is achieved through liquid crystal spatial and spectral arrays of an image beam. The spatial and spectral modulation frequencies form intermodulation frequency products that are recorded on the single photodiode and can be uncovered through Fourier-domain filtering.

TOA Estimation of Chirp Signal in Dense Multipath Environment for Low-Cost Acoustic Ranging

In this paper, a novel time of arrival (TOA) estimation method is proposed based on an iterative cleaning process to extract the first path signal. The purpose is to address the challenge in dense multipath indoor environments that the power of the first path component is normally smaller than other multipath components, where the traditional match filtering (MF)-based TOA estimator causes huge errors. Along with parameter estimation, the proposed process is trying to detect and extract the first path component by eliminating the strongest multipath component using a band-elimination filter in fractional Fourier domain at each iterative procedure. To further improve the stability, a slack threshold and a strict threshold are introduced. Six simple and easily calculated termination criteria are proposed to monitor the iterative process. When the iterative “cleaning” process is done, the outputs include the enhanced first path component and its estimated parameters. Based on these outputs, an optimal reference signal for the MF estimator can be constructed, and a more accurate TOA estimation can be conveniently obtained. The results from numerical simulations and experimental investigations verified that, for acoustic chirp signal TOA estimation, the accuracy of the proposed method is superior to those obtained by the conventional MF estimators.

True damage state and cracking in highly deformed metal matrix composites revealed by synchrotron microtomography

The characterisation of the damage state contained in materials using synchrotron microtomography with phase contrast is challenging. The uncertainty in quantifying such tomographic datasets containing objects that displays strong phase contrast sensitivity is explicitly treated for the first time. It is achieved by developing novel quantification protocol for a dataset obtained by scanning SiCP/A6061 composite strained upto ∼ 1 at 500 °C. The protocol involves designing and optimising Fourier domain filters to process the reconstructed image slices prior to quantification. It is shown that the application of these filters modulates intensity distribution at the damage – matrix interfaces. The performance of three different types of filters, namely Box, Gaussian and Butterworth are compared. For this purpose optimising functions based on minimising the difference of volume fraction and number density of damage quantified in the unfiltered dataset are developed. Despite redistribution of the grey scale intensity in the slices obtained from the application of optimised Fourier domain filter, the image quality is found to remain uncompromised. The optimum Gauss filter is found best to be applied to process the tomographic dataset of the severely deformed region of SiCP/A6061composite undergoing in-homogenous compression. The state of damage in the region quantified in terms of different types of pores and cracks and their spatial proximity is rationalised with reference to the established mechanism of cracking in particulate reinforced composites at high strains.

Detecting Weak Spectral Lines in Interferometric Data through Matched Filtering

Abstract Modern radio interferometers enable observations of spectral lines with unprecedented spatial resolution and sensitivity. In spite of these technical advances, many lines of interest are still at best weakly detected and therefore necessitate detection and analysis techniques specialized for the low signal-to-noise ratio (S/N) regime. Matched filters can leverage knowledge of the source structure and kinematics to increase sensitivity of spectral line observations. Application of the filter in the native Fourier domain improves S/N while simultaneously avoiding the computational cost and ambiguities associated with imaging, making matched filtering a fast and robust method for weak spectral line detection. We demonstrate how an approximate matched filter can be constructed from a previously observed line or from a model of the source, and we show how this filter can be used to robustly infer a detection significance for weak spectral lines. When applied to ALMA Cycle 2 observations of CH3OH in the protoplanetary disk around TW Hya, the technique yields a ≈53% S/N boost over aperture-based spectral extraction methods, and we show that an even higher boost will be achieved for observations at higher spatial resolution. A Python-based open-source implementation of this technique is available under the MIT license at http://github.com/AstroChem/VISIBLE.

Multispectral Photoacoustic Imaging Artifact Removal and Denoising Using Time Series Model-Based Spectral Noise Estimation.

The aim of this study is to solve a problem of denoising and artifact removal from in vivo multispectral photoacoustic imaging when the level of noise is not known a priori. The study analyzes Wiener filtering in Fourier domain when a family of anisotropic shape filters is considered. The unknown noise and signal power spectral densities are estimated using spectral information of images and the autoregressive of the power 1 ( AR(1)) model. Edge preservation is achieved by detecting image edges in the original and the denoised image and superimposing a weighted contribution of the two edge images to the resulting denoised image. The method is tested on multispectral photoacoustic images from simulations, a tissue-mimicking phantom, as well as in vivo imaging of the mouse, with its performance compared against that of the standard Wiener filtering in Fourier domain. The results reveal better denoising and fine details preservation capabilities of the proposed method when compared to that of the standard Wiener filtering in Fourier domain, suggesting that this could be a useful denoising technique for other multispectral photoacoustic studies.

