Richardson-Lucy Algorithm Research Articles

Point spread function engineering enable resolution enhanced imaging for Interferenceless coded aperture correlation holography

The point spread function (PSF) of an optical system could characterize the resolving ability of the whole optical system for point light sources. Therefore, the imaging performance of the system could be significantly improved by regulating and optimizing the PSF. In this paper, we innovatively propose a single-exposure hologram resolution enhanced cross-correlation (RECC) method for Interferenceless coded aperture holography(I-COACH) system, circumventing the necessity to obtain the point spread hologram (PSH) of an ideal point object. The RECC method firstly acquires an approximate image of a large-size point object by Lucy-Richardson (LR) algorithm in lens imaging mode, and takes it as a PSF to acquire a PSH with ideal size of the I-COACH system by LR algorithm again, and finally acquires a reconstructed image by the single-exposure hologram RECC method. In the RECC method, the approximate ideal PSHs at different axial positions of the system are acquired by offline operation, therefore, it has a high imaging temporal resolution, and the imaging transverse resolution is not affected by the size of the point objects at the time of recording the PSH, which provides a high imaging signal-to-noise ratio and stable resolution. The proposed method provides powerful technical support for further extending the application field of the I-COACH system, and provides technical reference for other incoherent imaging.

Image processing tools for petabyte-scale light sheet microscopy data.

Light sheet microscopy is a powerful technique for high-speed three-dimensional imaging of subcellular dynamics and large biological specimens. However, it often generates datasets ranging from hundreds of gigabytes to petabytes in size for a single experiment. Conventional computational tools process such images far slower than the time to acquire them and often fail outright due to memory limitations. To address these challenges, we present PetaKit5D, a scalable software solution for efficient petabyte-scale light sheet image processing. This software incorporates a suite of commonly used processing tools that are optimized for memory and performance. Notable advancements include rapid image readers and writers, fast and memory-efficient geometric transformations, high-performance Richardson-Lucy deconvolution and scalable Zarr-based stitching. These features outperform state-of-the-art methods by over one order of magnitude, enabling the processing of petabyte-scale image data at the full teravoxel rates of modern imaging cameras. The software opens new avenues for biological discoveries through large-scale imaging experiments.

Reconstruction of Bremsstrahlung γ-rays spectrum in heavy ion reactions with Richardson-Lucy algorithm

The high momentum tail (HMT) in the momentum distribution of nucleons above the Fermi surface has been regarded as an evidence of short-range correlations (SRCs) in atomic nuclei. It has been showcased recently that the np Bremsstrahlung radiation in heavy ion reactions can be used to extract HMT information. The Richardson-Lucy (RL) algorithm is introduced to the reconstruction of the original Bremsstrahlung γ-ray energy spectrum from experimental measurements. By solving the inverse problem of the detector response to the γ-rays, the original energy spectrum of the Bremsstrahlung γ in 25 MeV/u 86Kr + 124Sn has been reconstructed and compared to the isospin- and momentum-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) simulations. The analysis based on hypothesis test suggests the existence of the HMT of nucleons in nuclei, in accordance with the previous conclusions. With its effectiveness being demonstrated, it is feasible to apply the RL algorithm in future experiments of measuring the Bremsstrahlung γ-rays in heavy ion reactions.

Gaussian second derivative blur kernels for image deblurring

Image blur is a common image degradation phenomenon that occurs in case of camera movement and lens defocusing. In order to deblur the image, point spread function (PSF) model is often used to match the real blur kernel, but currently the matching effect is poor. In this paper, an image restoration technique based on the Gaussian Second Derivative (GSD) fitted PSF is proposed to address this problem. Firstly, a GSD model is proposed. The actual image Line spread function (LSF) extracted by knife-edge method is modeled as a linear combination of a series of Gaussian second derivatives. Then, an improved annihilation filtering algorithm is proposed. The algorithm is used to estimate the parameters of the GSD model, so as to remove the errors in the actual complex scenarios. Finally, the image PSF is obtained by using the LSF curve fitted and corrected by the GSD model, and combined with the existing Richardson-Lucy (R-L) algorithm, the clear image is finally restored. Experimental results show that compared with the existing image restoration strategies based on other PSF models, this method can effectively improve the image restoration accuracy.

