Richardson-Lucy Deconvolution Algorithm Research Articles

Rapid deconvolution of low-resolution time-of-flight data using Bayesian inference.

The deconvolution of low-resolution time-of-flight data has numerous advantages, including the ability to extract additional information from the experimental data. We augment the well-known Lucy-Richardson deconvolution algorithm using various Bayesian prior distributions and show that a prior of second-differences of the signal outperforms the standard Lucy-Richardson algorithm, accelerating the rate of convergence by more than a factor of four, while preserving the peak amplitude ratios of a similar fraction of the total peaks. A novel stopping criterion and boosting mechanism are implemented to ensure that these methods converge to a similar final entropy and local minima are avoided. Improvement by a factor of two in mass resolution allows more accurate quantification of the spectra. The general method is demonstrated in this paper through the deconvolution of fragmentation peaks of the 2,5-dihydroxybenzoic acid matrix and the benzyltriphenylphosphonium thermometer ion, following femtosecond ultraviolet laser desorption.

The Richardson-Lucy deconvolution method to extract LAMOST 1D spectra

We use the Richardson-Lucy deconvolution algorithm to extract one-dimensional (1D) spectra from Large Sky Area Multi-Object Fiber Spectroscopic Telescope (LAMOST) spectrum images. Compared with other deconvolution algorithms, this algorithm is much faster. The application on a real LAMOST image illustrates that the 1D spectrum resulting from this method has a higher signal-to-noise ratio and resolution than those extracted by the LAMOST pipeline. Furthermore, our algorithm can effectively suppress the ringings that are often present in the 1D resulting spectra generated by other deconvolution methods.

Compact and low-cost structured illumination microscopy using an optical fiber coupler

In this paper, a compact and low-cost structured illumination microscope (SIM) based on a 2X2 fiber coupler is presented. Fringe illumination is achieved by placing two output fiber tips at a conjugate Fourier plane of the sample plane as the point sources. Raw structured illumination (SI) images in different pattern orientations are captured when rotating the fiber mount. Following this, high resolution images are reconstructed from no-phase-shift raw SI images by using a joint Richardson-Lucy (jRL) deconvolution algorithm. Compared with an SLM-based SIM system, our method provides a much shorter illumination path, high power efficiency, and low cost.

Design and simulation of a snapshot multi-focal interferometric microscope.

Realizing both high temporal and spatial resolution across a large volume is a key challenge for 3D fluorescent imaging. Towards achieving this objective, we introduce an interferometric multifocus microscopy (iMFM) system, a combination of multifocus microscopy (MFM) with two opposing objective lenses. We show that the proposed iMFM is capable of simultaneously producing multiple focal plane interferometry that provides axial super-resolution and hence isotropic 3D resolution with a single exposure. We design and simulate the iMFM microscope by employing two special diffractive optical elements. The point spread function of this new iMFM microscope is simulated and the image formation model is given. For reconstruction, we use the Richardson-Lucy deconvolution algorithm with total variation regularization for 3D extended object recovery, and a maximum likelihood estimator (MLE) for single molecule tracking. A method for determining an initial axial position of the molecule is also proposed to improve the convergence of the MLE. We demonstrate both theoretically and numerically that isotropic 3D nanoscopic localization accuracy is achievable with an axial imaging range of 2um when tracking a fluorescent molecule in three dimensions and that the diffraction limited axial resolution can be improved by 3-4 times in the single shot wide-field 3D extended object recovery. We believe that iMFM will be a useful tool in 3D dynamic event imaging that requires both high temporal and spatial resolution.

Automated spectra analysis of in situ radioactivity measurements in the marine environment using NaI(Tl) detector

The NaI(Tl) detector has become the main way of research and application of in-situ radioactivity measurement in the marine environment due to many advantages on detection efficiency, power consumption, cost and applicability. But for the poor energy resolution and there is a high background in the low energy region of the spectrum measured mainly originating from the Compton scattering of natural radionuclides such as 40K with high concentrations in seawater, it is difficult and also an interesting topic for NaI(Tl) detector to identificate the radionuclides and calculate them in seawater by analyzing the spectra measured. In this paper, an in situ NaI(Tl) detector developed for the marine environment was energy, resolution and efficiency calibrated. The detection response matrix was calculated by taking all the responsible processes and interactions of gamma rays in water as well as in the detector into account using Monte Carlo simulation method. And then an improved Richardson-Lucy (R-L) deconvolution algorithm was proposed to reconstruct the gamma spectrum measured in the seawater to remove as efficiently as possible the background counts into the corresponding photopeaks. The original spectrum was transformed from poor energy resolution to the corresponding deconvolution spectrum of the high energy resolution with several isolated photopeaks. The experiments of synthetic spectrum and measured spectrum both showed promising results for the radionuclide qualitative and quantitative analysis.

