Richardson-Lucy Algorithm Research Articles

High-resolution and low-sidelobe forward-look sonar imaging using deconvolution

For the two-dimensional forward-look sonar imaging, the conventional beamformer (CBF) and the matched filter (MF) are often used due to the simplicity and robustness. However, the angular and range resolutions are limited and the sidelobes (SLs) are high. In this paper, we propose a deconvolution method to improve the resolutions and reduce the SLs. The proposed method uses a two-step Richardson-Lucy (R-L) algorithm to deconvolve the raw sonar image produced by CBF and MF, which is actually a post-beamformer processing method. In the first step the R-L algorithm is applied to the angular dimension, where the CBF beampattern is used as the point spread function (PSF); in the second step the R-L algorithm is applied to the range dimension where the auto-correlation function (ACF) of the transmitted linear frequency modulation (LFM) pulse is taken as the PSF. Furthermore, the non-ideal conditions including the low signal-to-noise ratio, the array manifold vector error and the echo distortion error are considered. Via numerical simulations and real data analysis, we show that the proposed method can improve the angular and range resolutions and reduce SLs significantly, while maintains a good robustness against these non-ideal conditions.

An Efficient FPGA Implementation of Richardson-Lucy Deconvolution Algorithm for Hyperspectral Images

This paper proposes an implementation of a Richardson-Lucy (RL) deconvolution method to reduce the spatial degradation in hyperspectral images during the image acquisition process. The degradation, modeled by convolution with a point spread function (PSF), is reduced by applying both standard and accelerated RLdeconvolution algorithms on the individual images in spectral bands. Boundary conditions are introduced to maintain a constant image size without distorting the estimated image boundaries. The RL deconvolution algorithm is implemented on a field-programmable gate array (FPGA)-based Xilinx Zynq-7020 System-on-Chip (SoC). The proposed architecture is parameterized with respect to the image size and configurable with respect to the algorithm variant, the number of iterations, and the kernel size by setting the dedicated configuration registers. A speed-up by factors of 61 and 21 are reported compared to software-only and FPGA-based state-of-the-art implementations, respectively.

Superresolution Reconstruction of Severely Undersampled Point-spread Functions Using Point-source Stacking and Deconvolution

Abstract Point-spread function (PSF) estimation in spatially undersampled images is challenging because large pixels average fine-scale spatial information. This is problematic when fine-resolution details are necessary, as in optimal photometry where knowledge of the illumination pattern beyond the native spatial resolution of the image may be required. Here, we introduce a method of PSF reconstruction where point sources are artificially sampled beyond the native resolution of an image and combined together via stacking to return a finely sampled estimate of the PSF. This estimate is then deconvolved from the pixel-gridding function to return a superresolution kernel that can be used for optimally weighted photometry. We benchmark against the <1% photometric error requirement of the upcoming SPHEREx mission to assess performance in a concrete example. We find that standard methods like Richardson–Lucy deconvolution are not sufficient to achieve this stringent requirement. We investigate a more advanced method with significant heritage in image analysis called iterative back-projection (IBP) and demonstrate it using idealized Gaussian cases and simulated SPHEREx images. In testing this method on real images recorded by the LORRI instrument on New Horizons, we are able to identify systematic pointing drift. Our IBP-derived PSF kernels allow photometric accuracy significantly better than the requirement in individual SPHEREx exposures. This PSF reconstruction method is broadly applicable to a variety of problems and combines computationally simple techniques in a way that is robust to complicating factors such as severe undersampling, spatially complex PSFs, noise, crowded fields, or limited source numbers.

