Statistical Models of Signal and Noise and Fundamental Limits of Segmentation Accuracy in Retinal Optical Coherence Tomography

Score Prior Guided Iterative Solver for Speckles Removal in Optical Coherent Tomography Images

Optical coherence tomography (OCT) is a widely used non-invasive imaging modality for ophthalmic diagnosis. However, the inherent speckle noise becomes the leading cause of OCT image quality, and efficient speckle removal algorithms can improve image readability and benefit automated clinical analysis. As an ill-posed inverse problem, it is of utmost importance for speckle removal to learn suitable priors. In this work, we develop a score prior guided iterative solver (SPIS) with logarithmic space to remove speckles in OCT images. Specifically, we model the posterior distribution of raw OCT images as a data consistency term and transform the speckle removal from a nonlinear into a linear inverse problem in the logarithmic domain. Subsequently, the learned prior distribution through the score function from the diffusion model is utilized as a constraint for the data consistency term into the linear inverse optimization, resulting in an iterative speckle removal procedure that alternates between the score prior predictor and the subsequent non-expansive data consistency corrector. Experimental results on the private and public OCT datasets demonstrate that the proposed SPIS has an excellent performance in speckle removal and out-of-distribution (OOD) generalization. Further downstream automatic analysis on the OCT images verifies that the proposed SPIS can benefit clinical applications.

Automatic 3-D segmentation and volumetric light fluence correction for photoacoustic tomography based on optimal 3-D graph search

Preclinical imaging with photoacoustic tomography (PAT) has attracted wide attention in recent years since it is capable of providing molecular contrast with deep imaging depth. The automatic extraction and segmentation of the animal in PAT images is crucial for improving image analysis efficiency and enabling advanced image post-processing, such as light fluence (LF) correction for quantitative PAT imaging. Previous automatic segmentation methods are mostly two-dimensional approaches, which failed to conserve the 3-D surface continuity because the image slices were processed separately. This discontinuity problem further hampers LF correction, which, ideally, should be carried out in 3-D due to spatially diffused illumination. Here, to solve these problems, we propose a volumetric auto-segmentation method for small animal PAT imaging based on the 3-D optimal graph search (3-D GS) algorithm. The 3-D GS algorithm takes into account the relation among image slices by constructing a 3-D node-weighted directed graph, and thus ensures surface continuity. In view of the characteristics of PAT images, we improve the original 3-D GS algorithm on graph construction, solution guidance and cost assignment, such that the accuracy and smoothness of the segmented animal surface were guaranteed. We tested the performance of the proposed method by conducting in vivo nude mice imaging experiments with a commercial preclinical cross-sectional PAT system. The results showed that our method successfully retained the continuous global surface structure of the whole 3-D animal body, as well as smooth local subcutaneous tumor boundaries at different development stages. Moreover, based on the 3-D segmentation result, we were able to simulate volumetric LF distribution of the entire animal body and obtained LF corrected PAT images with enhanced structural visibility and uniform image intensity.

Noise Reduction for SD-OCT Using a Structure-Preserving Domain Transfer Approach

Spectral-domain optical coherence tomography (SD-OCT) images inevitably suffer from multiplicative speckle noise caused by random interference. This study proposes an unsupervised domain adaptation approach for noise reduction by translating the SD-OCT to the corresponding high-quality enhanced depth imaging (EDI)-OCT. We propose a structure-persevered cycle-consistent generative adversarial network for unpaired image-to-image translation, which can be applied to imbalanced unpaired data, and can effectively preserve retinal details based on a structure-specific cross-domain description. It also imposes smoothness by penalizing the intensity variation of the low reflective region between consecutive slices. Our approach was tested on a local data set that consisted of 268 SD-OCT volumes and two public independent validation datasets including 20 SD-OCT volumes and 17 B-scans, respectively. Experimental results show that our method can effectively suppress noise and maintain the retinal structure, compared with other traditional approaches and deep learning methods in terms of qualitative and quantitative assessments. Our proposed method shows good performance for speckle noise reduction and can assist downstream tasks of OCT analysis.

