Richardson-Lucy Deconvolution Algorithm Research Articles

RedLionfish – fast Richardson-Lucy Deconvolution package for efficient point spread function suppression in volumetric data

The experimental limitations with optics observed in many microscopy and astronomy instruments result in detrimental effects for the imaging of objects. This can be generally described mathematically as a convolution of the real object image with the point spread function that characterizes the optical system. The popular Richardson-Lucy (RL) deconvolution algorithm is widely used for the inverse process of restoring the data without these optical aberrations, often a critical step in data processing of experimental data. Here we present the versatile RedLionfish python package, that was written to make the RL deconvolution of volumetric (3D) data easier to run, very fast (by exploiting GPU computing capabilities) and with automatic handling of hardware limitations for large datasets. It can be used programmatically in Python/numpy using conda or PyPi package managers, or with a graphical user interface as a napari plugin.

Deblurring the early Universe: reconstruction of primordial power spectrum from Planck CMB using image analysis techniques

While the simplest inflationary models predict the primordial perturbations to be near scale-invariant, the primordial power spectrum (PPS) can exhibit oscillatory features in many physically well-motivated models. We search for hints of such features via free-form reconstructions of the PPS based on Planck 2018 CMB temperature and polarization anisotropies. In order to robustly invert the oscillatory integrals and handle noisy unbinned data, we draw inspiration from image analysis techniques. In previous works, the Richardson-Lucy deconvolution algorithm for deblurring images has been modified for reconstructing PPS from the CMB temperature angular power spectrum. We extensively develop the methodology by including CMB polarization and introducing two new regularization techniques, also inspired by image analysis and adapted for our cosmological context. Regularization is essential for improving the fit to the temperature and polarization channels (TT, TE and EE) simultaneously without sacrificing one for another. The reconstructions we obtain are consistent with previous findings from temperature-only analyses. We evaluate the statistical significance of the oscillatory features in our reconstructions using mock data and find the observations to be consistent with having a featureless PPS. The machinery developed here will be a complimentary tool in the search for features with upcoming CMB surveys. Our methodology also shows competitive performance in image deconvolution tasks, which have various applications from microscopy to medical imaging.

Retrieval of Tree Height Percentiles over Rugged Mountain Areas via Target Response Waveform of Satellite Lidar

The retrieval of tree height percentiles from satellite lidar waveforms observed over mountainous areas is greatly challenging due to the broadening and overlapping of the ground return and vegetation return. To accurately represent the shape distributions of the vegetation and ground returns, the target response waveform (TRW) is resolved using a Richardson–Lucy deconvolution algorithm with adaptive iteration. Meanwhile, the ground return is identified as the TRW component within a 4.6 m ground signal extent above the end point of the TRW. Based on the cumulative TRW distribution, the height metrics of the energy percentiles of 25%, 50%, 75%, and 95% are determined using their vertical distances relative to the ground elevation in this study. To validate the proposed algorithm, we select the received waveforms of the Global Ecosystem Dynamics Investigation (GEDI) lidar over the Pahvant Mountains of central Utah, USA. The results reveal that the resolved TRWs closely resemble the actual target response waveforms from the coincident airborne lidar data, with the mean values of the coefficient of correlation, total bias, and root-mean-square error (RMSE) taking values of 0.92, 0.0813, and 0.0016, respectively. In addition, the accuracies of the derived height percentiles from the proposed algorithm are greatly improved compared with the conventional Gaussian decomposition method and the slope-adaptive waveform metrics method. The mean bias and RMSE values decrease by the mean values of 1.68 m and 2.32 m and 1.96 m and 2.72 m, respectively. This demonstrates that the proposed algorithm can eliminate the broadening and overlapping of the ground return and vegetation return and presents good potential in the extraction of forest structure parameters over rugged mountainous areas.

Leon B. Lucy (1938–2018)

Lucy introduced smoothed-particle dynamics, invented a method to combine radiative transfer calculations in expanding atmospheres using Monte Carlo methods and co-developed the Richardson-Lucy deconvolution algorithm.

Impact of spatiotemporal heterogeneity in COVID-19 disease surveillance on epidemiological parameters and case growth rates

SARS-CoV-2 case data are primary sources for estimating epidemiological parameters and for modelling the dynamics of outbreaks. Understanding biases within case-based data sources used in epidemiological analyses is important as they can detract from the value of these rich datasets. This raises questions of how variations in surveillance can affect the estimation of epidemiological parameters such as the case growth rates. We use standardised line list data of COVID-19 from Argentina, Brazil, Mexico and Colombia to estimate delay distributions of symptom-onset-to-confirmation, -hospitalisation and -death as well as hospitalisation-to-death at high spatial resolutions and throughout time. Using these estimates, we model the biases introduced by the delay from symptom-onset-to-confirmation on national and state level case growth rates (rt) using an adaptation of the Richardson-Lucy deconvolution algorithm. We find significant heterogeneities in the estimation of delay distributions through time and space with delay difference of up to 19 days between epochs at the state level. Further, we find that by changing the spatial scale, estimates of case growth rate can vary by up to 0.13 d−1. Lastly, we find that states with a high variance and/or mean delay in symptom-onset-to-diagnosis also have the largest difference between the rt estimated from raw and deconvolved case counts at the state level. We highlight the importance of high-resolution case-based data in understanding biases in disease reporting and how these biases can be avoided by adjusting case numbers based on empirical delay distributions. Code and openly accessible data to reproduce analyses presented here are available.