Comparison Analysis of Five Waveform Decomposition Algorithms for the Airborne LiDAR Echo Signal

The information from the components obtained by waveform decomposition is usually used to inverse topography, and classify tree species, etc. Many efforts on waveform decomposition algorithms have been presented, but they lack comparison analysis and evaluation. Thereby, this article compares and analyzes the performance of five waveform decomposition algorithms, which are Gaussian, Adaptive Gaussian, Weibull, Richardson–Lucy (RL), and Gold, under different topographic conditions such as forests, glaciers, lakes, and residential areas. The experimental results reveal that: first, the Gaussian algorithm causes the biggest fitting error at 9.96 mV in the forested area. It is easy to identify multiple dense peaks as single peaks. Second, there are many misjudged, superimposed, and overlapped waveform components separated by the Weibull algorithm. The Adaptive Gaussian is more capable of fitting complex waveforms but has 122 more outliers than the Weibull algorithm does. Third, the Gold and RL algorithms decompose the largest number of waveform components (272.2k and 265.9k) in the forested area; both RL and Gold algorithms can effectively improve the separability of peaks. Fourth, the RL algorithm is only more effective for the area with sparse vegetation than the Gold algorithm does, i.e., the Gold algorithm is capable of processing data with dense vegetation areas at a lowest false component detection rate of 1.3%, 0.9%, 1.1%, and 0.1% in four areas. Finally, the Gaussian and Gold algorithms have much faster decomposition speed at 1000/s and 2000/s than the other three algorithms do. These results are useful for selecting different algorithms under different environments.

Quality assessment of image deburring algorithms

Camera shake during video recording is a major source of image defocus. Restoring these defocuses is one of the most important tasks in image processing. This article examines and evaluates the most commonly used algorithms in practice, namely: Richardson-Lucy algorithm, Tikhonov regularization, and Blind deconvolution. The comparisons were made using structural similarity, image sharpness, and root mean square error.

Photon Counting Integral Imaging Based on Lucy-Richardson Algorithm

Photon Counting Integral Imaging Based on Lucy-Richardson Algorithm

Superresolving, Artifact-Free Optical Coherence Tomography with Deconvolution-Random Phase Modulation

Deconvolution is widely used to improve resolution in microscopy. Unfortunately, deconvolution in optical coherence tomography (OCT) is sensitive to noise which inherently results in additive artifacts. These artifacts severely impair the fidelity of deconvolved images and limit its use in OCT imaging. Here we propose a framework that encodes numerical random phase masks in the Fourier space of a deconvolved OCT image, to produce a sub-resolution image with the artifacts removed. The optimized joint operation of an iterative Richardson-Lucy deconvolution and a numerical synthesis of random phase masks (RPM), termed as Deconv-RPM, enables a 2.7-fold enhancement in both transverse and axial resolutions. We demonstrate that the Deconv-RPM method allows imaging previously unresolved cellular-level details in the human labial mucosa in vivo with significantly improved clarity.

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.

Removal of ghost particles from the reconstruction of dusty plasma in integral photography by three-dimensional deconvolution

The integral photography and deconvolution techniques have been applied to identify the three-dimensional (3D) positions of particles levitating in plasma. Artifacts in the light field, i.e. ghost particles, are removed by collating between results of integral photography and direct Richardson-Lucy deconvolution (RLD). Our reconstruction system is tested with known target particles and it is found that it works well in the range of our dust experiment. By applying the integral photography and RLD techniques to the obtained experimental image, we identified the 3D positions of dust particles floating in a radio-frequency plasma. Ghost particles are eliminated from the results by deconvolution and we succeeded in obtaining the 3D structure of a dusty plasma from a single-exposure image obtained from one view port.

A Deconvolutional Reconstruction Method Based on Lucy–Richardson Algorithm for Joint Scanning Laser Thermography

