Richardson-Lucy Algorithm Research Articles

Signal-to-Noise Ratio Improvement for Multiple-Pinhole Imaging Using Supervised Encoder–Decoder Convolutional Neural Network Architecture

Digital image devices have been widely applied in many fields, such as individual recognition and remote sensing. The captured image is a degraded image from the latent observation, where the degradation processing is affected by some factors, such as lighting and noise corruption. Specifically, noise is generated in the processing of transmission and compression from the unknown latent observation. Thus, it is essential to use image denoising techniques to remove noise and recover the latent observation from the given degraded image. In this research, a supervised encoder–decoder convolution neural network was used to fix image distortion stemming from the limited accuracy of inverse filter methods (Wiener filter, Lucy–Richardson deconvolution, etc.). Particularly, we will correct image degradation that mainly stems from duplications arising from multiple-pinhole array imaging.

Image Processing for Improvement of Facial Keypoints Detector

This paper discusses the improvement of facial detection algorithms using the DCT algorithm and image processing. Face key point is very needed in the face recognition system. Some important factors that have effects to detect its result are noise and illuminations. These two factors can be overcome by eliminating some DCT coefficients, both high and low. However, after handling the problem, most likely the image quality will become decrease, which will adversely influence the performance of the feature detector algorithm. Therefore, it is very important to test the performance of the feature detector algorithm on images that are implemented noise and illumination handling and how to improve the quality again. This research implemented Discrete Cosine Transform (DCT), by eliminating the high and low coefficient because there is noise and illumination. However, it is not known at what coefficient level is the most effective, so testing in this study was carried out. Four deblurring algorithms are tested in this research, Blind Deconvolution, Wiener Filter Deconvolution, Lucy-Richardson Deconvolution, and Regularization Deconvolution. And tested the CLAHE algorithm to overcome the effect of removing low coefficient DCT. The best coefficient value to be removed at the DCT frequency is 0.75 with the best SURF algorithm, without the use of other algorithms. Also, the highest F-score is produced by the SURF detector at removing DCT low frequency in combination with the CLAHE algorithm. With the most ideal coefficient of 0.25.

Boosting background suppression in the NEXT experiment through Richardson-Lucy deconvolution

The NEXT collaboration aims to observe neutrinoless double beta decay in gaseous 136Xe using a high pressure gaseous Xe time projection chamber with signal amplification by means of electroluminescence (EL). One of the advantages of the technique is that it allows for track reconstruction making use of a sensor plane equipped with SiPMs located nearby the EL region. However, the signals recorded in the TPC are degraded by electron diffusion and spread of light produced in the EL process, limiting the potential of the detection scheme. We have recently developed an improved reconstruction procedure based on the Richardson-Lucy deconvolution [], an iterative algorithm well-known in image processing and de-blurring. Deconvolution allows reversing the smearing mechanisms in the NEXT TPC and significantly enhances the definition of reconstructed tracks. Consequently, detector performance is strongly boosted, with a five-fold improvement in background rejection demonstrated on experimental data. The algorithm application in the context of the NEXT experiment is detailed with a focus on the performance in NEXT-White, a 50 cm TPC which operated underground at Laboratorio Subterráneo de Canfranc until July 2021. The procedure applied to characterize the optical response of the chamber and obtain the point spread function that best describes the observed signals is described.

Speckle-free laser projection structured illumination microscopy based on a digital micromirror device

In the structured illumination microscopy (SIM) family, interferometric implementations using traditional physical gratings or advanced liquid crystal on silicon spatial light modulators are popular but have the disadvantages of expensive and limited speed. A promising alternative of a digital micromirror device (DMD) has improved the situation for its lower cost and higher speed, furthermore, it has contributed to the proposal of a simple and compact projection DMD-SIM. However, the projection DMD-SIM method is accused of erroneously measuring the resolution because of the scattering characteristic of gold beads, despite the inferior experimental resolution that is because of the low fringe contrast and the resulting low signal-to-noise ratio (SNR). As an improvement, we use a high-brightness laser for illumination to achieve higher SNR, and the accompanying problems of speckle and inhomogeneity originating from the laser’s high coherence are solved by a high-frequency phase-randomization deformable mirror in conjunction with a square-core multimode fiber, which does not limit the image acquisition speed and with fewer energy losses compared to the existing methods. Also, in terms of the problem of low SNR, we apply a parallel-iteration Richardson–Lucy deconvolution algorithm for SIM reconstruction to further improve the imaging performance based on ensuring the resolution. Based on these advances, we image fluorescent nanoparticles and other non-biological and biological fluorescent samples, and the experimental results demonstrate the improved imaging performance of our modified system.