A Fault Diagnosis Scheme for Rolling Bearing Based on Particle Swarm Optimization in Variational Mode Decomposition

Variational mode decomposition (VMD) is a new method of signal adaptive decomposition. In the VMD framework, the vibration signal is decomposed into multiple mode components by Wiener filtering in Fourier domain, and the center frequency of each mode component is updated as the center of gravity of the mode’s power spectrum. Therefore, each decomposed mode is compact around a center pulsation and has a limited bandwidth. In view of the situation that the penalty parameter and the number of components affect the decomposition effect in VMD algorithm, a novel method of fault feature extraction based on the combination of VMD and particle swarm optimization (PSO) algorithm is proposed. In this paper, the numerical simulation and the measured fault signals of the rolling bearing experiment system are analyzed by the proposed method. The results indicate that the proposed method is much more robust to sampling and noise. Additionally, the proposed method has an advantage over the EMD in complicated signal decomposition and can be utilized as a potential method in extracting the faint fault information of rolling bearings compared with the common method of envelope spectrum analysis.

A Cartoon-Texture Decomposition Based Multiplicative Noise Removal Method

We propose a new frame for multiplicative noise removal. To improve the multiplicative denoising performance, we add the regularization of texture component in the denoising model, designing a multiscale multiplicative noise removal model. The proposed model is jointly convex and can be easily solved by optimization algorithms. We introduce Douglas-Rachford splitting method to solve the proposed model. In the algorithm, we make full use of some important proximity operators, which have closed expression or can be executed in one time iteration. In particular, the proximity ofH-1norm is deduced, which is just the Fourier domain filtering. In the process of simulation experiments, we first analyze and select the needed parameters and then test the experiments on several images using the designed algorithm and the given parameters. Finally, we compare the denoising performance of the proposed model with the existing models, in which the signal to noise ratio (SNR) and the peak signal to noise ratios (PSNRs) are applied to evaluate the noise suppressing effects. Experimental results demonstrate that the designed algorithms can solve the model perfectly and the recovery images of the proposed model have higher SNRs/PSNRs and better visual quality.

Robust Fingerprint Enhancement by Directional Filtering in Fourier Domain

Reliabe extraction of true minutiae in fingerprint image is critical to the performance of an automated fingerprint identification system (AFIS). In order to utilize AFIZ in law enforcement agencies first step is to digitalize an archyve of fingerprints obtained by ink method. For improving the quality of automatically extracted minutiae (both in number and type) enhancement is previously performed, but, nevertheless, quite a number of spuirious minutiae (especially in blurry or regions containing scars and creases) are extracted. It is crucial for AFIS performance that number of extracted (and consequently saved in fingerprint template) spurious minutia is minimized to maximal extent. In order to do so, we propose directional Log-Gabor filtering in frequency domain. Results proved to be preferable for a wide range of input digitized fingerprint images.

An adaptive filtered back-projection for photoacoustic image reconstruction.

The purpose of this study is to develop an improved filtered-back-projection (FBP) algorithm for photoacoustic tomography (PAT), which allows image reconstruction with higher quality compared to images reconstructed through traditional algorithms. A rigorous expression of a weighting function has been derived directly from a photoacoustic wave equation and used as a ramp filter in Fourier domain. The authors' new algorithm utilizes this weighting function to precisely calculate each photoacoustic signal's contribution and then reconstructs the image based on the retarded potential generated from the photoacoustic sources. In addition, an adaptive criterion has been derived for selecting the cutoff frequency of a low pass filter. Two computational phantoms were created to test the algorithm. The first phantom contained five spheres with each sphere having different absorbances. The phantom was used to test the capability for correctly representing both the geometry and the relative absorbed energy in a planar measurement system. The authors also used another phantom containing absorbers of different sizes with overlapping geometry to evaluate the performance of the new method for complicated geometry. In addition, random noise background was added to the simulated data, which were obtained by using an arc-shaped array of 50 evenly distributed transducers that spanned 160° over a circle with a radius of 65 mm. A normalized factor between the neighbored transducers was applied for correcting measurement signals in PAT simulations. The authors assumed that the scanned object was mounted on a holder that rotated over the full 360° and the scans were set to a sampling rate of 20.48 MHz. The authors have obtained reconstructed images of the computerized phantoms by utilizing the new FBP algorithm. From the reconstructed image of the first phantom, one can see that this new approach allows not only obtaining a sharp image but also showing the correct signal strength of the absorbers. The reconstructed image of the second phantom further demonstrates the capability to form clear images of the spheres with sharp borders in the overlapping geometry. The smallest sphere is clearly visible and distinguishable, even though it is surrounded by two big spheres. In addition, image reconstructions were conducted with randomized noise added to the observed signals to mimic realistic experimental conditions. The authors have developed a new FBP algorithm that is capable for reconstructing high quality images with correct relative intensities and sharp borders for PAT. The results demonstrate that the weighting function serves as a precise ramp filter for processing the observed signals in the Fourier domain. In addition, this algorithm allows an adaptive determination of the cutoff frequency for the applied low pass filter.