Joint scanning laser thermography (JLST) is well-known for its efficiency to overcome the field of view (FOV) limitation of thermal imagers. However, JSLT requires a data reconstruction to reveal the location of the defective area straightforwardly. Moreover, its detection capacity is limited by the lack of a deconvolution algorithm adaptive to the reconstructed data. In this study, a deconvolutional reconstruction method based on the Lucy–Richardson (LR) algorithm has been developed for JST, which is effective in suppressing random noise and the blur effect caused by the thermal diffusion. A JSLT inspection is carried out on a functional coating material with cylinder-like defects to test the performance of the proposed method. In comparison to the directly processed method on the original data, the proposed method is processed on the reconstructed data and then compared with principal component analysis (PCA), restored pseudo heat flux (RPHF), fast Fourier transform (FFT) methods and non-negative matrix factorization (NMF). The experimental results indicated that our proposed LR method exhibited a higher signal-to-noise ratio. Besides, it can detect the cylinder-mocked debonding defects with a diameter of 1.5 mm and a depth of 2.0 mm buried under the 1.0-mm coating. In addition, the defect detection diameter-to-depth ratio reached 1.5, while the defect detection rate of the test specimens can approach 90%.

Improving the depth resolution of STEM-ADF sectioning by 3D deconvolution.

Although the possibility of locating single atom in three dimensions using the scanning transmission electron microscope (STEM) has been discussed with the advent of aberration correction technology, it is still a big challenge. In this report we have developed deconvolution routines based on maximum entropy method (MEM) and Richardson-Lucy algorithm (RLA), which are applicable to the STEM-annular dark-field (ADF) though-focus images to improve the depth resolution. The new three-dimensional (3D) deconvolution routines require a limited defocus-range of STEM-ADF images that covers a whole sample and some vacuum regions. Since the STEM-ADF probe is infinitely elongated along the optical axis, a 3D convolution is performed with a two-dimensional (2D) convolution over xy-plane using the 2D fast Fourier transform in reciprocal space, and a one-dimensional convolution along the z-direction in real space. Using our new deconvolution routines, we have processed simulated focal series of STEM-ADF images for single Ce dopants embedded in wurtzite-type AlN. Applying the MEM, the Ce peaks are clearly localized along the depth, and the peak width is reduced down to almost one half. We also applied the new deconvolution routines to experimental focal series of STEM-ADF images of a monolayer graphene. The RLA gives smooth and high-P/B ratio scattering distribution, and the graphene layer can be easily detected. Using our deconvolution algorithms, we can determine the depth locations of the heavy dopants and the graphene layer within the precision of 0.1 and 0.2 nm, respectively. Thus, the deconvolution must be extremely useful for the optical sectioning with 3D STEM-ADF images.

Toward image quality assessment in optical coherence tomography (OCT) of rat kidney

Optical coherence tomography (OCT) is a useful tool for the evaluation of structure and function of the kidney, but the image quality can be effected by many factors. The objective of this study was to assess the image quality of different OCT systems in OCT imaging of the living kidney. One swept-source OCT (SSOCT) of 1300 nm, one spectral domain OCT (SDOCT) of 1300 nm and another of 900 nm were used. A FeO phantom was used to establish the point spread function (PSF). Rat kidneys were imaged for image quality assessment. Light penetration in the kidney and the optical attenuation coefficient were also evaluated. The quantification of uriniferous tubules was carried out via the threshold segmentation of 3D OCT images. The quality of kidney images was resolution dependent. SDOCT of 900 nm showed higher peak signal-to noise ratio and dynamic range. The spatial resolution in the light field could be derived from the PSF distribution along three mutually orthogonal axes. In conjunction with the PSF, the Lucy-Richardson algorithm could improve image quality but could not reveal more microstructural information. The penetration depth of 1300 nm was deeper than that of 900 nm. The attenuation coefficient of the kidney was 29 cm-1 at 1300 nm and 50 cm-1 at 900 nm (P < 0.001). More accurate measurement of uriniferous tubules was achieved with the SDOCT-900 due to its higher resolution. Both SSOCT and SDOCT systems could be useful for imaging uriniferous tubules in the superficial layers of the cortex. The OCT image quality was highly correlated with the spatial resolution of OCT system.

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.

Correction of refractive index mismatch-induced aberrations under radially polarized illumination by deep learning.

