Generalized Gaussian Markov Random Field Research Articles

Reconstruction of optical parameter fields in graded refractive index media based on laser beam deflection and attenuation measurement.

Graded refractive index media (GRIM) are widely applied as special functional materials in many practical engineering fields. Accurate knowledge of the optical parameters is key to using GRIM. In this study, simultaneous reconstruction of the refractive index and absorption coefficient fields of GRIM based on laser beam deflection and attenuation measurement is studied. A set of rays from the given positions along the given directions transits GRIM, and the deflection and attenuation of rays at the exit boundary are recorded as measurement information. A two-step reconstruction strategy is proposed to reconstruct the refractive index and absorption coefficient fields. First, the refractive index field is reconstructed from the ray deflection measurement information. Then, the ray trajectory can be obtained by the Runge-Kutta ray tracing technique based on the reconstructed refractive index field. Afterwards, the absorption coefficient field is reconstructed from the ray attenuation measurement according to the Bouguer law. The regularization technique based on the generalized Gaussian Markov random field model is employed to improve the reconstruction results. All test results show that the two-step reconstruction strategy is accurate and can be regarded as a promising reconstruction technique.

A pyramidal deep learning pipeline for kidney whole-slide histology images classification

Renal cell carcinoma is the most common type of kidney cancer. There are several subtypes of renal cell carcinoma with distinct clinicopathologic features. Among the subtypes, clear cell renal cell carcinoma is the most common and tends to portend poor prognosis. In contrast, clear cell papillary renal cell carcinoma has an excellent prognosis. These two subtypes are primarily classified based on the histopathologic features. However, a subset of cases can a have a significant degree of histopathologic overlap. In cases with ambiguous histologic features, the correct diagnosis is dependent on the pathologist’s experience and usage of immunohistochemistry. We propose a new method to address this diagnostic task based on a deep learning pipeline for automated classification. The model can detect tumor and non-tumoral portions of kidney and classify the tumor as either clear cell renal cell carcinoma or clear cell papillary renal cell carcinoma. Our framework consists of three convolutional neural networks and the whole slide images of kidney which were divided into patches of three different sizes for input into the networks. Our approach can provide patchwise and pixelwise classification. The kidney histology images consist of 64 whole slide images. Our framework results in an image map that classifies the slide image on the pixel-level. Furthermore, we applied generalized Gauss-Markov random field smoothing to maintain consistency in the map. Our approach classified the four classes accurately and surpassed other state-of-the-art methods, such as ResNet (pixel accuracy: 0.89 Resnet18, 0.92 proposed). We conclude that deep learning has the potential to augment the pathologist’s capabilities by providing automated classification for histopathological images.

Improved optical tomography based on hybrid frequency-domain and time-domain radiative transfer model

Based on the hybrid frequency-domain (FD) and time-domain (TD) radiative transfer equation (RTE), a novel reconstruction strategy is developed to retrieve the optical parameter fields in the participating medium. The discrete ordinate method is employed to solve the forward FD and TD RTE to simulate the radiative transfer process. The sequential quadratic programming is utilized to solve the inverse problem for obtaining the optical parameters combined with an adjoint method. The Otsu algorithm is applied to the FD reconstructed results to distinguish the target region and the background region. To overcome the ill-posedness of the inverse problem, the generalized Gaussian Markov random field model is employed as the regularization term in the objective function. Various numerical experiments are studied and all results demonstrate that the proposed hybrid reconstruction scheme is suitable for efficient and accurate optical tomography by combining the FD and TD radiative transfer models. Meanwhile, the crosstalk of the ill-posed inverse problem can be alleviated effectively.

Far-field thermal imaging below diffraction limit.