A hybrid method for strong low-frequency noise suppression in prestack seismic data

Abstract Low-frequency components are important portion of seismic data in exploration geophysics, and have great effects on seismic imaging of deep subsurface and full waveform inversion. Unfortunately, seismic data usually suffers from various kinds of noises and has low signal to noise ratio (SNR) in low-frequency band, although this situation has been improved by developments of acquisition technology. In this paper, we propose a low-frequency cascade filter (LFCF) in Fourier domain for strong low-frequency noise suppression in prestack gathers. LFCF includes a 1D adaptive median filter in f–x domain and a 2D notch filter in f–k domain, which is able to process high-amplitude swell noise, random noise, and seismic interference noise. We employ traces rearrangement and spike-detection mechanisms in adaptive f–x median filter, which can handle strong noise specifically, such as wide-spreading swell noise and tug noise. And a notch filter in f–k domain is designed to separate reflection signal and random noise by different apparent velocities. Through these means, our method can effectively attenuate low-frequency random and coherent noise while simultaneously protect the signal. Experiments on synthetic example and field data are conducted, and the results demonstrate that our method is practical and effective and can preserve signal down to 2 Hz.

Parameters Estimation and Waveform Reconstruction of Chirp Signal Based on FRFT

The fractional Fourier transform (FRFT) is a generalization of the Fourier transform. The article first introduces the definition of FRFT transformation; then analyzed FRFT Chirp signal based on this humble proposed restoration Chirp signal in a noisy background in two ways: one is based on parameter estimation, and the other is based on the scores Fourier domain filtering to achieve signal reconstruction; Finally, simulation verify the feasibility of the above analysis.

Denoising of measured lightning electric field signals using adaptive filters in the fractional Fourier domain

In this paper, adaptive filters are applied (in the fractional Fourier transform domain – FRFd) for denoising lightning electric-field signals, both in high and low signal-to-noise-ratio (SNR) environments. These filters are based on the concentration energy property of the fractional Fourier transform (FRFT). The proposed method integrates the advantages of leakage least mean square (LLMS) and normalized least mean square (NLMS) algorithms, including a leakage factor γ and a normalized step-size μ, in order to reduce the memory effect when tracking a non-stationary signal and also to reduce the effect of the input signal power on the algorithm performance, respectively. Parameter estimation of adaptive filters is analyzed in several case studies for various lightning-generated electric field signals. The adaptive algorithm is shown to provide better performance in low SNR environments. Finally, some analyses (in terms of temporal parameters of lightning electric-field signals) are included to demonstrate the validity of the method.

High-speed thermoreflectance microscopy using charge-coupled device-based Fourier-domain filtering

We present a Fourier-domain filtering method for charge-coupled device (CCD)-based thermoreflectance microscopy to improve the thermal imaging speed while maintaining high thermal sensitivity. The time-varying reflected light distribution from the surface of bias-modulated microresistor was recorded by a CCD camera in free-run mode and converted to the frequency domain using the fast Fourier transform (FFT) for all pixels of the CCD. After frequency peak filtering followed by inverse FFT, a thermoreflectance image was obtained. The imaging results of the proposed method were quantitatively compared with those of the conventional four-bucket method, showing that the Fourier-domain filtering method can provide thermal imaging 24-42 times faster than the four-bucket method, depending on the required thermal sensitivity.

Arbitrary quantum control of qubits in the presence of universal noise

We address the problem of deriving analytic expressions for calculating universal decoherence-induced errors in qubits undergoing arbitrary, unitary, time-dependent quantum control protocols. We show that the fidelity of a control operation may be expressed in terms of experimentally relevant spectral characteristics of the noise and of the control, over all Cartesian directions. We formulate control matrices in the time domain to capture the effects of piecewise-constant control, and convert them to generalized Fourier-domain filter functions. These generalized filter functions may be derived for complex temporally modulated control protocols, accounting for susceptibility to rotations of the qubit state vector in three dimensions. Taken together, we show that this framework provides a computationally efficient means to calculate the effects of universal noise on arbitrary quantum control protocols, producing results comparable with those obtained via time-consuming simulations of Bloch vector evolution. As a concrete example, we apply our method to treating the problem of dynamical decoupling incorporating realistic control pulses of arbitrary duration or form, including the replacement of simple π-pulses with complex dynamically corrected gates.