Virtual-point-based deconvolution for optical-resolution photoacoustic microscopy.

Optical-resolution photoacoustic microscopy (OR-PAM) has been increasingly utilized for in vivo imaging of biological tissues, offering structural, functional, and molecular information. In OR-PAM, it is often necessary to make a trade-off between imaging depth, lateral resolution, field of view, and imaging speed. To improve the lateral resolution without sacrificing other performance metrics, we developed a virtual-point-based deconvolution algorithm for OR-PAM (VP-PAM). VP-PAM has achieved a resolution improvement ranging from 43% to 62.5% on a single-line target. In addition, it has outperformed Richardson-Lucy deconvolution with 15 iterations in both structural similarity index and peak signal-to-noise ratio on an OR-PAM image of mouse brain vasculature. When applied to an in vivo glass frog image obtained by a deep-penetrating OR-PAM system with compromised lateral resolution, VP-PAM yielded enhanced resolution and contrast with better-resolved microvessels.

A correction algorithm of geometric unsharpness for neutron radiographs via adaptive fusion and total variation

The mobility of accelerator-based neutron sources has laid the foundation for the miniaturization of neutron radiography facilities in response to the increasing industrial requirements. Compared to traditional reactors and spallation neutron sources, miniaturized neutron radiography facilities based on accelerator neutron sources face challenges in achieving a sufficiently high collimation ratio. It leads to a pronounced level of geometric unsharpness on neutron radiographs, which arises from a finite source size and beam divergence. The presence of blurriness in radiographs significantly impairs the ability to accurately visualize the internal structures of the test objects, thus hindering observation. An algorithm combining adaptive fusion with total variation was proposed to correct the geometric unsharpness for neutron radiographs in this paper. In contrast to most traditional restoration algorithms that relied on regularization terms or filters, our proposed method offered both initial restoration and further restoration. The initial restoration procedure involved the utilization of the Richardson-Lucy algorithm coupled with the l0 smoothing method. This adaptive fusion technique was employed to enhance the sharpness of edges and denoise the neutron radiographs. Finally, the result of the adaptive fusion was embedded into a deblurring model based on total variation to further preserve the edges and restore more details during further restoration. In the experiments, it was demonstrated that our correction algorithm effectively preserved the prominent edges and the details in both the simulated and real neutron radiographs of thin and thick objects, exhibiting fewer ringing effects than traditional algorithms. It is worth mentioning that our work is primarily applicable and significant to neutron generators, but not for reactors or spallation neutron sources that can deliver much better images.

Deblurring of Beamformed Images in the Ocean Acoustic Waveguide Using Deep Learning-Based Deconvolution

A horizontal towed linear coherent hydrophone array is often employed to estimate the spatial intensity distribution of incident plane waves scattered from the geological and biological features in an ocean acoustic waveguide using conventional beamforming. However, due to the physical limitations of the array aperture, the spatial resolution after conventional beamforming is often limited by the fat main lobe and the high sidelobes. Here, we propose a method originated from computer vision deblurring based on deep learning to enhance the spatial resolution of beamformed images. The effect of image blurring after conventional beamforming can be considered a convolution of beam pattern, which acts as a point spread function (PSF), and the original spatial intensity distributions of incident plane waves. A modified U-Net-like network is trained on a simulated dataset. The instantaneous acoustic complex amplitude is assumed following circular complex Gaussian random (CCGR) statistics. Both synthetic data and experimental data collected from the South China Sea Experiment in 2021 are used to illustrate the effectiveness of this approach, showing a maximum 700% reduction in a 3 dB width over conventional beamforming. A lower normalized mean square error (NMSE) is provided compared with other deconvolution-based algorithms, such as the Richardson–Lucy algorithm and the approximate likelihood model-based deconvolution algorithm. The method is applicable in various acoustic imaging applications that employ linear coherent hydrophone arrays with one-dimensional conventional beamforming, such as ocean acoustic waveguide remote sensing (OAWRS).

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.