Rapid 3D image scanning microscopy with multi-spot excitation and double-helix point spread function detection.

Refocusing after Scanning using Helical phase engineering (RESCH) microscopy has previously been demonstrated to provide volumetric information from a single 2D scan. However, the practical application of this method is challenging due to its limited image acquisition speed and spatial resolution. Here, we report on a combination of RESCH and multifocal structured illumination microscopy (MSIM) to improve the image acquisition speed and spatial resolution. A phase mask is introduced to modulate the conventional point spread function (PSF) to the double-helix PSF (DH-PSF), which provides volumetric information, and meanwhile, sparse multifocal illumination patterns are generated by a digital micromirror device (DMD) for parallel 3D subdiffractive imaging information acquisition. We also present a strategy for processing the collected raw data with a Richardson-Lucy deconvolution and pixel reassignment algorithm to improve the spatial resolution of the depth estimation and imaging performance. The proposed 3D image scanning microscopy can record 3D specimen information and the corresponding depth information from a single multi-spot 2D planar scan, which ensures faster data acquisition, larger field of view, and higher spatial resolution than RESCH. Finally, we demonstrate the capability of our system with actual experiments.

Septal penetration correction in I-131 imaging following thyroid cancer treatment

Whole body gamma camera images acquired after I-131 treatment for thyroid cancer can suffer from collimator septal penetration artefacts because of the high energy of the gamma photons. This results in the appearance of ‘spoke’ artefacts, emanating from regions of high activity concentration, caused by the non-isotropic attenuation of the collimator. Deconvolution has the potential to reduce such artefacts, by taking into account the non-Gaussian point-spread-function (PSF) of the system. A Richardson–Lucy deconvolution algorithm, with and without prior scatter-correction was tested as a method of reducing septal penetration in planar gamma camera images. Phantom images (hot spheres within a warm background) were acquired and deconvolution using a measured PSF was applied. The results were evaluated through region-of-interest and line profile analysis to determine the success of artefact reduction and the optimal number of deconvolution iterations and damping parameter (λ). Without scatter-correction, the optimal results were obtained with 15 iterations and λ = 0.01, with the counts in the spokes reduced to 20% of the original value, indicating a substantial decrease in their prominence. When a triple-energy-window scatter-correction was applied prior to deconvolution, the optimal results were obtained with six iterations and λ = 0.02, which reduced the spoke counts to 3% of the original value. The prior application of scatter-correction therefore produced the best results, with a marked change in the appearance of the images. The optimal settings were then applied to six patient datasets, to demonstrate its utility in the clinical setting. In all datasets, spoke artefacts were substantially reduced after the application of scatter-correction and deconvolution, with the mean spoke count being reduced to 10% of the original value. This indicates that deconvolution is a promising technique for septal penetration artefact reduction that could potentially improve the diagnostic accuracy of I-131 imaging.Novelty and significanceThis work has demonstrated that scatter correction combined with deconvolution can be used to substantially reduce the appearance of septal penetration artefacts in I-131 phantom and patient gamma camera planar images, enable improved visualisation of the I-131 distribution. Deconvolution with symmetric PSF has previously been used to reduce artefacts in gamma camera images however this work details the novel use of an asymmetric PSF to remove the angularly dependent septal penetration artefacts.

