Blind Monte Carlo detection-estimation method for optical coherence tomography

Abstract

We consider the parametric analysis of frequency-domain optical coherence tomography (OCT) signals. A Monte Carlo (Gibbs sampler) detection-estimation method for determining the depths and reflection coefficients of tissue interfaces (reflective sites in the tissue) is proposed. Our method is blind since it estimates the instrumentationdependent "fringe" function along with the tissue parameters. Sparsity of the detected interfaces is enforced by an impulse detector and a modified Bernoulli-Gaussian prior with a minimum distance constraint. Numerical results using synthetic and real signals demonstrate the excellent performance and fast convergence of our method.

A partially collapsed Gibbs sampler for parameters with local constraints

“…For each realization of x, we generated a Markov chain according to each of the four sampler algorithms. Detection and estimation were performed as in [2]. The result of one such simulation run (corresponding to one realization of x) is shown in Fig.…”

“…This example is relevant to several signal processing applications (e.g., [2]). For reasons that will become clear later, the binary sequence is now denoted by b k , rather than by θ k .…”

“…b k is the product of independent Bernoulli distributions with "1-probability" π1 (a fixed hyperparameter) and IC(b) is an indicator function enforcing the minimum-distance constraint b ∈ C. The pulse f is represented by a basis expansion f = Hα α, where α α is a length-N random coefficient vector and H is a known K × N matrix (chosen as in [2]). The weights a, pulse coefficients α α, and noise n are modeled as mutually independent with complex Gaussian priors p(a) = CN (a; 0, σ We now develop some PCGSs for our application.…”

“…. , K that is multiplied by random weights a k , convolved with a random pulse f k , and corrupted by additive noise n k (see [2] for more details). Thus, the observed sequence is given by…”

“…A simple example is a random sequence of nonuniformly spaced binary pulses with a known minimum distance between any two pulses and weak dependencies otherwise. This example, which will be discussed in the course of this paper, is interesting for many signal processing applications including signal segmentation [1], layer detection [2], and electromyography [3].…”