Point-spread Function Deconvolution of the IFU Data and Restoration of Galaxy Stellar Kinematics

Abstract We present a performance test of the point-spread function (PSF) deconvolution algorithm applied to astronomical integral field unit (IFU) spectroscopy data for restoration of galaxy kinematics. We deconvolve the IFU data by applying the Lucy–Richardson algorithm to the 2D image slice at each wavelength. We demonstrate that the algorithm can effectively recover the true stellar kinematics of the galaxy, by using mock IFU data with a diverse combination of surface brightness profile, signal-to-noise ratio, line-of-sight geometry, and line-of-sight velocity distribution (LOSVD). In addition, we show that the proxy of the spin parameter λ R e can be accurately measured from the deconvolved IFU data. We apply the deconvolution algorithm to the actual SDSS-IV MaNGA IFU survey data. The 2D LOSVD, geometry, and λ R e measured from the deconvolved MaNGA IFU data exhibit noticeable differences compared to the ones measured from the original IFU data. The method can be applied to any other regular-grid IFU data to extract the PSF-deconvolved spatial information.

Visualizing minute details in light-sheet and confocal microscopy data by combining 3D rolling ball filtering and deconvolution.

We developed an open-source deconvolution software that stunningly increases the visibility of minute details, as for example, neurons or nerve fibers in light-sheet microscopy or confocal microscopy data by combining rolling ball background subtraction in three directions with deconvolution using a synthetic or measured point spread function. Via automatic block-wise processing image stacks of virtually unlimited size can be deconvolved even on small computers with 8 or 16 GB RAM. By parallelization and optional GPU-acceleration, the software works with high speed: On a PC equipped with a state-of-the-art NVidia graphic board a three dimensional (3D)-stack of about 1 billion voxels can be deconvolved within 5 to 10minutes. The implemented variation of the Richardson-Lucy deconvolution algorithm preserves the photogrammetry of the image data by using flux-preserving regularization, an approach that to our knowledge has not been applied for deconvolving microscopy data before.

Using deconvolution to suppress range sidelobes for MIMO sonar imaging

A multiple- input multiple-output (MIMO) sonar can produce a large-aperture virtual array with the use of a small size array and a limited number of elements, which is very useful when applied to underwater acoustic imaging. However, the range sidelobes (SLs) in the MIMO sonar imaging result is high due to the non-ideal orthogonality of transmitting waveforms. In this paper, we propose a deconvolution method to suppress the range SLs. We consider that the range SLs in the imaging result are composed of cross-correlation functions (CCFs) and SLs of auto-correlation functions (ACFs) of transmitting waveforms. And they can be treated as the “noise” term in the output of the convolution between the original distributions of scatterers and a Dirac-like point spread function (PSF). Accordingly, we use the deconvolution method (i.e., the Richardson-Lucy algorithm) to suppress these range SLs. We give the basic processing procedure of the proposed deconvolution method. Simultaneously, we give a simple searching method to find the best PSF corresponding to the lowest range SL level after deconvolution. Numerical simulations and a tank experiment show the proposed deconvolution method can suppress the range SLs effectively.