Improving reconstruction of targets hidden in scattering media by introducing the Lucy-Richardson deconvolution algorithm into a system of multiview optical projections

A method that combines Lucy-Richardson deconvolution algorithm (LRA) with a multiview projection setup to improve imaging reconstruction of objects embedded in scattering media is presented. In the first step, the medium was illuminated with a laser beam and single-shot multiple images of the object were obtained from different viewpoints. Next, the above procedure was performed under the same conditions but only the medium, without the object, was illuminated by a light point source to obtain the system PSF. Third, each sub-image of the object was digitally cropped, extracted from the array, and deconvolved with the average PSF image following the LRA. Finally, all the sub-deconvolved images were shifted to a common point and superimposed to reveal the shape of the hidden object. Various setup conditions including medium turbidity, thickness, target shape, and illumination state were tested and compared. Results indicate an effective performance of the proposed method.

Penalized least-squares for imaging with hypertelescopes.

Practical considerations such as cost constrain the aperture size of conventional telescopes, which, combined with atmospheric turbulence effects, even in the presence of adaptive optics, limit achievable angular resolution. Sparse aperture telescopes represent a viable alternative for achieving improved angular resolution by combining light collected from small apertures distributed over a wide spatial area either using amplitude interferometry or a direct imaging approach to beam-combining. The so-called densified hypertelescope imaging concept in particular provides a methodology for direct image formation from large sparse aperture arrays. The densification system suppresses wide-angle side lobes and concentrates that energy in the center of the focal plane, significantly improving the signal-to-noise ratio of the measurement. Even with densification, an inevitable consequence of sparse aperture sampling is that the point-spread function associated with the direct image contains an additional structure not present in full aperture imaging systems. Postdetection image reconstruction is performed here to compute a high-fidelity estimate of the measured object in the presence of noise. In this paper, we describe a penalized least-squares object-estimation approach and compare the results with the classical Richardson-Lucy deconvolution algorithm as it is applied to hypertelescope image formation. The parameters of the algorithm are selected based on a comprehensive simulation study using the structure similarity metric to assess reconstruction performance. We find that the penalized least-squares formulation with optimized parameters provides significantly improved reconstructions compared with the conventional Richardson-Lucy algorithm.

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.

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.

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.

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.

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.

High-Resolution Time Delay Estimation Algorithms Through Cross-Correlation Post-Processing

Conventional cross-correlation (CC) and matched filter (MF) algorithms fail to resolve the multipath signals in cases when they are spaced within a Rayleigh resolution limit. Further post-processing of the CC outputs is necessary to improve the performance of CC. In this work, we propose two high-resolution time delay estimation algorithms by post-processing of the CC outputs. The first method applies a Richardson-Lucy deconvolution algorithm used in image deblurring to the CC outputs (Dec-CC). The proposed Dec-CC algorithm yields narrow beams to improve the estimation resolution and accuracy and achieve excellent performance in low signal-to-noise ratio (SNR) environments. The second method reformulates CC as a sparse signal recovery (SSR) problem and estimates time delay via weighted L1 norm minimization (CC-WL1). CC-WL1 also performs excellently for low SNR cases. Simulation results show that the proposed Dec-CC and CC-WL1 algorithms outperform other counterparts.

Inflation wars: a new hope

We explore a class of primordial power spectra that can fit the observed anisotropies in the cosmic microwave background well and that predicts a value for the Hubble parameter consistent with the local measurement of H0 = 74 km/s/Mpc. This class of primordial power spectrum consists of a continuous deformation between the best-fit power law primordial power spectrum and the primordial power spectrum derived from the modified Richardson-Lucy deconvolution algorithm applied to the Cℓs of best-fit power law primordial power spectrum. We find that linear interpolation half-way between the power law and modified Richardson-Lucy power spectra fits the Planck data better than the best-fit ΛCDM by Δ log ℒ = 2.5. In effect, this class of deformations of the primordial power spectra offer a new dimension which is correlated with the Hubble parameter. This correlation causes the best-fit value for H0 to shift and the uncertainty to expand to H0 = 70.2 ± 1.2 km/s/Mpc. When considering the Planck dataset combined with the Cepheid H0 measurement, the best-fit H0 becomes H0 = 71.8 ± 0.9 km/s/Mpc. We also compute a Bayes factor of log K = 5.7 in favor of the deformation model.

Spatially-Variant CNN-based Point Spread Function Estimation for Blind Deconvolution and Depth Estimation in Optical Microscopy.

Optical microscopy is an essential tool in biology and medicine. Imaging thin, yet non-flat objects in a single shot (without relying on more sophisticated sectioning setups) remains challenging as the shallow depth of field that comes with highresolution microscopes leads to unsharp image regions and makes depth localization and quantitative image interpretation difficult. Here, we present a method that improves the resolution of light microscopy images of such objects by locally estimating image distortion while jointly estimating object distance to the focal plane. Specifically, we estimate the parameters of a spatiallyvariant Point Spread Function (PSF) model using a Convolutional Neural Network (CNN), which does not require instrument- or object-specific calibration. Our method recovers PSF parameters from the image itself with up to a squared Pearson correlation coefficient of 0.99 in ideal conditions, while remaining robust to object rotation, illumination variations, or photon noise. When the recovered PSFs are used with a spatially-variant and regularized Richardson-Lucy (RL) deconvolution algorithm, we observed up to 2.1 dB better Signal-to-Noise Ratio (SNR) compared to other Blind Deconvolution (BD) techniques. Following microscope-specific calibration, we further demonstrate that the recovered PSF model parameters permit estimating surface depth with a precision of 2 micrometers and over an extended range when using engineered PSFs. Our method opens up multiple possibilities for enhancing images of non-flat objects with minimal need for a priori knowledge about the optical setup.