MO-FG-CAMPUS-TeP1-05: Rapid and Efficient 3D Dosimetry for End-To-End Patient-Specific QA of Rotational SBRT Deliveries Using a High-Resolution EPID

Purpose: EPID-based patient-specific quality assurance provides verification of the planning setup and delivery process that phantomless QA and log-file based virtual dosimetry methods cannot achieve. We present a method for EPID-based QA utilizing spatially-variant EPID response kernels that allows for direct calculation of the entrance fluence and 3D phantom dose. Methods: An EPID dosimetry system was utilized for 3D dose reconstruction in a cylindrical phantom for the purposes of end-to-end QA. Monte Carlo (MC) methods were used to generate pixel-specific point-spread functions (PSFs) characterizing the spatially non-uniform EPID portal response in the presence of phantom scatter. The spatially-variant PSFs were decomposed into spatially-invariant basis PSFs with the symmetric central-axis kernel as the primary basis kernel and off-axis representing orthogonal perturbations in pixel-space. This compact and accurate characterization enables the use of a modified Richardson-Lucy deconvolution algorithm to directly reconstruct entrance fluence from EPID images without iterative scatter subtraction. High-resolution phantom dose kernels were cogenerated in MC with the PSFs enabling direct recalculation of the resulting phantom dose by rapid forward convolution once the entrance fluence was calculated. A Delta4 QA phantom was used to validate the dose reconstructed in this approach. Results: The spatially-invariant representation of the EPID response accurately reproduced the entrance fluence with >99.5% fidelity with a simultaneous reduction of >60% in computational overhead. 3D dose for 106 voxels was reconstructed for the entire phantom geometry. A 3D global gamma analysis demonstrated a >95% pass rate at 3%/3mm. Conclusion: Our approach demonstrates the capabilities of an EPID-based end-to-end QA methodology that is more efficient than traditional EPID dosimetry methods. Displacing the point of measurement external to the QA phantom reduces the necessary complexity of the phantom itself while offering a method that is highly scalable and inherently generalizable to rotational and trajectory based deliveries. This research was partially supported by Varian.

An effective motion-blurred image restoration approach for automated optical inspection

This paper presents a real-time restoration method for linear local motion-blurred images in automated optical inspection (AOI). The proposed approach is to firstly divide such an image into many sub-images and then detect the blurred sub-image by the gradient distribution and the cepstrum maximum. For a blurred sub-image, the blur direction and blur length are estimated in order to calculate the parameters of the point spread function (PSF). The Richardson–Lucy deconvolution algorithm and Wiener filtering are employed to restore this blurred sub-image. Through experimentation, the proposed algorithm produces good results on blurred images caused by the linear motion AOI equipment. To test its performance, the proposed algorithm is compared with other approaches by using a real captured printed circuit board (PCB) image, and it is proven to be superior to the others in terms of accuracy.

Kinematic model for the space-variant image motion of star sensors under dynamical conditions

A kinematic description of a star spot in the focal plane is presented for star sensors under dynamical conditions, which involves all necessary parameters such as the image motion, velocity, and attitude parameters of the vehicle. Stars at different locations of the focal plane correspond to the slightly different orientation and extent of motion blur, which characterize the space-variant point spread function. Finally, the image motion, the energy distribution, and centroid extraction are numerically investigated using the kinematic model under dynamic conditions. A centroid error of eight successive iterations <0.002 pixel is used as the termination criterion for the Richardson-Lucy deconvolution algorithm. The kinematic model of a star sensor is useful for evaluating the compensation algorithms of motion-blurred images.

Enhanced Fault Diagnosis of Bearings in Gearbox Based on Lucy-Richardson Deconvolution and Discussion

Bearings are one of the most important components in rotating machineries. Their failures will lead to great production loss and increase the maintenance cost. So, condition monitoring work of bearings can save and avoid the potential loss caused by bearing fault. Lucy-Richardson deconvolution (LRD) algorithm, as an image processing technique, started to be used in bearing fault diagnosis. However, only data of bearings working in electric motor are used to validate the method. In engineering cases, most bearings are working in gearbox. Therefore, the bearing fault signals are very weak compared to the gear vibration signal. It is usually difficult to detect the bearing fault in this case. LRD algorithm is used to enhance the bearing fault diagnosis and some characteristics in this case are discussed. Experiment data analysis demonstrates that LRD can enhance the periodic impulse signal effectively. Otherwise, if the desired fault signal is weak compared to non-desired signal, then, the desired fault signal will be continued weaken by LRD which is not benefit to bearing’s incipient fault detection.

A novel partial volume effects correction technique integrating deconvolution associated with denoising within an iterative PET image reconstruction.