Statistical modeling of retinal optical coherence tomography using the Weibull mixture model

In this paper, a novel statistical model is proposed for retinal optical coherence tomography (OCT) images. According to the layered structure of the retina, a mixture of six Weibull distributions is proposed to describe the main statistical features of OCT images. We apply Weibull distribution to establish a more comprehensive model but with fewer parameters that has better goodness of fit (GoF) than previous models. Our new model also takes care of features such as asymmetry and heavy-tailed nature of the intensity distribution of retinal OCT data. In order to test the effectiveness of this new model, we apply it to improve the low quality of the OCT images. For this purpose, the spatially constrained Gaussian mixture model (SCGMM) is implemented. Since SCGMM is designed for data with Gaussian distribution, we convert our Weibull mixture model to a Gaussian mixture model using histogram matching before applying SCGMM. The denoising results illustrate the remarkable performance in terms of the contrast to noise ratio (CNR) and texture preservation (TP) compared to other peer methods. In another test to evaluate the efficiency of our proposed model, the parameters and GoF criteria are considered as a feature vector for support vector machine (SVM) to classify the healthy retinal OCT images from pigment epithelial detachment (PED) disease. The confusion matrix demonstrates the impact of the proposed model in our preliminary study on the OCT classification problem.

Modeling of Retinal Optical Coherence Tomography Based on Stochastic Differential Equations: Application to Denoising

In this paper a statistical modeling, based on stochastic differential equations (SDEs), is proposed for retinal Optical Coherence Tomography (OCT) images. In this method, pixel intensities of image are considered as discrete realizations of a Levy stable process. This process has independent increments and can be expressed as response of SDE to a white symmetric alpha stable (s [Formula: see text]) noise. Based on this assumption, applying appropriate differential operator makes intensities statistically independent. Mentioned white stable noise can be regenerated by applying fractional Laplacian operator to image intensities. In this way, we modeled OCT images as s [Formula: see text] distribution. We applied fractional Laplacian operator to image and fitted s [Formula: see text] to its histogram. Statistical tests were used to evaluate goodness of fit of stable distribution and its heavy tailed and stability characteristics. We used modeled s [Formula: see text] distribution as prior information in maximum a posteriori (MAP) estimator in order to reduce the speckle noise of OCT images. Such a statistically independent prior distribution simplified denoising optimization problem to a regularization algorithm with an adjustable shrinkage operator for each image. Alternating Direction Method of Multipliers (ADMM) algorithm was utilized to solve the denoising problem. We presented visual and quantitative evaluation results of the performance of this modeling and denoising methods for normal and abnormal images. Applying parameters of model in classification task as well as indicating effect of denoising in layer segmentation improvement illustrates that the proposed method describes OCT data more accurately than other models that do not remove statistical dependencies between pixel intensities.

Contrast enhancement and speckle suppression in OCT images based on a selective weighted variational enhancement model and an SP-FOOPDE algorithm

Simultaneous contrast enhancement and speckle suppression in optical coherence tomography (OCT) are of great significance to medical diagnosis. In this paper, we propose a selective weighted variational enhancement (SWVE) model to enhance the structural parts of OCT images, and then present a shape-preserving fourth-order-oriented partial differential equations (SP-FOOPDE) algorithm to suppress speckle noise. To be specific, in the SWVE model, we first introduce the fast and robust fuzzy c-means clustering (FRFCM) algorithm to generate masks based on the gray-level histograms of the reconstructed OCT images and utilize the masks to distinguish the structural parts from the background. Then the retinex-based weighted variational model, combined with gamma correction, is adopted to enhance the structural parts by multiplying the estimated reflectance with the adjusted illumination. In the despeckling process, we present an SP-FOOPDE algorithm with the fidelity term modified by the shearlet transform to strike a splendid balance between noise suppression and structural preservation. Experimental results show that the proposed method performs well in contrast enhancement and speckle suppression, with better quality metrics of the MSE, PSNR, CNR, ENL, EKI, and ν and better noise immunity than the related method. Moreover, the application to the segmentation preprocessing exhibits that the retinal structure of the OCT images processed by the proposed method can be completely segmented.