Deep learning based automated detection of intraretinal cystoid fluid

AbstractThe diversified ocular disorders in which cystoid macular edema (CME) occurs, are strongly associated with the vision loss. Optical coherence tomography (OCT) scans that allow screening of the retina, contain artifacts including blur‐edges, speckle noise, and so forth, which create difficulty in identifying retinal fluid. In this work, major image preprocessing techniques such as minimum filtering, block‐matching and 3D filtering, and Richardson–Lucy deconvolution method are applied to minimize noise and other degradation effects from OCT scans, ensured by maintaining image quality assessment scores, that is, blind‐less image spatial quality evaluator and sharpness estimation score. Furthermore, this work develops an automated method based on deep learning (DL) to detect the presence and progression of retinal fluid, that is, CME and its quantification. Specifically, U‐net model with efficient tuning of hyperparameters is proposed to obtain optimal results. The algorithm's performance is evaluated for accurate identification of fluid localization in the case of diabetic macular edema (DME), having CME regions, and compared against the manual segmentation of fluid by experts, which are highly correlated. This enhanced DL method achieves better performance than the algorithms previously reported. The proposed algorithm is evaluated on several performance metrics during training and reports the best score of 99.81, 0.50, 83.34, 86.56, 80.89, and 99.48% for model accuracy, binary cross‐entropy loss, Dice coefficient (DC), precision, recall, and area under the ROC‐curve, respectively. Additionally, fourfold cross‐validation technique is also applied and an average DC score of 84.00% is obtained. This approach can be helpful to prevent vision loss.

Frequency response of a continuously tuning narrow-band optical filter based on stimulated Brillouin scattering.

Tunable narrow-band optical filter (TNOF) based on stimulated Brillouin scattering (SBS) has been applied in various applications such as microwave photonics and a high-resolution optical spectrum analyzer (OSA). While the frequency response of a SBS-based filter has always been an important characteristic in the reported studies, few have addressed the issue of the filter response under a continuously tuning condition. When the tuning speed is too fast, the filter response will change and cause spectral distortion. In this paper, the frequency response of SBS-TNOF under a wavelength-swept pump (i.e., continuously tuning) condition is investigated and modeled. Experimental results are in good agreement with the theoretical analysis and verify that the broadening of the SBS-TNOF response is induced by the pump wavelength difference along different positions of the fiber, which can be explained as convolution with broadband pump as well. Based on the widely used Richardson-Lucy deconvolution algorithm and proposed SBS-TNOF response model, the distorted responses are successfully reconstructed and the sweep speed dependency is almost eliminated. Commonly used on-off keying signal is tested using the proposed reconstruction method to assess its performance in the SBS-OSA. Both the overall profile and the detail of the signal spectra are significantly recovered, and the quantitatively evaluation illustrates that the feasible sweep speed can be improved from ∼45 nm/s to over 95 nm/s.

Single voxel vascular transport functions of arteries, capillaries and veins; and the associated arterial input function in dynamic susceptibility contrast magnetic resonance brain perfusion imaging

PurposeThe composite vascular transport function of a brain voxel consists of one convolutional component for the arteries, one for the capillaries and one for the veins in the voxel of interest. Here, the goal is to find each of these three convolutional components and the associated arterial input function. Pharmacokinetic modellingThe single voxel vascular transport functions for arteries, capillaries and veins were all modelled as causal exponential functions. Each observed multipass tissue contrast function was as a first approximation modelled as the resulting parametric composite vascular transport function convolved with a nonparametric and voxel specific multipass arterial input function. Subsequently, the residue function was used in the true perfusion equation to optimize the three parameters of the exponential functions. Deconvolution methodsFor each voxel, the parameters of the three exponential functions were estimated by successive iterative blind deconvolutions using versions of the Lucy-Richardson algorithm. The final multipass arterial input function was then computed by nonblind deconvolution using the Lucy-Richardson algorithm and the estimated composite vascular transport function. ResultsSimulations showed that the algorithm worked. The estimated mean transit time of arteries, capillaries and veins of the simulated data agreed with the known input values. For real data, the estimated capillary mean transit times agreed with known values for this parameter. The nonparametric multipass arterial input functions were used to derive the associated map of the arrival time. The arrival time map of a healthy volunteer agreed with known arterial anatomy and physiology. ConclusionClinically important new voxelwise hemodynamic information for arteries, capillaries and veins separately can be estimated using multipass tissue contrast functions and the iterative blind Lucy-Richardson deconvolution algorithm.