Non-uniform self-heating and temperature hotspots are major concerns compromising the performance and reliability of submicron electronic and optoelectronic devices. At deep submicron scales where effects such as contact-related artifacts and diffraction limits accurate measurements of temperature hotspots, non-contact thermal characterization can be extremely valuable. In this work, we use a Bayesian optimization framework with generalized Gaussian Markov random field (GGMRF) prior model to obtain accurate full-field temperature distribution of self-heated metal interconnects from their thermoreflectance thermal images (TRI) with spatial resolution 2.5 times below Rayleigh limit for 530nm illumination. Finite element simulations along with TRI experimental data were used to characterize the point spread function of the optical imaging system. In addition, unlike iterative reconstruction algorithms that use ad hoc regularization parameters in their prior models to obtain the best quality image, we used numerical experiments and finite element modeling to estimate the regularization parameter for solving a real experimental inverse problem.

A novel computer-aided diagnosis system for the early detection of hypertension based on cerebrovascular alterations.

Hypertension is a leading cause of mortality in the USA. While simple tools such as the sphygmomanometer are widely used to diagnose hypertension, they could not predict the disease before its onset. Clinical studies suggest that alterations in the structure of human brains' cerebrovasculature start to develop years before the onset of hypertension. In this research, we present a novel computer-aided diagnosis (CAD) system for the early detection of hypertension. The proposed CAD system analyzes magnetic resonance angiography (MRA) data of human brains to detect and track the cerebral vascular alterations and this is achieved using the following steps: i) MRA data are preprocessed to eliminate noise effects, correct the bias field effect, reduce the contrast inhomogeneity using the generalized Gauss-Markov random field (GGMRF) model, and normalize the MRA data, ii) the cerebral vascular tree of each MRA volume is segmented using a 3-D convolutional neural network (3D-CNN), iii) cerebral features in terms of diameters and tortuosity of blood vessels are estimated and used to construct feature vectors, iv) feature vectors are then used to train and test various artificial neural networks to classify data into two classes; normal and hypertensive. A balanced data set of 66 subjects were used to test the CAD system. Experimental results reported a classification accuracy of 90.9% which supports the efficacy of the CAD system components to accurately model and discriminate between normal and hypertensive subjects. Clinicians would benefit from the proposed CAD system to detect and track cerebral vascular alterations over time for people with high potential of developing hypertension and to prepare appropriate treatment plans to mitigate adverse events.

Simultaneous measurement of flame temperature and species concentration distribution from nonlinear tomographic absorption spectroscopy

This research introduces the evolution strategy based on covariance matrix adaption algorithm, which has been proven applicable for solving highly inseparable and nonlinear optimization problems, to resolve the nonlinear tomography absorption spectroscopy inverse optimization problem and simultaneously reconstruct a two-dimensional temperature and species concentration distribution fields in an absorption flame. Severe ill-posedness and crosstalk issues exist during multi-parameter field simultaneous reconstruction. To alleviate the ill-posedness in nonlinear tomography absorption spectroscopy equations, two regularization methods, Tikhonov regularization and the regularization based on the generalized Gaussian Markov random field, are applied to reconstruct the temperature distribution field. The impacts of different regularization factors (the temperature and the concentration regularization factors) are investigated as well, and optimal intervals are suggested for reference. Simulation results show that the evolution strategy based on covariance matrix adaption algorithm worked well in retrieving multi-parameter distribution fields on both symmetric and asymmetric flame distribution models. Moreover, the evolution strategy based on covariance matrix adaption algorithm alleviated the severe crosstalk issue between temperature and species concentration to improve the accuracy of the reconstructed species concentration distribution field.

Automated framework for accurate segmentation of leaf images for plant health assessment.

Leaf segmentation is significantly important in assisting ecologists to automatically detect symptoms of disease and other stressors affecting trees. This paper employs state-of-the-art techniques in image processing to introduce an accurate framework for segmenting leaves and diseased leaf spots from images. The proposed framework integrates an appearance model that visually represents the current input image with the color prior information generated from RGB color images that were formerly saved in our database. Our framework consists of four main steps: (1) Enhancing the accuracy of the segmentation at minimum time by making use of contrast changes to automatically identify the region of interest (ROI) of the entire leaf, where the pixel-wise intensity relations are described by an electric field energy model. (2) Modeling the visual appearance of the input image using a linear combination of discrete Gaussians (LCDG) to predict the marginal probability distributions of the grayscale ROI main three classes. (3) Calculating the pixel-wise probabilities of these three classes for the color ROI based on the color prior information of database images that are segmented manually, where the current and prior pixel-wise probabilities are used to find the initial labels. (4) Refining the labels with the generalized Gauss-Markov random field model (GGMRF), which maintains the continuity. The proposed segmentation approach was applied to the leaves of mangrove trees in Abu Dhabi in the United Arab Emirates. Experimental validation showed high accuracy, with a Dice similarity coefficient 90% for distinguishing leaf spot from healthy leaf area.