Radially polarized field under strong focusing has emerged as a powerful manner for fluorescence microscopy. However, the refractive index (RI) mismatch-induced aberrations seriously degrade imaging performance, especially under high numerical aperture (NA). Traditional adaptive optics (AO) method is limited by its tedious procedure. Here, we present a computational strategy that uses artificial neural networks to correct the aberrations induced by RI mismatch. There are no requirements for expensive hardware and complicated wavefront sensing in our framework when the deep network training is completed. The structural similarity index (SSIM) criteria and spatial frequency spectrum analysis demonstrate that our deep-learning-based method has a better performance compared to the widely used Richardson-Lucy (RL) deconvolution method at different imaging depth on simulation data. Additionally, the generalization of our trained network model is tested on new types of samples that are not present in the training procedure to further evaluate the utility of the network, and the performance is also superior to RL deconvolution.

An optimized Ly α forest inversion tool based on a quantitative comparison of existing reconstruction methods

ABSTRACT We present a same-level comparison of the most prominent inversion methods for the reconstruction of the matter density field in the quasi-linear regime from the Ly α forest flux. Moreover, we present a pathway for refining the reconstruction in the framework of numerical optimization. We apply this approach to construct a novel hybrid method. The methods which are used so far for matter reconstructions are the Richardson–Lucy algorithm, an iterative Gauss–Newton method and a statistical approach assuming a one-to-one correspondence between matter and flux. We study these methods for high spectral resolutions such that thermal broadening becomes relevant. The inversion methods are compared on synthetic data (generated with the lognormal approach) with respect to their performance, accuracy, their stability against noise, and their robustness against systematic uncertainties. We conclude that the iterative Gauss–Newton method offers the most accurate reconstruction, in particular at small S/N, but has also the largest numerical complexity and requires the strongest assumptions. The other two algorithms are faster, comparably precise at small noise-levels, and, in the case of the statistical approach, more robust against inaccurate assumptions on the thermal history of the intergalactic medium (IGM). We use these results to refine the statistical approach using regularization. Our new approach has low numerical complexity and makes few assumptions about the history of the IGM, and is shown to be the most accurate reconstruction at small S/N, even if the thermal history of the IGM is not known. Our code will be made publicly available.

Nanoparticle size distribution from inversion of wide angle X-ray total scattering data

An increasingly important issue in nanoscience and nanotechnology is the accurate determination of nanoparticle sizing. Wide angle X-ray total scattering (WAXTS) data are frequently used to retrieve the Particle Size Distributions (PSDs) of nanocrystals of highly technological relevance; however, the PSD shape typically relies on an a-priori assumption. Here, we propose a modified version of the classical iterative Lucy-Richardson (LR) algorithm, which is simple, fast and highly reliable against noise, and demonstrate that the inversion of WAXTS data can be profitably used for recovering accurate PSD regardless of its shape. Computer simulations based on the use of the Debye Scattering Equation (DSE) modelling WAXTS data show that the algorithm is capable of recovering accurate PSDs even when the sample is made of a mixture of different polymorphs and/or exhibits microstrain effects. When applied to the inversion of WAXTS data taken on real samples, the method requires accurate modelling of the nanoparticle crystal structure, which includes structural defects, microstrain and surface induced distortions. Provided that this information is correctly fed to the program, the inversion algorithm reconstructs the WAXTS data with high accuracy and recovers highly robust (against noise) PSDs. Two examples reporting the characterization of Magnetite-Maghemite and commercial P25-Titania nanopowders, are discussed. We demonstrate that pre-assumption of wrong PSD shape leads to inaccurate number-based average sizes in highly polydisperse samples.

A Quantum Richardson–Lucy image restoration algorithm based on controlled rotation operation and Hamiltonian evolution

The problems of the real-time and high-precision image processing, even the powerful classical computers and their algorithms, are not satisfactory solution. With the emerging quantum technology, quantum image representation that shines can ease these solutions. The quantum Richardson–Lucy algorithm is proposed on controlled rotation operation and Hamiltonian evolution. To begin with, a flexible representation of the quantum image model is used as the basis of image representation, and the amplitude is manipulated by controlled rotation gate. Then, the controlled rotation operation is completed, and then, the algorithm only needs the quantum state on the first quantum register, and the algorithm constructs an quantum gate by Hamiltonian evolution on the register, which is to realize the quantum gate Richardson–Lucy function. Finally, the quantum state after controlled rotation is further operated by the quantum gate constructed by non-sparse Hamiltonian evolution technique, and all quantum states storing color information are reduced to clear quantum images. The simulation results show that the algorithm has the best effect on motion blur, and the peak signal-to-noise ratio can reach 31.3985 under small blur degree. The processing result of Gaussian noise is worse than that of pure motion blur, with a peak signal-to-noise ratio of 26.5232.