DOA estimation method for underwater acoustic signals based on two-dimensional power distribution (TPD) for few element array

Direction-of-arrival (DOA) estimation has always been one of the significant techniques in underwater acoustic signal processing, which can be used to obtain the spatial angular information of the targets. High resolution performance is one of the concerns in the DOA estimation. The DOA estimation method based on the Richardson-Lucy deconvolution algorithm (RL-dCv) proposed in recent years can obtain higher resolution and lower sidelobe beam power than the CBF method. However, the method suffers from a low resolution and estimation precision in the case of insufficient array elements. Addressing the problem, a DOA estimation method based on the two-dimensional power distribution (TPD) is proposed in this paper. The method uses the Kronecker product operation to extract the two-dimensional power distribution matrix (TM) from the beam power function, and then uses the compression sensing algorithm to solve the matrix with the least influence of the noise. Since the value in the TM is restricted by the two angle sets, the method improves the estimation precision, and reduces the requirement for the number of array elements. It can get more accurate estimation results and higher resolution in the case of insufficient elements array. Experiments including simulations in different scenes and real lake experiments are implemented to validate the effectiveness of the proposed method.

Deriving high contrast fluorescence microscopy images through low contrast noisy image stacks.

Contrast in fluorescence microscopy images allows for the differentiation between different structures by their difference in intensities. However, factors such as point-spread function and noise may reduce it, affecting its interpretability. We identified that fluctuation of emitters in a stack of images can be exploited to achieve increased contrast when compared to the average and Richardson-Lucy deconvolution. We tested our methods on four increasingly challenging samples including tissue, in which case results were comparable to the ones obtained by structured illumination microscopy in terms of contrast.

A MUSE spectro-imaging study of the Th 28 jet: Precession in the inner jet

Context. Th 28 is a Classical T Tauri star in the Lupus 3 cloud that drives an extended bipolar jet. Previous studies of the inner jet identified signatures of rotation around the outflow axis, a key result for theories of jet launching. Thus this is an important source in which to investigate the poorly understood jet launching mechanism. Aims. In this study we investigate the morphology and kinematics of the Th 28 micro-jets, with the aim of characterising their structure and outflow activity, using optical integral-field spectroscopy observations obtained with VLT/MUSE. Methods. We use spectro-imaging and position–velocity maps to investigate the kinematic and morphological features of the jet and to obtain a catalogue of emission lines in which the jet is visible. A Lucy-Richardson deconvolution procedure is used to differentiate the structure of the inner micro-jet region in selected emission lines. Spatial profiles extracted perpendicular to the jet axis are fitted to investigate the jet width, opening angle, and the evolution of the jet axis. Results. We confirm the previously identified knot HHW2 within the red-shifted jet and identify three additional knots in each lobe for the first time. We also find [O III]λ5007 emission from the blue-shifted micro-jet, including the knot closest to the star. Proper motions for the innermost knots on each side are estimated to be 0′′.35 yr−1 and 0′′.47 yr−1 for the red- and blue-shifted jets, respectively. Based on this we show that new knots are ejected on an approximate timescale of 10–15 yr. Gaussian fitting to the jet axis centroids shows a point-symmetric wiggle within the inner portion of both micro-jets, indicating precession of the jet. We use the jet shape to measure a precession period of 8 yr, with a half-opening angle β < 0.6°. This precession may provide an alternative explanation for the rotation signatures previously reported. Conclusions. We find that these parameters are compatible with precession due to a brown dwarf companion orbiting at a separation of ≤0.3 au. Further observations with higher spatial resolution may help to clarify the source of this precession.

Deblurring of Images using Novel Deconvolutional Neural Network (DNN) Algorithm to Enhance the Accuracy and Comparing with Richardson-Lucy Deconvolution Algorithm (RLD)

Aim- Machine learning techniques are rapidly used in the area of digital image processing research due to its impressive results in deconvolution and deblurring of images. The objective of this study is to evaluate the performance of Novel DNN algorithm in deblurring of images by comparing it with the RLD algorithm. Materials and Methods - Novel Deconvolutional Neural Network (DNN) and Richardson-Lucy Deconvolution (RLD) algorithms were implemented to deblur the input images upto 256 pixels range. These algorithms were implemented to enhance the accuracy rate of deblurred images using MATLAB Software and analyzed by collecting the dataset of 40 samples with 80% of pretest power. Results - From the MATLAB simulation result, DNN achieves image deblurring rate with 98% accuracy and RLD method achieves image deblurring rate with 92% accuracy. The significance value obtained as (P < 0.002). Conclusion - Novel DNN classifier appears to have better accuracy compared to RLD Classifier.

