Maximum-likelihood Deconvolution Research Articles

Maximum Likelihood Deconvolution of Beamforming Images with Signal-Dependent Speckle Fluctuations

Ocean Acoustic Waveguide Remote Sensing (OAWRS) typically utilizes large-aperture linear arrays combined with coherent beamforming to estimate the spatial distribution of acoustic scattering echoes. The conventional maximum likelihood deconvolution (DCV) method uses a likelihood model that is inaccurate in the presence of multiple adjacent targets with significant intensity differences. In this study, we propose a deconvolution algorithm based on a modified likelihood model of beamformed intensities (M-DCV) for estimation of the spatial intensity distribution. The simulated annealing iterative scheme is used to obtain the maximum likelihood estimation. An approximate expression based on the generalized negative binomial (GNB) distribution is introduced to calculate the conditional probability distribution of the beamformed intensity. The deconvolution algorithm is further simplified with an approximate likelihood model (AM-DCV) that can reduce the computational complexity for each iteration. We employ a direct deconvolution method based on the Fourier transform to enhance the initial solution, thereby reducing the number of iterations required for convergence. The M-DCV and AM-DCV algorithms are validated using synthetic and experimental data, demonstrating a maximum improvement of 73% in angular resolution and a sidelobe suppression of 15 dB. Experimental examples demonstrate that the imaging performance of the deconvolution algorithm based on a linear small-aperture array consisting of 16 array elements is comparable to that obtained through conventional beamforming using a linear large-aperture array consisting of 96 array elements. The proposed algorithm is applicable for Ocean Acoustic Waveguide Remote Sensing (OAWRS) and other sensing applications using linear arrays.

Image deblurring to improve the grain monitoring in a rice combine harvester

One of the most important sources of grain losses happens during harvesting. A machine vision system is capable to send online information of the grain condition to the adjustment units in order to reduce the grain losses. However, the continuous vibration of combine during harvesting prevents to acquire desirable images for grain monitoring. To solve this issue, several image deblurring algorithms were investigated and the best one was introduced. The x-y-z accelerometer sensors were installed on the combine tank cap and then the acceleration data was extracted. These data were then used for fabrication of a small-scale combine tank simulator for preparation of the image dataset. Five algorithms were used for deblurring, including Fast Image Deconvolution Hyper-Laplacian Priors, Wiener, Lucy-Richardson, Maximum likelihood deconvolution, and regularized iterative image restoration algorithm. Also, three filters of Motion, Average, and Disk were used. Blind/Reference-less Image Spatial QUality Evaluator (BRISQUE) and Natural Image Quality Evaluator (NIQE) were used as the image quality indices. The results showed that Lucy-Richardson had the best performance in image deblurring (NIQE=6.0539 and BRISQUE=43.0489). Maximum Likelihood showed similar performance (NIQE=6.1974 and BRISQUE=43.4288). Analyzing the execution time of the algorithms showed that Lucy-Richardson was the fastest one (0.8538 s) and therefore, this is preferred to Maximum Likelihood in online applications. The results of the applied filters based on the subjective criterion showed that motion filter has produced sharper images while, disk filter performs better in de-noising. Comparing two objective indices showed that both indices performed well in evaluating the quality of deblurred images. However, the results of original images (blurred images) revealed that NIQE showed more sensitivity to image contrast and noise, compared to BRISQUE.

Imaging resolution and properties analysis of super resolution microscopy with parallel detection under different noise, detector and image restoration conditions

Parallel detection, which can use the additional information of a pinhole plane image taken at every excitation scan position, could be an efficient method to enhance the resolution of a confocal laser scanning microscope. In this paper, we discuss images obtained under different conditions and using different image restoration methods with parallel detection to quantitatively compare the imaging quality. The conditions include different noise levels and different detector array settings. The image restoration methods include linear deconvolution and pixel reassignment with Richard–Lucy deconvolution and with maximum-likelihood estimation deconvolution. The results show that the linear deconvolution share properties such as high-efficiency and the best performance under all different conditions, and is therefore expected to be of use for future biomedical routine research.

