Analysis of scattering statistics and governing distribution functions in optical coherence tomography

Statistical analysis of corneal OCT speckle: a non-parametric approach

In biomedical optics, it is often of interest to statistically model the amplitude of the speckle using some distributional approximations with their parameters acting as biomarkers. In this paper, a paradigm shift is being advocated in which non-parametric approaches are used. Specifically, a range of distances, evaluated in different domains, between an empirical non-parametric distribution of the normalized speckle amplitude sample and the benchmark Rayleigh distribution, is considered. Using OCT images from phantoms, two ex-vivo experiments with porcine corneas and an in-vivo experiment with human corneas, an evidence is provided that the non-parametric approach, despite its simplicity, could lead to equivalent or better results than the parametric approaches with distributional approximations. Concluding, in practice, the non-parametric approach should be considered as the first choice to speckle modeling before a particular distributional approximation is utilized.

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.

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.

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

Optical coherence tomography (OCT) has revolutionized diagnosis and prognosis of ophthalmic diseases by visualization and measurement of retinal layers. To speed up the quantitative analysis of disease biomarkers, an increasing number of automatic segmentation algorithms have been proposed to estimate the boundary locations of retinal layers. While the performance of these algorithms has significantly improved in recent years, a critical question to ask is how far we are from a theoretical limit to OCT segmentation performance. In this paper, we present the Cramèr-Rao lower bounds (CRLBs) for the problem of OCT layer segmentation. In deriving the CRLBs, we address the important problem of defining statistical models that best represent the intensity distribution in each layer of the retina. Additionally, we calculate the bounds under an optimal affine bias, reflecting the use of prior knowledge in many segmentation algorithms. Experiments using in vivo images of human retina from a commercial spectral domain OCT system are presented, showing potential for improvement of automated segmentation accuracy. Our general mathematical model can be easily adapted for virtually any OCT system. Furthermore, the statistical models of signal and noise developed in this paper can be utilized for the future improvements of OCT image denoising, reconstruction, and many other applications.

K-distribution three-dimensional mapping of biological tissues in optical coherence tomography

Probability density function (PDF) analysis with K-distribution model of optical coherence tomography (OCT) intensity signals has previously yielded a good representation of the average number of scatterers in a coherence volume for microspheres-in-water systems, and has shown initial promise for biological tissue characterization. In this work, we extend these previous findings, based on single point M-mode or two-dimenstional slice analysis, to full three-dimensional (3D) imaging maps of the shape parameter α of the K-distribution PDF. After selecting a suitably sized 3D evaluation window, and verifying methodology in phantoms, the resultant parametric α images obtained in different animal tissues (rat liver and brain) show new contrasting ability not seen in conventional OCT intensity images.

OCT Amplitude and Speckle Statistics of Discrete Random Media

Speckle, amplitude fluctuations in optical coherence tomography (OCT) images, contains information on sub-resolution structural properties of the imaged sample. Speckle statistics could therefore be utilized in the characterization of biological tissues. However, a rigorous theoretical framework relating OCT speckle statistics to structural tissue properties has yet to be developed. As a first step, we present a theoretical description of OCT speckle, relating the OCT amplitude variance to size and organization for samples of discrete random media (DRM). Starting the calculations from the size and organization of the scattering particles, we analytically find expressions for the OCT amplitude mean, amplitude variance, the backscattering coefficient and the scattering coefficient. We assume fully developed speckle and verify the validity of this assumption by experiments on controlled samples of silica microspheres suspended in water. We show that the OCT amplitude variance is sensitive to sub-resolution changes in size and organization of the scattering particles. Experimentally determined and theoretically calculated optical properties are compared and in good agreement.

Assessment of corneal properties based on statistical modeling of OCT speckle

A new approach to assess the properties of the corneal micro-structure in vivo based on the statistical modeling of speckle obtained from Optical Coherence Tomography (OCT) is presented. A number of statistical models were proposed to fit the corneal speckle data obtained from OCT raw image. Short-term changes in corneal properties were studied by inducing corneal swelling whereas age-related changes were observed analyzing data of sixty-five subjects aged between twenty-four and seventy-three years. Generalized Gamma distribution has shown to be the best model, in terms of the Akaike's Information Criterion, to fit the OCT corneal speckle. Its parameters have shown statistically significant differences (Kruskal-Wallis, p < 0.001) for short and age-related corneal changes. In addition, it was observed that age-related changes influence the corneal biomechanical behaviour when corneal swelling is induced. This study shows that Generalized Gamma distribution can be utilized to modeling corneal speckle in OCT in vivo providing complementary quantified information where micro-structure of corneal tissue is of essence.