Imaging the 511 keV Positron Annihilation Sky with COSI

Abstract The balloon-borne Compton Spectrometer and Imager (COSI) had a successful 46-day flight in 2016. The instrument is sensitive to photons in the energy range 0.2–5 MeV. Compton telescopes have the advantage of a unique imaging response and provide the possibility of strong background suppression. With its high-purity germanium detectors, COSI can precisely map γ-ray line emission. The strongest persistent and diffuse γ-ray line signal is the 511 keV emission line from the annihilation of electrons with positrons from the direction of the Galactic center. While many sources have been proposed to explain the amount of positrons, , the true contributions remain unsolved. In this study, we aim at imaging the 511 keV sky with COSI and pursue a full-forward modeling approach, using a simulated and binned imaging response. For the strong instrumental background, we describe an empirical approach to take the balloon environment into account. We perform two alternative methods to describe the signal: Richardson–Lucy deconvolution, an iterative method toward the maximum likelihood solution, and model fitting with predefined emission templates. Consistently with both methods, we find a 511 keV bulge signal with a flux between 0.9 and , confirming earlier measurements, and also indications of more extended emission. The upper limit we find for the 511 keV disk, , is consistent with previous detections. For large-scale emission with weak gradients, coded aperture mask instruments suffer from their inability to distinguish isotropic emission from instrumental background, while Compton telescopes provide a clear imaging response, independent of the true emission.

Rapid image deconvolution and multiview fusion for optical microscopy.

The contrast and resolution of images obtained with optical microscopes can be improved by deconvolution and computational fusion of multiple views of the same sample, but these methods are computationally expensive for large datasets. Here we describe theoretical and practical advances in algorithm and software design that result in image processing times that are tenfold to several thousand fold faster than with previous methods. First, we show that an 'unmatched back projector' accelerates deconvolution relative to the classic Richardson-Lucy algorithm by at least tenfold. Second, three-dimensional image-based registration with a graphics processing unit enhances processing speed 10- to 100-fold over CPU processing. Third, deep learning can provide further acceleration, particularly for deconvolution with spatially varying point spread functions. We illustrate our methods from the subcellular to millimeter spatial scale on diverse samples, including single cells, embryos and cleared tissue. Finally, we show performance enhancement on recently developed microscopes that have improved spatial resolution, including dual-view cleared-tissue light-sheet microscopes and reflective lattice light-sheet microscopes.

Validation of iterative multi-resolution method for partial volume correction and quantification improvement in PET image

The partial volume effect (PVE) is a prime limitation that characterizes the Positron Emission Tomography (PET). This effect is mainly caused by the limited spatial resolution and the tissue fraction effect. In fact, the quantification accuracy is significantly affected by the quality of the image. Various post-corrections PVE methods were evaluated in the literature to improve the quantitative information. The deconvolution algorithm is commonly used for partial volume correction (PVC) where no a prior knowledge or information from other modalities expect the PET are invoked. In this context, a new approach based on Richardson-Lucy algorithm is presented in this paper. A normal inverse Gaussian distribution model in shearlet domain was incorporated to the approach as a regularization step. The aim of the proposed method (RL-NIG) is to provide an accurate quantification parameters with an efficient intensity recovery and noise reduction. Experimental results on simulated phantom and preclinical dataset have shown that the present method achieve notable correction in term of the Myocardium Metabolic Rate for Glucose (MMRGlu) value and efficient noise diminution.