Resolution enhancement and realistic speckle recovery with generative adversarial modeling of micro-optical coherence tomography

A resolution enhancement technique for optical coherence tomography (OCT), based on Generative Adversarial Networks (GANs), was developed and investigated. GANs have been previously used for resolution enhancement of photography and optical microscopy images. We have adapted and improved this technique for OCT image generation. Conditional GANs (cGANs) were trained on a novel set of ultrahigh resolution spectral domain OCT volumes, termed micro-OCT, as the high-resolution ground truth (∼1 μm isotropic resolution). The ground truth was paired with a low-resolution image obtained by synthetically degrading resolution 4x in one of (1-D) or both axial and lateral axes (2-D). Cross-sectional image (B-scan) volumes obtained from in vivo imaging of human labial (lip) tissue and mouse skin were used in separate feasibility experiments. Accuracy of resolution enhancement compared to ground truth was quantified with human perceptual accuracy tests performed by an OCT expert. The GAN loss in the optimization objective, noise injection in both the generator and discriminator models, and multi-scale discrimination were found to be important for achieving realistic speckle appearance in the generated OCT images. The utility of high-resolution speckle recovery was illustrated by an example of micro-OCT imaging of blood vessels in lip tissue. Qualitative examples applying the models to image data from outside of the training data distribution, namely human retina and mouse bladder, were also demonstrated, suggesting potential for cross-domain transferability. This preliminary study suggests that deep learning generative models trained on OCT images from high-performance prototype systems may have potential in enhancing lower resolution data from mainstream/commercial systems, thereby bringing cutting-edge technology to the masses at low cost.

Multivariate Statistical Modeling of Retinal Optical Coherence Tomography

In this paper a new statistical multivariate model for retinal Optical Coherence Tomography (OCT) B-scans is proposed. Due to the layered structure of OCT images, there is a horizontal dependency between adjacent pixels at specific distances, which led us to propose a more accurate multivariate statistical model to be employed in OCT processing applications such as denoising. Due to the asymmetric form of the probability density function (pdf) in each retinal layer, a generalized version of multivariate Gaussian Scale Mixture (GSM) model, which we refer to as GM-GSM model, is proposed for each retinal layer. In this model, the pixel intensities in each retinal layer are modeled with an asymmetric Bessel K Form (BKF) distribution as a specific form of the GM-GSM model. Then, by combining some layers together, a mixture of GM-GSM model with eight components is proposed. The proposed model is then easily converted to a multivariate Gaussian Mixture model (GMM) to be employed in the spatially constrained GMM denoising algorithm. The Q-Q plot is utilized to evaluate goodness of fit of each component of the final mixture model. The improvement in the noise reduction results based on the GM-GSM model, indicates that the proposed statistical model describes the OCT data more accurately than other competing methods that do not consider spatial dependencies between neighboring pixels.

Approaches to quantify optical coherence tomography angiography metrics

Optical coherence tomography (OCT) has revolutionized the field of ophthalmology in the last three decades. As an OCT extension, OCT angiography (OCTA) utilizes a fast OCT system to detect motion contrast in ocular tissue and provides a three-dimensional representation of the ocular vasculature in a non-invasive, dye-free manner. The first OCT machine equipped with OCTA function was approved by U.S. Food and Drug Administration in 2016 and now it is widely applied in clinics. To date, numerous methods have been developed to aid OCTA interpretation and quantification. In this review, we focused on the workflow of OCTA-based interpretation, beginning from the generation of the OCTA images using signal decorrelation, which we divided into intensity-based, phase-based and phasor-based methods. We further discussed methods used to address image artifacts that are commonly observed in clinical settings, to the algorithms for image enhancement, binarization, and OCTA metrics extraction. We believe a better grasp of these technical aspects of OCTA will enhance the understanding of the technology and its potential application in disease diagnosis and management. Moreover, future studies will also explore the use of ocular OCTA as a window to link ocular vasculature to the function of other organs such as the kidney and brain.