Decomposition of full-waveform LiDAR data utilizing an adaptive B-spline-based model and particle swarm optimization

High-precision waveform decomposition is crucial for LiDAR applications. Existing methods encounter challenges including poor target detection and low accuracy in extracting parameters of irregular components, especially in complex echoes. We introduce an adaptive B-spline-based decomposition (AdaptB-spline) method, which uses B-spline curves to adaptively adjust the shape and position of component through the particle swarm optimization (PSO); and proposes an initial parameter estimation method based on the B-spline and Richardson-Lucy (RL) deconvolution, which improves the noise immunity and component detection. Experiments were conducted on synthetic waveforms and satellite LiDAR waveforms by AdaptB-spline and other four methods (Gaussian (Gauss), B-spline-based (B-spline), skew-normal (SkewN), and multi-Gaussian (MultiGauss) decomposition). We concluded that AdaptB-spline exhibits superior performance in terms of component RMSE, CC, R2, component parameter error and range error metrics compared to the four methods. So AdaptB-spline can enhance component detection and accurately fit Gaussian or non-Gaussian waveforms, demonstrating outstanding target detection and ranging precision.

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.

Beyond synthetic aperture focusing: deconvolution-based elevation resolution enhancement using simulated point spread function for linear array-based three-dimensional photoacoustic imaging.

This paper introduces a deconvolution-based method to enhance the elevation resolution of a linear array-based three-dimensional (3D) photoacoustic (PA) imaging system. PA imaging combines the high contrast of optical imaging with the deep, multi-centimeter spatial resolution of ultrasound (US) imaging, providing structural and functional information about biological tissues. Linear array-based 3D PA imaging is easily accessible and applicable for ex vivo studies, small animal research, and clinical applications in humans. However, its elevation resolution is limited by the acoustic lens geometry, which establishes a single elevation focus. Previous work used synthetic aperture focusing (SAF) to enhance elevation resolution, but the resolution achievable by SAF is constrained by the size of the elevation focus. Here, we introduce the application of Richardson-Lucy deconvolution, grounded in simulated point-spread-functions, to surpass the elevation resolution attainable with SAF alone. We validated this approach using both simulation and experimental data, demonstrating that the full-width-at-half-maximum of point targets on the elevation plane was reduced compared to using SAF only, suggesting resolution improvement. This method shows promise for improving 3D image quality of existing linear array-based PA imaging systems, offering potential benefits for disease diagnosis and monitoring.

Super-resolution image reconstruction of a neutron thick pinhole imaging system using image denoiser prior based on half quadratic splitting method

Thick pinhole imaging system is a powerful tool to diagnose intense pulsed radiation sources. However, high spatial resolution of a thick pinhole imaging system cannot be achieved due to the limitation of field of view (FOV) and detection efficiency. In this paper, we propose a novel super-resolution image reconstruction algorithm to improve the spatial resolution of a practical thick pinhole imaging system designed for 14.1 MeV neutrons with 100 mm FOV. Point spread function (PSF) of the imaging system is obtained through complete simulation methods, indicating that the spatial resolution of the imaging system is about 500 μ m. A 4 × super-resolution image reconstruction algorithm using image denoiser as implicit image prior, named image denoiser prior, based on half quadratic splitting (HQS) method is firstly applied to restore more details of neutron sources. The results show that the proposed algorithm performs better than the Richardson-Lucy (RL) algorithm with fewer artifacts and sharper boundaries in reconstructed images. Notably, at a low noise level, the proposed algorithm can surpass the Nyquist sampling limit of 200 μ m, which is determined by the equivalent camera pixel size, to achieve a spatial resolution of 150 μ m.

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.

Neutron penumbral image reconstruction with a convolution neural network using fast Fourier transform.

In Inertial Confinement Fusion (ICF), the asymmetry of a hot spot is an important influence factor in implosion performance. Neutron penumbral imaging, which serves as an encoded-aperture imaging technique, is one of the most important diagnostic methods for detecting the shape of a hot spot. The detector image is a uniformly bright range surrounded by a penumbral area, which presents the strength distribution of hot spots. The present diagnostic modality employs an indirect imaging technique, necessitating the reconstruction process to be a pivotal aspect of the imaging protocol. The accuracy of imaging and the applicable range are significantly influenced by the reconstruction algorithm employed. We develop a neural network named Fast Fourier transform Neural Network (FFTNN) to reconstruct two-dimensional neutron emission images from the penumbral area of the detector images. The FFTNN architecture consists of 16 layers that include a FFT layer, convolution layer, fully connected layer, dropout layer, and reshape layer. Due to the limitations in experimental data, we propose a phenomenological method for describing hot spots to generate datasets for training neural networks. The reconstruction performance of the trained FFTNN is better than that of the traditional Wiener filtering and Lucy-Richardson algorithm on the simulated dataset, especially when the noise level is high as indicated by the evaluation metrics, such as mean squared error and structure similar index measure. This proposed neural network provides a new perspective, paving the way for integrating neutron imaging diagnosis into ICF.

