DoPAMINE: Double-sided Masked CNN for Pixel Adaptive Multiplicative Noise Despeckling

We propose DoPAMINE, a new neural network based multiplicative noise despeckling algorithm. Our algorithm is inspired by Neural AIDE (N-AIDE), which is a recently proposed neural adaptive image denoiser. While the original N-AIDE was designed for the additive noise case, we show that the same framework, i.e., adaptively learning a network for pixel-wise affine denoisers by minimizing an unbiased estimate of MSE, can be applied to the multiplicative noise case as well. Moreover, we derive a double-sided masked CNN architecture which can control the variance of the activation values in each layer and converge fast to high denoising performance during supervised training. In the experimental results, we show our DoPAMINE possesses high adaptivity via fine-tuning the network parameters based on the given noisy image and achieves significantly better despeckling results compared to SAR-DRN, a state-of-the-art CNN-based algorithm.Comment: AAAI 2019 Camera Ready Versio

Inversions of two wave-forward operators with variable coefficients

As the most successful example of a hybrid tomographic technique, photoacoustic tomography is based on generating acoustic waves inside an object of interest by stimulating electromagnetic waves. This acoustic wave is measured outside the object and converted into a diagnostic image. One mathematical problem is determining the initial function from the measured data. The initial function describes the spatial distribution of energy absorption, and the acoustic wave satisfies the wave equation with variable speed. In this article, we consider two types of problems: inverse problem with Robin boundary condition and inverse problem with Dirichlet boundary condition. We define two wave-forward operators that assign the solution of the wave equation based on the initial function to a given function and provide their inversions

Properties of Some Integral Transforms Arising in Tomography

This dissertation deals with several types of imaging: radio tomography, single scattering optical tomography, photoacoustic tomography, and Compton camera imaging. Each of these tomographic techniques leads to a Radon-type transform: radio tomography brings about an elliptical Radon transform, single scattering optical tomography reduces to the V-line Radon transform, and photoacoustic tomography with line detectors boils down to a cylindrical Radon transform. We also introduce a different Radon-type transform arising in photo acoustic tomography with circular detectors, and study mathematically similar object, a toroidal Radon transform. We also consider the cone transform arising in Compton camera imaging as well as the windowed ray transform. We provide inversion formulas for all these transforms. When given some Radon- type transform, we are interested not only in inversion formulas, but also in range conditions, and stability. We thus address range conditions, a stability estimate for some of the Radon-type transforms above

Self-supervised learning for a nonlinear inverse problem with forward operator involving an unknown function arising in Photoacoustic Tomography

In this article, we concern with a nonlinear inverse problem with forward operator involving an unknown function. The problem arises in diverse applications and is challenging by the presence of the unknown function, which makes it ill-posed. Additionally, the nonlinear nature of the problem makes it difficult to use traditional methods and thus the study has addressed a simplified version of the problem by either linearizing it or assuming knowledge of the unknown function. Here, we propose a self-supervised learning to directly tackle a nonlinear inverse problem involving an unknown function. In particular, we focus on an inverse problem derived in Photoacoustic Tomograpy (PAT) which is a hybrid medical imaging with high resolution and contrast. PAT can be modelled based on the wave equation. The measured data is the solution of the equation restricted to the surface and the initial pressure of the equation contains the biological information on the object of interest. The speed of sound wave in the equation is unknown. Our goal is to determine the initial pressure and the speed of sound wave simultaneously. Under a simple assumption that the sound speed is a function of the initial pressure, the problem becomes a nonlinear inverse problem involving an unknown function. The experimental results demonstrate that the proposed algorithm performs successfully

On the determination of a function from its conical radon transform with a fixed central axis

Over the past decade, a Radon-type transform called a conical Radon transform, which assigns to a given function its integral over various sets of cones, has arisen in the context of Compton cameras used in single photon emission computed tomography. Here, we study the conical Radon transform for which the central axis of the cones of integration is fixed. We present many of its properties, such as two inversion formulas, a stability estimate, and uniqueness and reconstruction for a local data problem. An existing inversion formula is generalized and a stability estimate is presented for general dimensions. The other properties are completely new results.clos