Automated Iris Segmentation from Anterior Segment OCT Images with Occludable Angles via Local Phase Tensor

Morphological changes in the iris are one of the major causes of angle-closure glaucoma, and an anteriorly-bowed iris may be further associated with greater risk of disease progression from primary angle-closure suspect (PACS) to chronic primary angle-closure glaucoma (CPCAG). In consequence, the automated detection of abnormalities in the iris region is of great importance in the management of glaucoma. In this paper, we present a new method for the extraction of the iris region by using a local phase tensor-based curvilinear structure enhancement method, and apply it to anterior segment optical coherence tomography (AS-OCT) imagery in the presence of occludable iridocorneal angle. The proposed method is evaluated across a dataset of 200 anterior chamber angle (ACA) images, and the experimental results show that the proposed method outperforms existing state-of-the-art method in applicability, effectiveness, and accuracy.

Speckle Reduction in Optical Coherence Tomography via Super-Resolution Reconstruction

Reducing speckle noise from the optical coherence tomograms (OCT) of human retina is a fundamental step to a better visualization and analysis in retinal imaging, as thus to support examination, diagnosis and treatment of many eye diseases. In this study, we propose a new method for speckle reduction in OCT images using the super-resolution technology. It merges multiple images for the same scene but with sub-pixel movements and restores the missing signals in one pixel, which significantly improves the image quality. The proposed method is evaluated on a dataset of 20 OCT volumes (5120 images), through the mean square error, peak signal to noise ratio and the mean structure similarity index using high quality line-scan images as reference. The experimental results show that the proposed method outperforms existing state-of-the-art approaches in applicability, effectiveness, and accuracy.

Automated Deformation-Based Analysis of 3D Optical Coherence Tomography in Diabetic Retinopathy

Diabetic retinopathy (DR) is a significant microvascular complication of diabetes mellitus and a leading cause of vision impairment in working age adults. Optical coherence tomography (OCT) is a routinely used clinical tool to observe retinal structural and thickness alterations in DR. Pathological changes that alter the normal anatomy of the retina, such as intraretinal edema, pose great challenges for conventional layer-based analysis of OCT images. We present an alternative approach for the automated analysis of OCT volumes in DR research based on nonlinear registration. In this paper, we first obtain an anatomically consistent volume of interest (VOI) in different OCT images via carefully designed masking and affine registration. After that, efficient B-spline transformations are computed using stochastic gradient descent optimization. Using the OCT volumes of normal controls, for which layer-based segmentation works well, we demonstrate the accuracy of our registration-based analysis in aligning layer boundaries. By nonlinearly registering the OCT volumes of DR subjects to an atlas constructed from normal controls and measuring the Jacobian determinant of the deformation, we can simultaneously visualize tissue contraction and expansion due to DR pathology. Tensor-based morphometry (TBM) can also be performed for quantitative analysis of local structural changes. In our experimental results, we apply our method to a dataset of 105 subjects and demonstrate that volumetric OCT registration and TBM analysis can successfully detect local retinal structural alterations due to DR.

Signal averaging improves signal-to-noise in OCT images: But which approach works best, and when?

The high acquisition speed of state-of-the-art optical coherence tomography (OCT) enables massive signal-to-noise ratio (SNR) improvements by signal averaging. Here, we investigate the performance of two commonly used approaches for OCT signal averaging. We present the theoretical SNR performance of (a) computing the average of OCT magnitude data and (b) averaging the complex phasors, and substantiate our findings with simulations and experimentally acquired OCT data. We show that the achieved SNR performance strongly depends on both the SNR of the input signals and the number of averaged signals when the signal bias caused by the noise floor is not accounted for. Therefore we also explore the SNR for the two averaging approaches after correcting for the noise bias and, provided that the phases of the phasors are accurately aligned prior to averaging, then find that complex phasor averaging always leads to higher SNR than magnitude averaging.