Size characterization of x-ray tube source with sphere encoded imaging method.

In x-ray imaging, the size of the x-ray tube light source significantly impacts image quality. However, existing methods for characterizing the size of the x-ray tube light source do not meet measurement requirements due to limitations in processing accuracy and mechanical precision. In this study, we introduce a novel method for accurately characterizing the size of the x-ray tube light source using spherical encoded imaging technology. This method effectively mitigates blurring caused by system tilting, making system alignment and assembly more manageable. We employ the Richardson-Lucy algorithm to iteratively deconvolve the image and recover spatial information about the x-ray tube source. Unlike traditional coded imaging methods, spherical coded imaging employs high-Z material spheres as coding elements, replacing the coded holes used in traditional approaches. This innovation effectively mitigates blurring caused by system tilting, making system alignment and assembly more manageable. In addition, the mean square error is reduced to 0.008. Our results demonstrate that spherical encoded imaging technology accurately characterizes the size of the x-ray tube light source. This method holds significant promise for enhancing image quality in x-ray imaging.

Three-dimensional thermophotonic super-resolution imaging by spatiotemporal diffusion reversal method.

Spatial super-resolution in thermophotonic imaging was achieved using a combination of spatial second-derivative forming, spatial gradient adaptive filtering, and Richardson-Lucy deconvolution in conjunction with the construction of an experimental point spread function. When implemented through enhanced truncation-correlation photothermal coherence tomography (eTC-PCT), it was possible to restore blurred infrared thermophotonic images to their prediffusion optical resolution state. This modality was tested in various biological applications and proved to be capable of imaging fine axial cracks in human teeth, well-patterned anatomical subsurface structures of a mouse brain, and neovascularization in a mouse thigh due to the rapid proliferation of cancer cells. This modality was found to be immune to optical scattering and could reveal the true spatial extent of biological features at subsurface depths that conventional thermal imaging cannot reach because of limitations imposed by the physics of spreading diffusion.

Volume holographic illuminator for Airy light-sheet microscopy.

Airy light sheets combined with the deconvolution approach can provide multiple benefits, including large field of view (FOV), thin optical sectioning, and high axial resolution. The efficient design of an Airy light-sheet fluorescence microscope requires a compact illumination system. Here, we show that an Airy light sheet can be conveniently implemented in microscopy using a volume holographic grating (VHG). To verify the FOV and the axial resolution of the proposed VHG-based Airy light-sheet fluorescence microscope, ex-vivo fluorescently labeled Caenorhabditis elegans (C. elegans) embryos were imaged, and the Richardson-Lucy deconvolution method was used to improve the image contrast. Optimized parameters for deconvolution were compared with different methods. The experimental results show that the FOV and the axial resolution were 196 µm and 3 µm, respectively. The proposed method of using a compact VHG to replace the common spatial light modulator provides a direct solution to construct a compact light-sheet fluorescence microscope.

Super-resolution stimulated Raman scattering microscopy enhanced by quantum light and deconvolution

Stimulated Raman scattering (SRS) microscopy is a powerful tool for label-free chemical contrast bio-imaging. However, its spatial resolution is limited by diffraction; its noise level is also fundamentally limited by the shot noise due to the quantum nature of light. In this work, we apply the squeezed light technique associated with the deconvolution method to achieve quantum-enhanced super-resolution SRS microscopy. To generate squeezed pump light, we design a unique cascaded scheme by using two nonlinear crystals, in which the second-harmonic generation (SHG) from the first crystal is used to boost the SHG of the second crystal sequentially. Such a cascaded light squeezed scheme suppresses the shot noise down to 89.7% (1 dB), which can be readily applied to the existing conventional SRS microscopy. We combine the squeezed light-controlled SRS with the Richardson–Lucy deconvolution method to break the diffraction limit by improving the spatial resolution of ∼2.2-fold compared to conventional SRS imaging. We realize the quantum-enhanced super-resolution SRS imaging in a variety of samples (e.g., oleic acid, porcine muscle tissue), suggesting the potential of squeezed light SRS with deconvolution for label-free super-resolution chemical imaging in biological and biomedical systems.

