Iterative statistical approach to blind image deconvolution

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.

Space-variant deconvolution of Cerenkov light images acquired from a curved surface

PURPOSE

Cerenkov photons are generated by high-energy radiation used in external beam radiation therapy (EBRT). This study expands upon the Cerenkov light dosimetry formula previously developed to relate an image of Cerenkov photons to the primary beam fluence. Extension of this formulation allows for deconvolution to be performed on images acquired from curved geometries.

METHODS

The integral equation, which represented the formation of Cerenkov photon image from an incident high-energy photon beam, was expanded to allow for space-variance of the convolution kernel called as the Cerenkov scatter function (CSF). The GAMOS (Geant4-based Architecture for Medicine-Oriented Simulations) Monte Carlo (MC) particle simulation software was used to obtain the CSF for different incident beam angles. The image of a curved surface was first projected to a flat plane by using a perspective correction method. Then, the planar image was partitioned into small segments (or blocks), where a CSF corresponding to a specific beam incident angle was applied for deconvolution. The block size and the margin around the block were optimized by studying the effects of those parameters on the deconvolution accuracy for a test image. We evaluated three deconvolution techniques: Richardson-Lucy, Blind, and Total Variation minimization (TV/L2) algorithms, to select the most accurate method for the current applications.

RESULTS

Analysis of deconvolution algorithms showed that the TV/L2 method provided the most accurate solution to the deconvolution problem for Cerenkov imaging. Optimization of space-variant deconvolution parameters showed that including a margin that is at least 42.9% of the image width provided the most accurate product image. There was no optimal size for the deconvolution area and should be chosen based on the presence of unique CSF kernels within an image. Space-variant deconvolution improved measured field size in Cerenkov photon images by 7.37%, as compared with 1.74% by space-invariant deconvolution. Space-variant deconvolution improved measured penumbra by 99.3%, as compared with 76.7% by space-invariant deconvolution. Space-variant deconvolution introduced artifacts in flat regions of the beam. Artifacts were avoided through selective space-variant deconvolution in only the penumbra region.

CONCLUSIONS

Primary photon fluence distributions of a curved surface can be obtained by using space-variant deconvolution methods in Cerenkov light dosimetry. The TV/L2 algorithm is the best method for deconvolution of Cerenkov photon images from an open-field beam derived from either a flat or curved surface. The partition size chosen for space-variant deconvolution should be at least six times the full width at half maximum (FWHM) of the corresponding scatter kernel used in deconvolution. Space-variant deconvolution is necessary if the incident beam angle difference is larger than 6 ∘ between regions of an image.

Resolution enhancement of wide-field interferometric microscopy by coupled deep autoencoders

Wide-field interferometric microscopy is a highly sensitive, label-free, and low-cost biosensing imaging technique capable of visualizing individual biological nanoparticles such as viral pathogens and exosomes. However, further resolution enhancement is necessary to increase detection and classification accuracy of subdiffraction-limited nanoparticles. In this study, we propose a deep-learning approach, based on coupled deep autoencoders, to improve resolution of images of L-shaped nanostructures. During training, our method utilizes microscope image patches and their corresponding manual truth image patches in order to learn the transformation between them. Following training, the designed network reconstructs denoised and resolution-enhanced image patches for unseen input.

Direct superresolution for realistic image reconstruction

Traditional superresolution techniques employ optimizers, priors, and regularizers to deliver stable, appealing restorations even though deviating from the real, ground-truth scene. We have developed a non-regularized superresolution algorithm that directly solves a fully-characterized multi-shift imaging reconstruction problem to achieve realistic restorations without being penalized by improper assumptions made in the inverse problem. An adaptive frequency-based filtering scheme is introduced to upper bound the reconstruction errors while still producing more fine details as compared with previous methods when inaccurate shift estimation, noise, and blurring scenarios are considered.

Towards better digital pathology workflows: programming libraries for high-speed sharpness assessment of Whole Slide Images

BACKGROUND

Since microscopic slides can now be automatically digitized and integrated in the clinical workflow, quality assessment of Whole Slide Images (WSI) has become a crucial issue. We present a no-reference quality assessment method that has been thoroughly tested since 2010 and is under implementation in multiple sites, both public university-hospitals and private entities. It is part of the FlexMIm R&D project which aims to improve the global workflow of digital pathology. For these uses, we have developed two programming libraries, in Java and Python, which can be integrated in various types of WSI acquisition systems, viewers and image analysis tools.

METHODS

Development and testing have been carried out on a MacBook Pro i7 and on a bi-Xeon 2.7GHz server. Libraries implementing the blur assessment method have been developed in Java, Python, PHP5 and MySQL5. For web applications, JavaScript, Ajax, JSON and Sockets were also used, as well as the Google Maps API. Aperio SVS files were converted into the Google Maps format using VIPS and Openslide libraries.