Boosting background suppression in the NEXT experiment through Richardson-Lucy deconvolution

Next-generation neutrinoless double beta decay experiments aim for half-life sensitivities of ∼ 1027 yr, requiring suppressing backgrounds to < 1 count/tonne/yr. For this, any extra background rejection handle, beyond excellent energy resolution and the use of extremely radiopure materials, is of utmost importance. The NEXT experiment exploits differences in the spatial ionization patterns of double beta decay and single-electron events to discriminate signal from background. While the former display two Bragg peak dense ionization regions at the opposite ends of the track, the latter typically have only one such feature. Thus, comparing the energies at the track extremes provides an additional rejection tool. The unique combination of the topology-based background discrimination and excellent energy resolution (1% FWHM at the Q-value of the decay) is the distinguishing feature of NEXT. Previous studies demonstrated a topological background rejection factor of ∼ 5 when reconstructing electron-positron pairs in the 208Tl 1.6 MeV double escape peak (with Compton events as background), recorded in the NEXT-White demonstrator at the Laboratorio Subterráneo de Canfranc, with 72% signal efficiency. This was recently improved through the use of a deep convolutional neural network to yield a background rejection factor of ∼ 10 with 65% signal efficiency. Here, we present a new reconstruction method, based on the Richardson-Lucy deconvolution algorithm, which allows reversing the blurring induced by electron diffusion and electroluminescence light production in the NEXT TPC. The new method yields highly refined 3D images of reconstructed events, and, as a result, significantly improves the topological background discrimination. When applied to real-data 1.6 MeV e−e+ pairs, it leads to a background rejection factor of 27 at 57% signal efficiency.

Magnetic flux structuring of the quiet Sun internetwork

Context. The small-scale magnetism of the quiet Sun has been investigated by various means in recent decades. It is now well established that the quiet Sun contains in total more magnetic flux than active regions and represents an important reservoir of magnetic energy. But the nature and evolution of these fields remain largely unknown. Aims. We investigate the solar-cycle and center-to-limb variations of magnetic-flux structures at small scales in internetwork regions of the quiet Sun. Methods. We used Hinode SOT/SP data from the irradiance program between 2008 and 2016. Maps of the magnetic-flux density are derived from the center-of gravity method applied to the circular polarization profiles in the FeI 630.15 nm and FeI 630.25 nm lines. To correct the maps from the instrumental smearing of the telescope, we applied a deconvolution method based on a principal component analysis of the line profiles and on a Richardson-Lucy deconvolution of their coefficients. We took defocus effects and the diffraction of the SOT telescope into account. We then performed a spectral analysis of the spatial fluctuations of the magnetic-flux density in 10″ × 10″ internetwork regions spanning a wide range of latitudes from ±70° to the equator. Results. At low and mid latitudes the power spectra normalized by the mean value of the unsigned flux in the regions do not vary significantly with the solar cycle. However at solar maximum for one scan in the activity belt showing an enhanced network, a marginal increase in the power of the magnetic fluctuations is observed at granular and larger scales in the internetwork. At high latitudes, we observe variations at granular and larger scales where the power decreases at solar maximum. At all the latitudes the power of the magnetic fluctuations at scales smaller than 0.5″ remains constant throughout the solar cycle. Conclusions. At the equator the unsigned flux density is related to the vertical component of the magnetic field, whereas at high latitudes this flux density is mainly related to the horizontal component and probe higher altitudes. Our results favor a small-scale dynamo that operates in the internetwork, but they show that the global dynamo also contributes to the internetwork fields. At solar maximum the high-latitude horizontal internetwork fields seem to be depleted from the structures at granular and larger scales that are seen at solar minimum, whereas the internetwork within enhanced network regions show more structures at those scales than at solar minimum.