Maximum Likelihood Deconvolution of Beamformed Images with Signal-Dependent Speckle Fluctuations from Gaussian Random Fields: With Application to Ocean Acoustic Waveguide Remote Sensing (OAWRS)

Wide area acoustic remote sensing often involves the use of coherent receiver arrays to determine the spatial distribution of sources and scatterers at any instant. The resulting acoustic intensity images are typically corrupted by signal-dependent noise from Gaussian random field fluctuations arising from the central limit theorem and have a spatial resolution that depends on the incident direction, sensing array aperture and wavelength. Here, we use the maximum likelihood method to deconvolve the intensity distribution measured on a coherent line array assuming a discrete angular distribution of incident plane waves. Instantaneous wide area population density images of fish aggregations measured with Ocean Acoustic Waveguide Remote Sensing (OAWRS) are deconvolved to illustrate the effectiveness of this approach in improving angular resolution over conventional planewave beamforming.

Deconvolution approach for 3D scanning microscopy with helical phase engineering.

RESCH (refocusing after scanning using helical phase engineering) microscopy is a scanning technique using engineered point spread functions which provides volumetric information. We present a strategy for processing the collected raw data with a multi-view maximum likelihood deconvolution algorithm, which inherently comprises the resolution gain of pixel-reassignment microscopy. The method, which we term MD-RESCH (for multi-view deconvolved RESCH), achieves in our current implementation a 20% resolution advantage along all three axes compared to RESCH and confocal microscopy. Along the axial direction, the resolution is comparable to that of image scanning microscopy. However, because the method inherently reconstructs a volume from a single 2D scan, a significantly higher optical sectioning becomes directly visible to the user, which would otherwise require collecting multiple 2D scans taken at a series of axial positions. Further, we introduce the use of a single-helical detection PSF to obtain an increased post-acquisition refocusing range. We present data from numerical simulations as well as experiments to confirm the validity of our approach.

Label-free multi-color superlocalization of plasmonic emission within metallic nano-interstice using femtosecond chirp-manipulated four wave mixing.

We demonstrate an as yet unused method to sieve, localize, and steer plasmonic hot spot within metallic nano-interstices close to percolation threshold. Multicolor superlocalization of plasmon mode within 60 nm was constantly achieved by chirp-manipulated superresolved four wave mixing (FWM) images. Since the percolated film is strongly plasmonic active and structurally multiscale invariant, the present method provides orders of magnitude enhanced light localization within single metallic nano-interstice, and can be universally applied to any region of the random film. The result, verified by the maximum likelihood estimation (MLE) and deconvolution stochastic optical reconstruction microscopy (deconSTORM) algorithm, may contribute to label-free multiplex superlocalized spectroscopy of single molecule and sub-cellular activity monitoring combining hot spot steering capability.

Point spread function estimation from projected speckle illumination.

The resolution of an imaging apparatus is ideally limited by the diffraction properties of the light passing through the system aperture, but in many practical cases, inhomogeneities in the light propagating medium or imperfections in the optics degrade the image resolution. Here we introduce a powerful and practical new approach for estimating the point spread function (PSF) of an imaging system on the basis of PSF Estimation from Projected Speckle Illumination (PEPSI). PEPSI uses the fact that the speckles’ phase randomness cancels the effects of the aberrations in the illumination path, thereby providing an objective pattern for measuring the deformation of the imaging path. Using this approach, both wide-field-of-view and local-PSF estimation can be obtained by calibration-free, single-speckle-pattern projection. Finally, we demonstrate the feasibility of using PEPSI estimates for resolution improvement in iterative maximum likelihood deconvolution.

A Locally Convoluted Cluster Model for Nucleosome Positioning Signals in Chemical Maps

The nucleosome is the fundamental packing unit of DNA in eukaryotic cells, and its positioning plays a critical role in regulation of gene expression and chromosome functions. Using a recently developed chemical mapping method, nucleosomes can be potentially mapped with an unprecedented single-base-pair resolution. Existence of overlapping nucleosomes due to cell mixture or cell dynamics, however, causes convolution of nucleosome positioning signals. In this article, we introduce a locally convoluted cluster model and a maximum likelihood deconvolution approach, and illustrate the effectiveness of this approach in quantification of the nucleosome positional signal in the chemical mapping data. Supplementary materials for this article are available online.