Super-resolution reconstruction of structured illumination microscopy using deep-learning and sparse deconvolution

Structured illumination microscopy (SIM) is one of the essential super-resolution microscopic imaging techniques, featuring fast imaging speed, low exposure dose, and having no special requirements for fluorescent probes. In this paper, we propose a super-resolution SIM reconstruction approach, which integrates an end-to-end multi-scale neural network (entitled Scale Richardson-Lucy Network, SRLN). SRLN fits the SIM imaging process through Richardson-Lucy deconvolution incorporated in the neural network. After being trained with sufficient data pairs, among which the ground-truth images were refined with sparse deconvolution, the SRLN network can yield super-resolution images with a spatial resolution of ∼70 nm from raw SIM intensity images. The feasibility and generalization capability of SRLN were experimentally demonstrated by reconstructing SR images for different biological structures, of which the raw images were acquired with different devices. The proposed network will be valuable for super-resolution imaging in the biology and medicine fields.

Full 3-D modulation transfer function estimation of tomosynthesis system using modified Richardson-Lucy deconvolution.

Tomosynthesis systems are three-dimensional (3-D) medical imaging devices that operate over limited acquisition angles using low radiation dosages. To measure the spatial resolution performance of a tomosynthesis system, the modulation transfer function (MTF) is widely used as a quantitative evaluationmetric. We previously introduced a method to estimate the full 3-D MTF of a cone-beam computed tomography system using two-dimensional (2-D) Richardson-Lucy (RL) deconvolution with Tikhonov-Miller regularization. However, this method can not be applied directly to estimate the 3-D MTF of a tomosynthesis system, since the unique artifacts (i.e., shadow artifacts, spreading tails, directional blurring, and high-level noise) of the system produce several errors that lower the estimation performance. Varying positions of the negative pixels due to shadow artifacts and spreading tails cause inconsistent deconvolution performances at each of the directional projections, and the severe noise in the reconstructed images cause noise amplification during estimation. This work proposes several modifications to the previous method to resolve the inconsistent performance and noise amplification errors to increase the full 3-D MTF estimationaccuracy. Three modifications were introduced to the 2-D RL deconvolution to prevent estimation errors and improve MTF estimation performance: non-negativity relaxation function, cost function to terminate the iterative process of RL deconvolution, and regularization strength for noise control. To validate the effectiveness of the proposed modifications, we reconstructed sphere phantoms from simulation and experimental tomosynthesis studies in the iso-center and offset-center positions as well as estimated the full 3-D MTFs using the previous and proposed methods. We compared the 3-D render images, central plane images, and center profiles of the estimated 3-D MTFs and calculated the full widths at half and tenth maximum for quantitativeevaluation. The previous method cannot estimate the full 3-D MTF of a tomosynthesis system; its inaccurate negative pixel relaxation produces circular-shaped errors, and the mean squared error based simple cost function for termination causes inconsistent estimation at each directional projection to diminish the clear edges of the low-frequency drop and missing sample regions. Noise amplification from lack of noise regularization is also seen in the previous method results. Compared to the previous method, the proposed method shows superior estimation performance at reducing errors in both the simulation and experimental studies regardless of object position. The proposed method preserves the low-frequency drop, missing sample regions from the limited acquisition angles, and missing cone region from the offset-center position; the estimated MTFs also show FWHM and FWTM values close to those of the ideal MTFs than with the previousmethod. This work presents a method to estimate the full 3-D MTF of a tomosynthesis system. The proposed modifications prevent circular-shaped errors and noise amplification due to the geometry for limited acquisition angles and high noise levels. Compared to our previous method, the proposed scheme show better performance for estimating the 3-D MTF of the tomosynthesissystem.