Partial volume effect (PVE) plays an important role in both qualitative and quantitative PET image accuracy, especially for small structures. A previously proposed voxelwise PVE correction method applied on PET reconstructed images involves the use of Lucy-Richardson deconvolution incorporating wavelet-based denoising to limit the associated propagation of noise. The aim of this study is to incorporate the deconvolution, coupled with the denoising step, directly inside the iterative reconstruction process to further improve PVE correction. The list-mode ordered subset expectation maximization (OSEM) algorithm has been modified accordingly with the application of the Lucy-Richardson deconvolution algorithm to the current estimation of the image, at each reconstruction iteration. Acquisitions of the NEMA NU2-2001 IQ phantom were performed on a GE DRX PET/CT system to study the impact of incorporating the deconvolution inside the reconstruction [with and without the point spread function (PSF) model] in comparison to its application postreconstruction and to standard iterative reconstruction incorporating the PSF model. The impact of the denoising step was also evaluated. Images were semiquantitatively assessed by studying the trade-off between the intensity recovery and the noise level in the background estimated as relative standard deviation. Qualitative assessments of the developed methods were additionally performed on clinical cases. Incorporating the deconvolution without denoising within the reconstruction achieved superior intensity recovery in comparison to both standard OSEM reconstruction integrating a PSF model and application of the deconvolution algorithm in a postreconstruction process. The addition of the denoising step permitted to limit the SNR degradation while preserving the intensity recovery. This study demonstrates the feasibility of incorporating the Lucy-Richardson deconvolution associated with a wavelet-based denoising in the reconstruction process to better correct for PVE. Future work includes further evaluations of the proposed method on clinical datasets and the use of improved PSF models.

A joint Richardson—Lucy deconvolution algorithm for the reconstruction of multifocal structured illumination microscopy data

We demonstrate the reconstruction of images obtained by multifocal structured illumination microscopy, MSIM, using a joint Richardson–Lucy, jRL-MSIM, deconvolution algorithm, which is based on an underlying widefield image-formation model. The method is efficient in the suppression of out-of-focus light and greatly improves image contrast and resolution. Furthermore, it is particularly well suited for the processing of noise corrupted data. The principle is verified on simulated as well as experimental data and a comparison of the jRL-MSIM approach with the standard reconstruction procedure, which is based on image scanning microscopy, ISM, is made. Our algorithm is efficient and freely available in a user friendly software package.

Toward 10 meV Electron Energy-Loss Spectroscopy Resolution for Plasmonics

Energy resolution is one of the most important parameters in electron energy-loss spectroscopy. This is especially true for measurement of surface plasmon resonances, where high-energy resolution is crucial for resolving individual resonance peaks, in particular close to the zero-loss peak. In this work, we improve the energy resolution of electron energy-loss spectra of surface plasmon resonances, acquired with a monochromated beam in a scanning transmission electron microscope, by the use of the Richardson-Lucy deconvolution algorithm. We test the performance of the algorithm in a simulated spectrum and then apply it to experimental energy-loss spectra of a lithographically patterned silver nanorod. By reduction of the point spread function of the spectrum, we are able to identify low-energy surface plasmon peaks in spectra, more localized features, and higher contrast in surface plasmon energy-filtered maps. Thanks to the combination of a monochromated beam and the Richardson-Lucy algorithm, we improve the effective resolution down to 30 meV, and evidence of success up to 10 meV resolution for losses below 1 eV. We also propose, implement, and test two methods to limit the number of iterations in the algorithm. The first method is based on noise measurement and analysis, while in the second we monitor the change of slope in the deconvolved spectrum.

Image quality improvement in optical coherence tomography using Lucy–Richardson deconvolution algorithm

Optical coherence tomography (OCT) has the potential for skin tissue characterization due to its high axial and transverse resolution and its acceptable depth penetration. In practice, OCT cannot reach the theoretical resolutions due to imperfections of some of the components used. One way to improve the quality of the images is to estimate the point spread function (PSF) of the OCT system and deconvolve it from the output images. In this paper, we investigate the use of solid phantoms to estimate the PSF of the imaging system. We then utilize iterative Lucy-Richardson deconvolution algorithm to improve the quality of the images. The performance of the proposed algorithm is demonstrated on OCT images acquired from a variety of samples, such as epoxy-resin phantoms, fingertip skin and basaloid larynx and eyelid tissues.