Spectral identification of a 90Sr source in the presence of masking nuclides using Maximum-Likelihood deconvolution

A technique for the spectral identification of strontium-90 is shown, utilising a Maximum-Likelihood deconvolution. Different deconvolution approaches are discussed and summarised. Based on the intensity distribution of the beta emission and Geant4 simulations, a combined response matrix is derived, tailored to the β− detection process in sodium iodide detectors. It includes scattering effects and attenuation by applying a base material decomposition extracted from Geant4 simulations with a CAD model for a realistic detector system. Inversion results of measurements show the agreement between deconvolution and reconstruction. A detailed investigation with additional masking sources like 40K, 226Ra and 131I shows that a contamination of strontium can be found in the presence of these nuisance sources. Identification algorithms for strontium are presented based on the derived technique. For the implementation of blind identification, an exemplary masking ratio is calculated.

Sub-diffraction Limit Localization of Proteins in Volumetric Space Using Bayesian Restoration of Fluorescence Images from Ultrathin Specimens

Photon diffraction limits the resolution of conventional light microscopy at the lateral focal plane to 0.61λ/NA (λ = wavelength of light, NA = numerical aperture of the objective) and at the axial plane to 1.4nλ/NA2 (n = refractive index of the imaging medium, 1.51 for oil immersion), which with visible wavelengths and a 1.4NA oil immersion objective is ∼220 nm and ∼600 nm in the lateral plane and axial plane respectively. This volumetric resolution is too large for the proper localization of protein clustering in subcellular structures. Here we combine the newly developed proteomic imaging technique, Array Tomography (AT), with its native 50–100 nm axial resolution achieved by physical sectioning of resin embedded tissue, and a 2D maximum likelihood deconvolution method, based on Bayes' rule, which significantly improves the resolution of protein puncta in the lateral plane to allow accurate and fast computational segmentation and analysis of labeled proteins. The physical sectioning of AT allows tissue specimens to be imaged at the physical optimum of modern high NA plan-apochormatic objectives. This translates to images that have little out of focus light, minimal aberrations and wave-front distortions. Thus, AT is able to provide images with truly invariant point spread functions (PSF), a property critical for accurate deconvolution. We show that AT with deconvolution increases the volumetric analytical fidelity of protein localization by significantly improving the modulation of high spatial frequencies up to and potentially beyond the spatial frequency cut-off of the objective. Moreover, we are able to achieve this improvement with no noticeable introduction of noise or artifacts and arrive at object segmentation and localization accuracies on par with image volumes captured using commercial implementations of super-resolution microscopes.

Maximum-Likelihood Deconvolution in the Spatial and Spatial-Energy Domain for Events With Any Number of Interactions

In previous works, maximum-likelihood expectation-maximization deconvolution for two-interaction events within a single CdZnTe detector with dimensions of was implemented. This deconvolution method is capable of estimating the source image for each energy range as well as the incident spectrum for each direction around the detector. To improve the detection efficiency and the image resolution, we have built a four-detector array system; each detector has dimensions of . Using this detector-array system, from a Co-60 measurement, 41.5% of recorded events in the energy window from 1100 keV to 1200 keV are two-interaction events. The goal of this work is to increase the efficiency of this deconvolution algorithm by extending the calculation of the system response functions to events with other number of interactions. We first analytically extend the system response function calculation to three-interaction events by deriving the probability density function, considering the measurement noise, and integrating over the digitization and pixelation volume. The system response function is then simplified, modularized, and extrapolated to events with other numbers of interactions from an array system. By including events with any number of interactions in the system model, imaging makes use of all recorded events, and the angular resolution is improved. This deconvolution algorithm is applicable to any gamma-ray detector system that has the capability of recording 3D interaction location and energy deposition for each interaction.