Reconstruction of Radiative Properties Fields in Participating Media by Using the Sequential Quadratic Programing Combined With Regularization Technique

The refractive index and absorption coefficient fields in participating media are reconstructed simultaneously in this work. In the direct model, the coupled radiation–conduction heat transfer in participating media exposed to a pulse laser irradiation is solved by finite volume method (FVM). In the inverse model, the sequential quadratic programming (SQP) algorithm combined with the generalized Gaussian Markov random field (GGMRF) model is employed to solve the reconstruction problem. It is found that the refractive index and absorption coefficient fields cannot be reconstructed simultaneously. A secondary reconstruction technique based on different regularization parameters is proposed to reconstruct the refractive index and absorption coefficient fields simultaneously. All the retrieval results indicate that the proposed secondary reconstruction technique performs accurately and effectively.

Experimental research on noninvasive reconstruction of optical parameter fields based on transient radiative transfer equation for diagnosis applications

The noninvasive reconstruction of optical parameter fields in participating phantom is investigated experimentally based on the measured time-resolved radiative signals, which are detected by the time-correlated single-photon counting system. The discrete ordinate method is employed to solve the forward transient radiative transfer equation to simulate the time-resolved radiative transfer in the physical phantom exposed to ultra-short pulse laser irradiation. On top of that, the sequential quadratic programming algorithm based on the generalized Gaussian Markov random field is applied to solve the inverse problem. To improve the computational efficiency, an adjoint equation technique is adopted to determine the gradient of objective function. Good agreement was obtained between the predicted optical parameter fields and realistic ones. All the reconstruction results demonstrate that the proposed reconstruction methods are proved to be accurate and efficient experimentally.

Deep Learning Role in Early Diagnosis of Prostate Cancer.

The objective of this work is to develop a computer-aided diagnostic system for early diagnosis of prostate cancer. The presented system integrates both clinical biomarkers (prostate-specific antigen) and extracted features from diffusion-weighted magnetic resonance imaging collected at multiple b values. The presented system performs 3 major processing steps. First, prostate delineation using a hybrid approach that combines a level-set model with nonnegative matrix factorization. Second, estimation and normalization of diffusion parameters, which are the apparent diffusion coefficients of the delineated prostate volumes at different b values followed by refinement of those apparent diffusion coefficients using a generalized Gaussian Markov random field model. Then, construction of the cumulative distribution functions of the processed apparent diffusion coefficients at multiple b values. In parallel, a K-nearest neighbor classifier is employed to transform the prostate-specific antigen results into diagnostic probabilities. Finally, those prostate-specific antigen–based probabilities are integrated with the initial diagnostic probabilities obtained using stacked nonnegativity constraint sparse autoencoders that employ apparent diffusion coefficient–cumulative distribution functions for better diagnostic accuracy. Experiments conducted on 18 diffusion-weighted magnetic resonance imaging data sets achieved 94.4% diagnosis accuracy (sensitivity = 88.9% and specificity = 100%), which indicate the promising results of the presented computer-aided diagnostic system.