Image Restoration Using Lucy Richardson Algorithm for Deblurring Images with Improved PSNR, SSIM, NC in Comparison with Wiener Filter

Aim: Image is the most powerful tool to analyze the information. Sometimes the captured image gets affected with blur and noise in the environment, which degrades the quality of the image. Image restoration is a technique in image processing where the degraded image can be restored or recovered to its nearest original image. Materials and Methods: In this research Lucy-Richardson algorithm is used for restoring blurred and noisy images using MATLAB software. And the proposed work is compared with Wiener filter, and the sample size for each group is 30. Results: The performance was compared based on three parameters, Power Signal to Noise Ratio (PSNR), Structural Similarity Index Measure (SSIM), Normalized Correlation (NC). High values of PSNR, SSIM and NC indicate the better performance of restoration algorithms. Lucy-Richardson provides a mean PSNR of 10.4086db, mean SSIM of 0.4173%, and NC of 0.7433% and Wiener filter provides a mean PSNR of 6.3979db, SSIM of 0.3016%, NC of 0.3276%. Conclusion: Based on the experimental results and statistical analysis using independent sample T test, image restoration using Lucy-Richardson algorithm significantly performs better than Wiener filter on restoring the degraded image with PSNR (P&lt;0.001) and SSIM (P&lt;0.001).

RESEARCH OF THE METHOD OF INCREASING THE OBJECT DETERMINATION ACCURACY ON THE LOW-RESOLUTION VIDEO STREAM

Study subject. The article proposes and investigates a method for increasing the accuracy of determination of the distance and the obstacle geometric parameters based on object contours determination using a computer vision system that uses low-resolution sensors. The goal is the effectiveness evaluation of the proposed method. Tasks: to conduct experimental researches of the quality indicators of the method of increasing the object contours determination accuracy; evaluate the effectiveness of this method. Used methods: statistical modeling, laboratory scale tests. The obtained results: the analysis of the proposed method efficiency was carried out and the influence of this method on the determination accuracy of the distance and object geometric parameters was evaluated. Conclusions: the considered method made it possible to achieve the increasing the determination accuracy of the distance and geometric object parameters by compensating for image blur using the Lucy-Richardson deconvolution algorithm. The obtained data showed a decrease in the maximum error in determining the distance from 8% to 4% and the error in the geometric object parameters from 7.7% to 5.8%. The implementation of this approach was carried out in the Python programming language.

Iterative-Trained Semi-Blind Deconvolution Algorithm to Compensate Straylight in Retinal Images.

The optical quality of an image depends on both the optical properties of the imaging system and the physical properties of the medium in which the light travels from the object to the final imaging sensor. The analysis of the point spread function of the optical system is an objective way to quantify the image degradation. In retinal imaging, the presence of corneal or cristalline lens opacifications spread the light at wide angular distributions. If the mathematical operator that degrades the image is known, the image can be restored through deconvolution methods. In the particular case of retinal imaging, this operator may be unknown (or partially) due to the presence of cataracts, corneal edema, or vitreous opacification. In those cases, blind deconvolution theory provides useful results to restore important spatial information of the image. In this work, a new semi-blind deconvolution method has been developed by training an iterative process with the Glare Spread Function kernel based on the Richardson-Lucy deconvolution algorithm to compensate a veiling glare effect in retinal images due to intraocular straylight. The method was first tested with simulated retinal images generated from a straylight eye model and applied to a real retinal image dataset composed of healthy subjects and patients with glaucoma and diabetic retinopathy. Results showed the capacity of the algorithm to detect and compensate the veiling glare degradation and improving the image sharpness up to 1000% in the case of healthy subjects and up to 700% in the pathological retinal images. This image quality improvement allows performing image segmentation processing with restored hidden spatial information after deconvolution.

Confocal super-resolution microscopy based on a spatial mode sorter

Spatial resolution is one of the most important specifications of an imaging system. Recent results in the quantum parameter estimation theory reveal that an arbitrarily small distance between two incoherent point sources can always be efficiently determined through the use of a spatial mode sorter. However, extending this procedure to a general object consisting of many incoherent point sources remains challenging, due to the intrinsic complexity of multi-parameter estimation problems. Here, we generalize the Richardson-Lucy (RL) deconvolution algorithm to address this challenge. We simulate its application to an incoherent confocal microscope, with a Zernike spatial mode sorter replacing the pinhole used in a conventional confocal microscope. We test different spatially incoherent objects of arbitrary geometry, and we find that the resolution enhancement of sorter-based microscopy is on average over 30% higher than that of a conventional confocal microscope using the standard RL deconvolution algorithm. Our method could potentially be used in diverse applications such as fluorescence microscopy and astronomical imaging.