Temporal speckle-averaging of optical coherence tomography volumes for in-vivo cellular resolution neuronal and vascular retinal imaging

It has been recently demonstrated that structures corresponding to the cell bodies of highly transparent cells in the retinal ganglion cell layer could be visualized noninvasively in the living human eye by optical coherence tomography (OCT) via temporal averaging. Inspired by this development, we explored the application of volumetric temporal averaging in mice, which are important models for studying human retinal diseases and therapeutic interventions. A general framework of temporal speckle-averaging (TSA) of OCT and optical coherence tomography angiography (OCTA) is presented and applied to mouse retinal volumetric data. Based on the image analysis, the eyes of mice under anesthesia exhibit only minor motions, corresponding to lateral displacements of a few micrometers and rotations of a fraction of 1 deg. Moreover, due to reduced eye movements under anesthesia, there is a negligible amount of motion artifacts within the volumes that need to be corrected to achieve volume coregistration. In addition, the relatively good optical quality of the mouse ocular media allows for cellular-resolution imaging without adaptive optics (AO), greatly simplifying the experimental system, making the proposed framework feasible for large studies. The TSA OCT and TSA OCTA results provide rich information about new structures previously not visualized in living mice with non-AO-OCT. The mechanism of TSA relies on improving signal-to-noise ratio as well as efficient suppression of speckle contrast due to temporal decorrelation of the speckle patterns, enabling full utilization of the high volumetric resolution offered by OCT and OCTA.

OCT Image Denoising Based on Asymmetric Normal Laplace Mixture Model

Optical Coherence Tomography (OCT) is one of the well-known imaging systems in ophthalmology that provides images with high resolution from retinal tissue. However, like other coherent imaging systems, OCT images suffer from speckle noise which decreases the image quality. Denoising can be considered as an estimation problem in a Bayesian framework. So, finding a suitable distribution for noiseless data is an important issue. We propose a statistical model for OCT data, namely Asymmetric Normal Laplace Mixture Model (ANLMM), and then convert its distribution to normal by Gaussianization Transform (GT). Finally, by applying the Spatially Constrained Gaussian Mixture Model (SC-GMM), a new OCT denoising algorithm is introduced, which significantly outperforms the other methods in terms of Contrast-to-Noise Ratio (CNR).

Parallel deep neural networks for endoscopic OCT image segmentation

We report parallel-trained deep neural networks for automated endoscopic OCT image segmentation feasible even with a limited training data set. These U-Net-based deep neural networks were trained using a modified dice loss function and manual segmentations of ultrahigh-resolution cross-sectional images collected by an 800 nm OCT endoscopic system. The method was tested on in vivo guinea pig esophagus images. Results showed its robust layer segmentation capability with a boundary error of 1.4 µm insensitive to lay topology disorders. To further illustrate its clinical potential, the method was applied to differentiating in vivo OCT esophagus images from an eosinophilic esophagitis (EOE) model and its control group, and the results clearly demonstrated quantitative changes in the top esophageal layers' thickness in the EOE model.

Automatic three-dimensional segmentation of endoscopic airway OCT images

Automatic delineation and segmentation of airway structures from endoscopic optical coherence tomography (OCT) images improve image analysis efficiency and thus has been of particular interest. Conventional two-dimensional automatic segmentation methods, such as the dynamic programming approach, ensures the edge-continuity in the xz-direction (intra-B-scan), but fails to preserve the surface-continuity when concerning the y-direction (inter-B-scan). To solve this, we present a novel automatic three-dimensional (3D) airway segmentation strategy. Our segmentation scheme includes an artifact-oriented pre-processing pipeline and a modified 3D optimal graph search algorithm incorporating adaptive tissue-curvature adjustment. The proposed algorithm is tested on endoscopic airway OCT image data sets acquired by different swept-source OCT platforms, and on different animal and human models. With our method, the results show continuous surface segmentation performance, which is both robust and accurate.

Aperture phase modulation with adaptive optics: a novel approach for speckle reduction and structure extraction in optical coherence tomography

Speckle is an inevitable consequence of the use of coherent light in imaging and acts as noise that corrupts image formation in most applications. Optical coherence tomographic imaging, as a technique employing coherence time gating, suffers from speckle. We present here a novel method of suppressing speckle noise intrinsically compatible with adaptive optics (AO) for confocal coherent imaging: modulation of the phase in the system pupil aperture with a segmented deformable mirror (DM) to introduce minor perturbations in the point spread function. This approach creates uncorrelated speckle patterns in a series of images, enabling averaging to suppress speckle noise while maintaining structural detail. A method is presented that efficiently determines the optimal range of modulation of DM segments relative to their AO-optimized position so that speckle noise is reduced while image resolution and signal strength are preserved. The method is active and independent of sample properties. Its effectiveness and efficiency are quantified and demonstrated by both ex vivo non-biological and in vivo biological applications.