Application of hybrid SPSO-SQP algorithm for simultaneous estimation of space-dependent absorption coefficient and scattering coefficient fields in participating media

A hybrid stochastic particle swarm optimization (SPSO) and sequential quadratic programming (SQP) algorithm is proposed to estimate the space-dependent absorption coefficient (κa) and scattering coefficient (κs) fields simultaneously. The retrieval results of SQP algorithm are highly affected by the initial guess, and thus, SPSO is adopted to obtain the initial value of SQP because of its global search capability and lesser dependence on initial guess. The regularization term based on the generalized Gaussian Markov random field model is employed to overcome the ill-posed characteristic of the inverse problem. The inverse coupled radiation-conduction problem is solved in a one-dimensional participating medium with uniform refractive and graded refractive indices exposed to a pulse laser, respectively. All the results show that the separate space-dependent κa and κs fields can be estimated simultaneously and accurately from the coupled optical and thermal signals.

Automated framework for accurate segmentation of pressure ulcer images

Ulcer tissue segmentation is of immense importance in helping medical personnel to assess wounds. This paper introduces a new computational framework employing state-of-the-art image processing techniques to segment pressure ulcer tissue structures from color images. The framework integrates a visual appearance model of an observed input image with prior color information from an available database of previously stored color RGB images. The following four processing steps are performed. First, to minimize the execution time and enhance the segmentation accuracy, a region-of-interest (ROI) of the whole ulcer area is automatically identified based on contrast changes. This step exploits synthetic frequencies of pixelwise intensities, which are calculated by using an electric field energy model to describe relations between the pixelwise intensities. Secondly, visual appearance of the observed image is modeled by a linear combination of discrete Gaussians (LCDG) model in order to estimate marginal probability distributions of three main tissue classes for the grayscale ROI image. Next, the pixel-wise probabilities of these classes for the color ROI image are calculated using the available prior information about the RGB colors on manually segmented database images. Initial labeling is obtained based on both the observed and prior probabilities of pixelwise colors. Finally, to preserve continuity, the labels are refined and normalized using the generalized Gauss-Markov random field (GGMRF) model. Experimental validation on 24 clinical images of pressure ulcers, provided by the Centre IGURCO, showed the high segmentation accuracy of 90.4%.

Automatic blood vessels segmentation based on different retinal maps from OCTA scans

The retinal vascular network reflects the health of the retina, which is a useful diagnostic indicator of systemic vascular. Therefore, the segmentation of retinal blood vessels is a powerful method for diagnosing vascular diseases. This paper presents an automatic segmentation system for retinal blood vessels from Optical Coherence Tomography Angiography (OCTA) images. The system segments blood vessels from the superficial and deep retinal maps for normal and diabetic cases. Initially, we reduced the noise and improved the contrast of the OCTA images by using the Generalized Gauss-Markov random field (GGMRF) model. Secondly, we proposed a joint Markov-Gibbs random field (MGRF) model to segment the retinal blood vessels from other background tissues. It integrates both appearance and spatial models in addition to the prior probability model of OCTA images. The higher order MGRF (HO-MGRF) model in addition to the 1st-order intensity model are used to consider the spatial information in order to overcome the low contrast between vessels and other tissues. Finally, we refined the segmentation by extracting connected regions using a 2D connectivity filter. The proposed segmentation system was trained and tested on 47 data sets, which are 23 normal data sets and 24 data sets for diabetic patients. To evaluate the accuracy and robustness of the proposed segmentation framework, we used three different metrics, which are Dice similarity coefficient (DSC), absolute vessels volume difference (VVD), and area under the curve (AUC). The results on OCTA data sets (DSC=95.04±3.75%, VVD=8.51±1.49%, and AUC=95.20±1.52%) show the promise of the proposed segmentation approach.

Application of SQP algorithm for fluorescence tomography with the time-domain equation of radiative transfer

A reconstruction scheme for the fluorescence tomography is investigated based on the time-domain radiative transfer equation (TD-RTE). Two coupled TD-RTEs, which can provide considerable measurement data, are used as the forward model and solved by the discrete ordinate method. The sequential quadratic programming (SQP) is employed to build the reconstruction scheme for solving the inverse problem. The gradient of objective function is calculated efficiently by the adjoint equation technique. Considering the ill-posed nature of the inverse problem, the regularization term based on the generalized Gaussian Markov random field (GGMRF) model is adopted to enhance the reconstructed image. Influence of the initial guess, contrast, noisy data, and shape of the fluorescent target are analyzed. Simulated results show that the proposed algorithm performs efficiently and accurately on reconstructing the distribution of the fluorescence yield.