RESULTS

We designed the Java library as a Service Provider Interface (SPI), extendable by third parties. Analysis is computed in real-time (3 billion pixels per minute). Tests were made on 5000 single images, 200 NDPI WSI, 100 Aperio SVS WSI converted to the Google Maps format.

CONCLUSIONS

Applications based on our method and libraries can be used upstream, as calibration and quality control tool for the WSI acquisition systems, or as tools to reacquire tiles while the WSI is being scanned. They can also be used downstream to reacquire the complete slides that are below the quality threshold for surgical pathology analysis. WSI may also be displayed in a smarter way by sending and displaying the regions of highest quality before other regions. Such quality assessment scores could be integrated as WSI's metadata shared in clinical, research or teaching contexts, for a more efficient medical informatics workflow.

Stability in computed optical interferometric tomography (part I): stability requirements

As imaging systems become more advanced and acquire data at faster rates, increasingly dynamic samples can be imaged without concern of motion artifacts. For optical interferometric techniques such as optical coherence tomography, it often follows that initially, only amplitude-based data are utilized due to unstable or unreliable phase measurements. As systems progress, stable phase maps can also be acquired, enabling more advanced, phase-dependent post-processing techniques. Here we report an investigation of the stability requirements for a class of phase-dependent post-processing techniques - numerical defocus and aberration correction with further extensions to techniques such as Doppler, phase-variance, and optical coherence elastography. Mathematical analyses and numerical simulations over a variety of instabilities are supported by experimental investigations.

Atmospheric turbulence mitigation using complex wavelet-based fusion

Restoring a scene distorted by atmospheric turbulence is a challenging problem in video surveillance. The effect, caused by random, spatially varying, perturbations, makes a model-based solution difficult and in most cases, impractical. In this paper, we propose a novel method for mitigating the effects of atmospheric distortion on observed images, particularly airborne turbulence which can severely degrade a region of interest (ROI). In order to extract accurate detail about objects behind the distorting layer, a simple and efficient frame selection method is proposed to select informative ROIs only from good-quality frames. The ROIs in each frame are then registered to further reduce offsets and distortions. We solve the space-varying distortion problem using region-level fusion based on the dual tree complex wavelet transform. Finally, contrast enhancement is applied. We further propose a learning-based metric specifically for image quality assessment in the presence of atmospheric distortion. This is capable of estimating quality in both full- and no-reference scenarios. The proposed method is shown to significantly outperform existing methods, providing enhanced situational awareness in a range of surveillance scenarios.

Estimating incidence curves of several infections using symptom surveillance data

We introduce a method for estimating incidence curves of several co-circulating infectious pathogens, where each infection has its own probabilities of particular symptom profiles. Our deconvolution method utilizes weekly surveillance data on symptoms from a defined population as well as additional data on symptoms from a sample of virologically confirmed infectious episodes. We illustrate this method by numerical simulations and by using data from a survey conducted on the University of Michigan campus. Last, we describe the data needs to make such estimates accurate.

Bayesian estimation of regularization and point spread function parameters for Wiener-Hunt deconvolution

This paper tackles the problem of image deconvolution with joint estimation of point spread function (PSF) parameters and hyperparameters. Within a Bayesian framework, the solution is inferred via a global a posteriori law for unknown parameters and object. The estimate is chosen as the posterior mean, numerically calculated by means of a Monte Carlo Markov chain algorithm. The estimates are efficiently computed in the Fourier domain, and the effectiveness of the method is shown on simulated examples. Results show precise estimates for PSF parameters and hyperparameters as well as precise image estimates including restoration of high frequencies and spatial details, within a global and coherent approach.

Three-dimensional microscopy and sectional image reconstruction using optical scanning holography

Fast acquisition and high axial resolution are two primary requirements for three-dimensional microscopy. However, they are sometimes conflicting: imaging modalities such as confocal imaging can deliver superior resolution at the expense of sequential acquisition at different axial planes, which is a time-consuming process. Optical scanning holography (OSH) promises to deliver a good trade-off between these two goals. With just a single scan, we can capture the entire three-dimensional volume in a digital hologram; the data can then be processed to obtain the individual sections. An accurate modeling of the imaging system is key to devising an appropriate image reconstruction algorithm, especially for real data where random noise and other imaging imperfections must be taken into account. In this paper we demonstrate sectional image reconstruction by applying an inverse imaging sectioning technique to experimental OSH data of biological specimens and visualizing the sections using the OSA Interactive Science Publishing software.

Blind sectional image reconstruction for optical scanning holography

Optical scanning holography is a powerful holographic recording technique in which only a single two-dimensional scan is needed to record three-dimensional information. As in standard digital holography, for the reconstruction of a sectional image, the resulting data must then be postprocessed to obtain sectional content. We propose a blind sectional image reconstruction technique to automate the data processing. This reconstruction uses edge information to determine the appropriate Fresnel zone plates automatically and applies inverse imaging to recover the sectional images with significant suppression of the defocus noise. The experimental data used to verify the algorithm are measured from a physical implementation of the optical scanning holography system.