Simultaneous Spectral Resolution and Sensitivity Enhancement in MR spectrum: Maximum Likelihood Deconvolution Reconstruction

Although the use of apodization functions in connection with postprocessing of a 2D NMR spectrum proves improved spectral quality, there is usually a trade-off between resolution enhancement and noise suppression due to a classical uncertainty principle. In this study, therefore, a mathematical deconvolution technique called Maximum Likelihood Deconvolution (MLD) was adopted to achieve the spectral resolution and sensitivity enhancement simultaneously. The MLD technique greatly facilitates visualization and restoration of the genuine spectral information from complex 2D NMR spectra that would be problematic with the conventional apodization/FT processing. In particular, application of the MLD to the 2D-NOE spectrum would be very useful to derive the important proton connectivities, which are essential to achieve elucidating the 3D molecular structure.

Optical Recording of Neuronal Spiking Activity From Unbiased Populations of Neurons With High Spike Detection Efficiency and High Temporal Precision

Activity in populations of neurons is essential for cortical function including signaling of information and signal transport. Previous methods have made advances in recording activity from many neurons but have both technical and analytical limitations. Here we present an optical method, dithered random-access functional calcium imaging, to record somatic calcium signals from up to 100 neurons, in vitro and in vivo. We further developed a maximum-likelihood deconvolution algorithm to detect spikes and precise spike timings from the recorded calcium fluorescence signals. Spike detection efficiency and spike timing detection was determined in acute slices of juvenile mice. The results indicate that the combination of the two methods detected precise spiking activity from unbiased and spatially distributed populations of neurons in acute slices with high efficiency of spike detection (>97%), low rate of false positives (0.0023 spikes/s), and high temporal precision. The results further indicate that there is only a small window of excitation intensities where high spike detection can be achieved consistently.

3D DECONVOLUTION OF VIBRATION CORRUPTED HYPERSPECTRAL IMAGES

We have developed a hyperspectral deconvolution algorithm that sharpens the spectral dimension in addition to the more usual across-track and along-track dimensions. Using an individual three-dimensional model for each pixel's point spread function, the algorithm iteratively applies maximum likelihood criteria to reveal previously hidden features in the spatial and spectral dimensions. Of necessity, our solution is adaptive to unreported across-track and along-track vibrations with amplitudes smaller than the ground sampling distance. We sense and correct these vibrations using a combination of maximum likelihood deconvolution and gradient descent registration that maximizes statistical correlations over many bands. Test panels in real hyperspectral imagery show significant improvement when locations are corrected. Tests on simulated imagery show that the precision of relative corrected positions improves by about a factor of two.

Maximum Likelihood Deconvolution for sequence analysis and improved structural resolution in the Vindhyan Basin, India

Exploration in the Proterozoic Vindhyan Basin in the north-central part of India has received much attention because a number of basins coeval to it (Amadeus and McArthur basins, Australia and Lena–Tunguska petroleum province, Siberia) are known hydrocarbon producers. The assemblage of interbedded clastics and carbonates in the thick Vindhyan sedimentary column is considered to be favourable for a petroleum system. This is supported by discovery of oil and gas in Vindhyan sediments. Wavelet processing and application of Maximum Likelihood Deconvolution (MLD) to post-stack seismic data have enhanced resolution significantly to facilitate identification of various stratigraphic features, including reflection pattern termination in the Jabera–Damoh area in the southeastern part of the basin. Sixteen seismic sequences correlatable with well data have been identified from the wavelet-processed data. MLD has also improved structural resolution and made identification of faults easier. This paper shows that MLD is a powerful tool for seismic sequence stratigraphy.

Blind image deconvolution subject to bandwidth and total variation constraints

We present a maximum likelihood (ML) deconvolution algorithm with bandwidth and total variation (TV) constraints for degraded image due to atmospheric turbulence. The bandwidth limit function is estimated in view of optical system parameters and Fourier optical theory. With the aid of bandwidth and TV minimization as compelling constraints, the algorithm can not only suppress noise effectively but also restrict the bandwidth of point-spread function (PSF) that may lead to trivial solution. Compared with the conventional ML method, the proposed algorithm is able to restore a noise-free image, and the detailed texture is better than that of ML.