A comprehensive non-invasive framework for diagnosing prostate cancer

Early detection of prostate cancer increases chances of patients' survival. Our automated non-invasive system for computer-aided diagnosis (CAD) of prostate cancer segments the prostate on diffusion-weighted magnetic resonance images (DW-MRI) acquired at different b-values, estimates its apparent diffusion coefficients (ADC), and classifies their descriptors – empirical cumulative distribution functions (CDF) – with a trained deep learning network. To segment the prostate, an evolving geometric (level-set-based) deformable model is guided by a speed function depending on intensity attributes extracted from the DW-MRI with nonnegative matrix factorization (NMF). For a more robust evolution, the attributes are fused with a probabilistic shape prior and estimated spatial dependencies between prostate voxels. To preserve continuity, the ADCs of the segmented prostate volume at different b-values are normalized and refined using a generalized Gauss-Markov random field image model. The CDFs of the refined ADCs at different b-values are considered global water diffusion features and used to distinguish between benign and malignant prostates. A deep learning network of stacked non-negativity-constrained auto-encoders (SNCAE) is trained to classify the benign or malignant prostates on the basis of the constructed CDFs. Our experiments on 53 clinical DW-MRI data sets resulted in 92.3% accuracy, 83.3% sensitivity, and 100% specificity, indicating that the proposed CAD system could be used as a reliable non-invasive diagnostic tool.

Accurate reconstruction of the optical parameter distribution in participating medium based on the frequency-domain radiative transfer equation**Project supported by the National Natural Science Foundation of China (Grant No. 51476043), the Major National Scientific Instruments and Equipment Development Special Foundation of China (Grant No. 51327803), and the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant

Reconstructing the distribution of optical parameters in the participating medium based on the frequency-domain radiative transfer equation (FD-RTE) to probe the internal structure of the medium is investigated in the present work. The forward model of FD-RTE is solved via the finite volume method (FVM). The regularization term formatted by the generalized Gaussian Markov random field model is used in the objective function to overcome the ill-posed nature of the inverse problem. The multi-start conjugate gradient (MCG) method is employed to search the minimum of the objective function and increase the efficiency of convergence. A modified adjoint differentiation technique using the collimated radiative intensity is developed to calculate the gradient of the objective function with respect to the optical parameters. All simulation results show that the proposed reconstruction algorithm based on FD-RTE can obtain the accurate distributions of absorption and scattering coefficients. The reconstructed images of the scattering coefficient have less errors than those of the absorption coefficient, which indicates the former are more suitable to probing the inner structure.

Application of the sequential quadratic programming algorithm for reconstructing the distribution of optical parameters based on the time-domain radiative transfer equation.

Sequential quadratic programming (SQP) is used as an optimization algorithm to reconstruct the optical parameters based on the time-domain radiative transfer equation (TD-RTE). Numerous time-resolved measurement signals are obtained using the TD-RTE as forward model. For a high computational efficiency, the gradient of objective function is calculated using an adjoint equation technique. SQP algorithm is employed to solve the inverse problem and the regularization term based on the generalized Gaussian Markov random field (GGMRF) model is used to overcome the ill-posed problem. Simulated results show that the proposed reconstruction scheme performs efficiently and accurately.