Deep longitudinal transfer learning-based automatic segmentation of photoreceptor ellipsoid zone defects on optical coherence tomography images of macular telangiectasia type 2

Photoreceptor ellipsoid zone (EZ) defects visible on optical coherence tomography (OCT) are important imaging biomarkers for the onset and progression of macular diseases. As such, accurate quantification of EZ defects is paramount to monitor disease progression and treatment efficacy over time. We developed and trained a novel deep learning-based method called Deep OCT Atrophy Detection (DOCTAD) to automatically segment EZ defect areas by classifying 3-dimensional A-scan clusters as normal or defective. Furthermore, we introduce a longitudinal transfer learning paradigm in which the algorithm learns from segmentation errors on images obtained at one time point to segment subsequent images with higher accuracy. We evaluated the performance of this method on 134 eyes of 67 subjects enrolled in a clinical trial of a novel macular telangiectasia type 2 (MacTel2) therapeutic agent. Our method compared favorably to other deep learning-based and non-deep learning-based methods in matching expert manual segmentations. To the best of our knowledge, this is the first automatic segmentation method developed for EZ defects on OCT images of MacTel2.

Real-time corneal segmentation and 3D needle tracking in intrasurgical OCT

Ophthalmic procedures demand precise surgical instrument control in depth, yet standard operating microscopes supply limited depth perception. Current commercial microscope-integrated optical coherence tomography partially meets this need with manually-positioned cross-sectional images that offer qualitative estimates of depth. In this work, we present methods for automatic quantitative depth measurement using real-time, two-surface corneal segmentation and needle tracking in OCT volumes. We then demonstrate these methods for guidance of ex vivo deep anterior lamellar keratoplasty (DALK) needle insertions. Surgeons using the output of these methods improved their ability to reach a target depth, and decreased their incidence of corneal perforations, both with statistical significance. We believe these methods could increase the success rate of DALK and thereby improve patient outcomes.

Comparison of chorioretinal layers in rhesus macaques using spectral-domain optical coherence tomography and high-resolution histological sections

Nonhuman primates are important preclinical models of retinal diseases because they uniquely possess a macula similar to humans. Ocular imaging technologies such as spectral-domain optical coherence tomography (SD-OCT) allow noninvasive, in vivo measurements of chorioretinal layers with near-histological resolution. However, the boundaries are based on differences in reflectivity, and detailed correlations with histological tissue layers have not been explored in rhesus macaques, which are widely used for biomedical research. Here, we compare the macular anatomy and thickness measurements of chorioretinal layers in rhesus macaque eyes using SD-OCT and high-resolution histological sections. Images were obtained from methylmethacrylate-embedded histological sections of 6 healthy adult rhesus macaques, and compared with SD-OCT images from 6 age-matched animals. Thicknesses of chorioretinal layers were measured across the central 3 mm macular region using custom semi-automated or manual software segmentation, and compared between the two modalities. We found that histological sections provide better distinction between the ganglion cell layer (GCL) and inner plexiform layer (IPL) than SD-OCT imaging. The first hyperreflective band between the external limiting membrane (ELM) and retinal pigment epithelium (RPE) appears wider on SD-OCT than the junction between photoreceptor inner and outer segments seen on histology. SD-OCT poorly distinguishes Henle nerve fibers from the outer nuclear layer (ONL), while histology correctly identifies these fibers as part of the outer plexiform layer (OPL). Overall, the GCL, inner nuclear layer (INL), and OPL are significantly thicker on histology, especially at the fovea; while the ONL, choriocapillaris (CC), and outer choroid (OC) are thicker on SD-OCT. Our results show that both SD-OCT and high-resolution histological sections allow reliable measurements of chorioretinal layers in rhesus macaques, with distinct advantages for different sublayers. These findings demonstrate the effects of tissue processing on chorioretinal anatomy, and provide normative values for chorioretinal thickness measurements on SD-OCT for future studies of disease models in these nonhuman primates.