Primordial power spectrum: a complete analysis with the WMAP nine-year data

We have improved further the error sensitive Richardson-Lucy deconvolution algorithm making it applicable directly on the un-binned measured angular power spectrum of Cosmic Microwave Background observations to reconstruct the form of the primordial power spectrum. This improvement makes the application of the method significantly more straight forward by removing some intermediate stages of analysis allowing a reconstruction of the primordial spectrum with higher efficiency and precision and with lower computational expenses. Applying the modified algorithm we fit the WMAP 9 year data using the optimized reconstructed form of the primordial spectrum with morethan 300 improvement in χ2eff with respect to the best fit power-law. This is clearly beyond the reach of other alternative approaches and reflects the efficiency of the proposed method in the reconstruction process and allow us to look for any possible feature in the primordial spectrum projected in the CMB data. Though the proposed method allow us to look at various possibilities for the form of the primordial spectrum, all having good fit to the data, proper error-analysis is needed to test for consistency of theoretical models since, along with possible physical artefacts, most of the features in the reconstructed spectrum might be arising from fitting noises in the CMB data. Reconstructed error-band for the form of the primordial spectrum using many realizations of the data, all bootstrapped and based on WMAP 9 year data, shows proper consistency of power-law form of the primordial spectrum with the WMAP 9 data at all wave numbers. Including WMAP polarization data in to the analysis have not improved much our results due to its low quality but we expect Planck data will allow us to make a full analysis on CMBobservations on both temperature and polarization separately and in combination.

Systematic studies of the Richardson–Lucy deconvolution algorithm applied to VHE gamma data

The Richardson–Lucy deconvolution algorithm was applied to astronomical images in the very high-energy regime with photon energies above 100GeV. Through a systematic study with respect to source significance, background level and source morphology we were able to derive optimal deconvolution parameters. The results presented show that deconvolution makes it possible to study structural details well below the angular resolution of the very high-energy γ-ray experiment.

Poisson Noise Reduction in Deconvolution Microscopy

Computational optical sectioning microscopy is a powerful tool to reconstruct three-dimensional images from optical two-dimensional sections of a biological specimen acquired by means of a fluorescence microscope. Due to limiting factors in the imaging systems, the images are degraded by both the optical system and detection process. Each of the two-dimensional section of the three-dimensional data set are blurred by contributions of light from other out-of-focus planes. Besides, they are also corrupted by noise due to quantum fluctuations of light. In this work we present a method to perform the restoration of three-dimensional data obtained by fluorescence microscopy. The algorithm consists of the use of a noise reduction procedure based on the Anscombe transformation followed by the Richardson-Lucy deconvolution algorithm. Results showed an improvement on deconvolution performance when using phantoms and real cell images.

Automatic estimation of point-spread-function for deconvoluting out-of-focus optical coherence tomographic images using information entropy-based approach

This paper proposes an automatic point spread function (PSF) estimation method to de-blur out-of-focus optical coherence tomography (OCT) images. The method utilizes Richardson-Lucy deconvolution algorithm to deconvolve noisy defocused images with a family of Gaussian PSFs with different beam spot sizes. Then, the best beam spot size is automatically estimated based on the discontinuity of information entropy of recovered images. Therefore, it is not required a prior knowledge of the parameters or PSF of OCT system for de-convoluting image. The model does not account for the diffraction and the coherent scattering of light by the sample. A series of experiments are performed on digital phantoms, a custom-built phantom doped with microspheres, fresh onion as well as the human fingertip in vivo to show the performance of the proposed method. The method may also be useful in combining with other deconvolution algorithms for PSF estimation and image recovery.

Increasing axial resolution of 3D data sets using deconvolution algorithms

Deconvolution algorithms are tools for the restoration of data degraded by blur and noise. An incorporation of regularization functions into the iterative form of reconstruction algorithms can improve the restoration performance and characteristics (e.g. noise and artefact handling). In this study, algorithms based on Richardson-Lucy deconvolution algorithm are tested. The ability of these algorithms to improve axial resolution of three-dimensional data sets is evaluated on model synthetic data. Finally, unregularized Richardson-Lucy algorithm is selected for the evaluation and reconstruction of three-dimensional chromosomal data sets of Drosophila melanogaster. Problems concerning the reconstruction process are discussed and further improvements are proposed.