SU‐G‐IeP4‐03: Cone Beam X‐Ray Luminescence Computed Tomography Based On Generalized Gaussian Markov Random Field

Purpose:Cone beam X‐ray luminescence computed tomography (CB‐XLCT), which aims to achieve molecular and functional imaging by X‐rays, has recently been proposed as a new imaging modality. However, the inverse problem of CB‐XLCT is seriously ill‐conditioned, hindering us to achieve good image quality. In this work, a novel reconstruction method based on Bayesian theory is proposed to tackle this problemMethods:Bayesian theory provides a natural framework for utilizing various kinds of available prior information to improve the reconstruction image quality. A generalized Gaussian Markov random field (GGMRF) model is proposed here to construct the prior model of the Bayesian theory. The most important feature of GGMRF model is the adjustable shape parameter p, which can be continuously adjusted from 1 to 2. The reconstruction image tends to have more edge‐preserving property when p is slide to 1, while having more noise tolerance property when p is slide to 2, just like the behavior of L1 and L2 regularization methods, respectively. The proposed method provides a flexible regularization framework to adapt to a wide range of applications.Results:Numerical simulations were implemented to test the performance of the proposed method. The Digimouse atlas were employed to construct a three‐dimensional mouse model, and two small cylinders were placed inside to serve as the targets. Reconstruction results show that the proposed method tends to obtain better spatial resolution with a smaller shape parameter, while better signal‐to‐noise image with a larger shape parameter. Quantitative indexes, contrast‐to‐noise ratio (CNR) and full‐width at half‐maximum (FWHM), were used to assess the performance of the proposed method, and confirmed its effectiveness in CB‐XLCT reconstruction.Conclusion:A novel reconstruction method for CB‐XLCT is proposed based on GGMRF model, which enables an adjustable performance tradeoff between L1 and L2 regularization methods. Numerical simulations were conducted to demonstrate its performance.

Robust Tracking of Small Displacements With a Bayesian Estimator.

Radiation-force-based elasticity imaging describes a group of techniques that use acoustic radiation force (ARF) to displace tissue to obtain qualitative or quantitative measurements of tissue properties. Because ARF-induced displacements are on the order of micrometers, tracking these displacements in vivo can be challenging. Previously, it has been shown that Bayesian-based estimation can overcome some of the limitations of a traditional displacement estimator such as normalized cross-correlation (NCC). In this work, we describe a Bayesian framework that combines a generalized Gaussian-Markov random field (GGMRF) prior with an automated method for selecting the prior's width. We then evaluate its performance in the context of tracking the micrometer-order displacements encountered in an ARF-based method such as ARF impulse (ARFI) imaging. The results show that bias, variance, and mean-square error (MSE) performance vary with prior shape and width, and that an almost one order-of-magnitude reduction in MSE can be achieved by the estimator at the automatically selected prior width. Lesion simulations show that the proposed estimator has a higher contrast-to-noise ratio but lower contrast than NCC, median-filtered NCC, and the previous Bayesian estimator, with a non-Gaussian prior shape having better lesion-edge resolution than a Gaussian prior. In vivo results from a cardiac, radio-frequency ablation ARFI imaging dataset show quantitative improvements in lesion contrast-to-noise ratio over NCC as well as the previous Bayesian estimator.

Multi-channel beam-scanning imaging at kHz frame rates by Lissajous trajectory microscopy.

A beam-scanning microscope based on Lissajous trajectory imaging is described for achieving streaming 2D imaging with continuous frame rates up to 1.4 kHz. The microscope utilizes two fast-scan resonant mirrors to direct the optical beam on a circuitous trajectory through the field of view. By separating the full Lissajous trajectory time-domain data into sub-trajectories (partial, undersampled trajectories) effective frame-rates much higher than the repeat time of the Lissajous trajectory are achieved with many unsampled pixels present. A model-based image reconstruction (MBIR) 3D in-painting algorithm is then used to interpolate the missing data for the unsampled pixels to recover full images. The MBIR algorithm uses a maximum a posteriori estimation with a generalized Gaussian Markov random field prior model for image interpolation. Because images are acquired using photomultiplier tubes or photodiodes, parallelization for multi-channel imaging is straightforward. Preliminary results show that when combined with the MBIR in-painting algorithm, this technique has the ability to generate kHz frame rate images across 6 total dimensions of space, time, and polarization for SHG, TPEF, and confocal reflective birefringence data on a multimodal imaging platform for biomedical imaging. The use of a multi-channel data acquisition card allows for multimodal imaging with perfect image overlay. Image blur due to sample motion was also reduced by using higher frame rates.