Abstract. In this paper, we investigate the reconstruction error, [Formula: see text], when a linear, filtered back-projection (FBP) algorithm is applied to noisy, discrete Radon transform data with sampling step-size [Formula: see text] in two dimensions. Specifically, we analyze [Formula: see text] for [Formula: see text] in small, [Formula: see text]-sized neighborhoods around a generic fixed point, [Formula: see text], in the plane, where the measurement noise values, [Formula: see text] (i.e., the errors in the sinogram space), are random variables. The latter are independent, but not necessarily identically distributed. We show, under suitable assumptions on the first three moments of the [Formula: see text], that the following limit exists: [Formula: see text] for [Formula: see text] in a bounded domain. Here, [Formula: see text] and [Formula: see text] are viewed as continuous random variables, and the limit is understood in the sense of distributions. Once the limit is established, we prove that [Formula: see text] is a zero mean Gaussian random field and compute explicitly its covariance. In addition, we validate our theory using numerical simulations and pseudorandom noise.

Diffuse Optical Tomography (DOT) is a well-known imaging technique for detecting the optical properties of an object in order to detect anomalies, such as diffusive or absorptive targets. More specifically, DOT has many applications in medical imaging including breast cancer screening. It is an affordable and noninvasive method to recover the optical properties of a body using photon density measurements from applying laser sources placed at its surface. Mathematically, the reconstruction of the internal absorption or scattering is a severely ill-posed inverse problem and yields a poor quality image reconstruction. Studying coefficient inverse problems in a stochastic setting has increasingly gained in prominence in the past couple of decades. In this work, we will show convergence and optimality for a Bayesian estimator for the absorption coefficient built from the noisy data obtained in a simplified DOT Model. We establish the rate of convergence of such an estimator in the supremum norm loss and show that it is optimal. We also present numerical experiments in support of our theoretical findings.