Computation lithography: virtual reality and virtual virtuality

Computation lithography is enabled by a combination of physical understanding, mathematical abstraction, and implementation simplification. An application in the virtual world of computation lithography can be a virtual reality or a virtual virtuality depending on its engineering sensibleness and technical feasibility. Examples under consideration include design-for-manufacturability and inverse lithography.

Maximum a posteriori blind image deconvolution with Huber-Markov random-field regularization

We propose a maximum a posteriori blind deconvolution approach using a Huber-Markov random-field model. Compared with the conventional maximum-likelihood method, our algorithm not only suppresses noise effectively but also significantly alleviates the artifacts produced by the deconvolution process. The performance of this method is demonstrated by computer simulations.

Joint deconvolution and classification with applications to passive acoustic underwater multipath

This paper addresses the problem of classifying signals that have been corrupted by noise and unknown linear time-invariant (LTI) filtering such as multipath, given labeled uncorrupted training signals. A maximum a posteriori approach to the deconvolution and classification is considered, which produces estimates of the desired signal, the unknown channel, and the class label. For cases in which only a class label is needed, the classification accuracy can be improved by not committing to an estimate of the channel or signal. A variant of the quadratic discriminant analysis (QDA) classifier is proposed that probabilistically accounts for the unknown LTI filtering, and which avoids deconvolution. The proposed QDA classifier can work either directly on the signal or on features whose transformation by LTI filtering can be analyzed; as an example a classifier for subband-power features is derived. Results on simulated data and real Bowhead whale vocalizations show that jointly considering deconvolution with classification can dramatically improve classification performance over traditional methods over a range of signal-to-noise ratios.

Blind deconvolution: multiplicative iterative algorithm

A new algorithm has been developed for performing blind deconvolution on degraded images. The algorithm naturally preserves the nonnegative constraint on the iterative solutions of blind deconvolution and can produce a restored image of high resolution. Furthermore, benefiting from the multiplicative form, the algorithm is free from the instability of numerical computation. Results of applying the algorithm to simulated and real degraded images are reported.

Relaxed ordered-subset algorithm for penalized-likelihood image restoration

The expectation-maximization (EM) algorithm for maximum-likelihood image recovery is guaranteed to converge, but it converges slowly. Its ordered-subset version (OS-EM) is used widely in tomographic image reconstruction because of its order-of-magnitude acceleration compared with the EM algorithm, but it does not guarantee convergence. Recently the ordered-subset, separable-paraboloidal-surrogate (OS-SPS) algorithm with relaxation has been shown to converge to the optimal point while providing fast convergence. We adapt the relaxed OS-SPS algorithm to the problem of image restoration. Because data acquisition in image restoration is different from that in tomography, we employ a different strategy for choosing subsets, using pixel locations rather than projection angles. Simulation results show that the relaxed OS-SPS algorithm can provide an order-of-magnitude acceleration over the EM algorithm for image restoration. This new algorithm now provides the speed and guaranteed convergence necessary for efficient image restoration.

Mathematical model of corneal surface smoothing after laser refractive surgery

PURPOSE

To construct a quantitative model of corneal surface smoothing after laser ablation for refractive correction.

DESIGN

Experimental study, interventional case series, and meta-analysis of literature.

METHODS

A theory of epithelial smoothing in response to corneal contour change is derived from differential equations that describe epithelial migration, growth, and loss. Computer simulations calculate the effects on postoperative epithelial thickness, topography, refraction, and spherical aberration. Model parameter is matched with laser in situ keratomileusis (LASIK) outcome in literature and in a retrospective study of primary spherical myopic (77 eyes) and hyperopic (19 eyes) corrections. Surgically induced refractive change was the main outcome measure.

RESULTS

Simulated epithelial remodeling after myopic ablation produces central epithelial thickening, reduction in achieved correction, and induction of oblate spherical aberration. Simulation of hyperopic ablation shows peripheral epithelial thickening, a larger reduction in correction, and induction of prolate spherical aberration. Simulation using a minus cylinder laser ablation pattern shows decreased astigmatism correction and increased hyperopic shift. In the LASIK series, linear regression of achieved correction vs ablation setting in hyperopic and minus cylinder corrections shows slopes of 0.97, 0.71, and 0.74, respectively. These clinical results match model predictions when the smoothing constant is set at 0.32, 0.63, and 0.55 mm, respectively.

CONCLUSIONS

Epithelial thickness modulations after ablation can be modeled mathematically to explain clinically observed regression and induction of aberration. The cornea appears to smooth over ablated features smaller than approximately 0.5 mm. The model provides an approach for designing ablation patterns that precompensate for the smoothing to improve final outcome.