Improving the Repeatability of Topographic Height Measurements in Confocal Scanning Laser Imaging Using Maximum-Likelihood Deconvolution

To evaluate maximum likelihood (ML) blind deconvolution as a technique for improving the repeatability of topographic height measurements obtained from scanning laser tomography (Heidelberg Retinal Tomograph [HRT]; Heidelberg Engineering, Heidelberg, Germany). ML blind deconvolution is an image-processing technique that estimates the original scene from a degraded image. This technique has been used in confocal scanning laser microscopy to remove "out-of-focus" haze in three-dimensional confocal image stacks. ML blind deconvolution requires no prior estimation of the point-spread function (PSF), as opposed to classic linear deconvolution methods. Instead, the algorithm estimates an initial PSF based on the optical setup of the confocal scanning device and optics of the eye and iteratively proceeds to a solution. The improvement in repeatability of height measurements from mean topography images within scan (intrascan) and between scans (interscan) afforded by ML deconvolution was evaluated in a test-retest series of HRT images from 40 ocular hypertensive and glaucomatous patients with varying degrees of media opacity. There was an improvement in intrascan repeatability in 38 out of the 40 mean topography images (median improvement 2.5 microm, inter-quartile range 2.19, P < 0.001), and an improvement in interscan repeatability in 33 of the 40 mean topographies (median improvement, 1.0 microm, interquartile range 3.49, P < 0.001). There was a positive association between the magnitude of the improvement in repeatability and the level of mean pixel height standard deviation (MPHSD), intrascan (P = 0.004) and interscan (P = 0.002). ML blind deconvolution algorithm improves the repeatability of topographic height measurements from the HRT. This improvement was greater in patients with poorer quality images.

Estimating missing information by maximum likelihood deconvolution

The ability of iteratively constrained maximum likelihood (ML) deconvolution to reconstruct out-of-band information is discussed and exemplified by simulations. The frequency dependent relative energy regain, a novel way of quantifying the reconstruction ability, is introduced. The positivity constraint of ML deconvolution allows reconstructing information outside the spatial frequency bandwidth which is set by the optical system. This is demonstrated for noise-free and noisy data. It is also shown that this property depends on the type of object under investigation. An object is constructed where no significant out-of-band reconstruction is possible. It is concluded that in practical situations the amount of possible out-of-band reconstruction depends on the agreement between reality and the model describing “typical objects” incorporated into the algorithm by appropriate penalty functions.

Anisoplanatic deconvolution of adaptive optics images

A modified method for maximum-likelihood deconvolution of astronomical adaptive optics images is presented. By parametrizing the anisoplanatic character of the point-spread function (PSF), a simultaneous optimization of the spatially variant PSF and the deconvolved image can be performed. In the ideal case of perfect information, it is shown that the algorithm is able to perfectly cancel the adverse effects of anisoplanatism down to the level of numerical precision. Exploring two different modes of deconvolution (using object bases of pixel values or stellar field parameters), we then quantify the performance of the algorithm in the presence of Poissonian noise for crowded and noncrowded stellar fields.

Deconvolution of ASCA X-ray data -- I. Spectral-imaging method

In this paper we describe a self-contained method for performing the spectral-imaging deconvolution of X-ray data on clusters of galaxies observed by the ASCA satellite. Spatially-resolved spectral studies of data from this satellite require such a correction because its optics redistribute photons over regions which are of comparable size to the angular scales of interest in clusters. This scattering is a function not only of spatial position but also energy. To perform a correction for these effects we employ Maximum-Likelihood deconvolution of the image (within energy bands of 1 keV) to determine the spatial redistribution, followed by a Monte-Carlo energy reassignment of photon energies with position to determine the spectral redistribution. We present tests on simulated cluster data, convolved with the various instrumental characteristics and the X-ray background, which show that our methodology can successfully recover a variety of intrinsic temperature profiles in typical observational circumstances. In Paper-II we apply our spectral-imaging deconvolution procedure to a large sample of galaxy clusters to determine temperature profiles, some of which will be used in subsequent mass determinations, presented in Paper-III.