arXiv subjects

Eric L. Miller

Publications and source records attributed to Eric L. Miller.

21 records · Page 2Linked to original sources

arXiv2011

Sensitivity Calculations for the Poisson's Equation via the Adjoint Field Method

Adjoint field methods are both elegant and efficient for calculating sensitivity information required across a wide range of physics-based inverse problems. Here we provide a unified approach to the derivation of such methods for problems whose physics are provided by Poisson's equation. Unlike existing approaches in the literature, we consider in detail and explicitly the role of general boundary conditions in the derivation of the associated adjoint field-based sensitivities. We highlight the relationship between the adjoint field computations required for both gradient decent and Gauss-Newton approaches to image formation. Our derivation is based on standard results from vector calculus coupled with transparent manipulation of the underlying partial different equations thereby making the concepts employed here easily adaptable to other systems of interest.

physics.geo-ph↗

arXiv2011

A Parametric Level Set Approach to Simultaneous Object Identification and Background Reconstruction for Dual Energy Computed Tomography

Dual energy computerized tomography has gained great interest because of its ability to characterize the chemical composition of a material rather than simply providing relative attenuation images as in conventional tomography. The purpose of this paper is to introduce a novel polychromatic dual energy processing algorithm with an emphasis on detection and characterization of piecewise constant objects embedded in an unknown, cluttered background. Physical properties of the objects, specifically the Compton scattering and photoelectric absorption coefficients, are assumed to be known with some level of uncertainty. Our approach is based on a level-set representation of the characteristic function of the object and encompasses a number of regularization techniques for addressing both the prior information we have concerning the physical properties of the object as well as fundamental, physics-based limitations associated with our ability to jointly recover the Compton scattering and photoelectric absorption properties of the scene. In the absence of an object with appropriate physical properties, our approach returns a null characteristic function and thus can be viewed as simultaneously solving the detection and characterization problems. Unlike the vast majority of methods which define the level set function non-parametrically, i.e., as a dense set of pixel values), we define our level set parametrically via radial basis functions (RBF's) and employ a Gauss-Newton type algorithm for cost minimization. Numerical results show that the algorithm successfully detects objects of interest, finds their shape and location, and gives a adequate reconstruction of the background.

cs.CV↗

arXiv2011

Multi-parameter acoustic imaging of uniform objects in inhomogeneous media

The problem studied in this paper is ultrasound image reconstruction from frequency-domain measurements of the scattered field from an object with contrast in attenuation and sound speed. The case where the object has uniform but unknown contrast in these properties relative to the background is considered. Background clutter is taken into account in a physically realistic manner by considering an exact scattering model for randomly located small scatterers that vary in sound speed. The resulting statistical characteristics of the interference is incorporated into the imaging solution, which includes applying a total-variation minimization based approach where the relative effect of perturbation in sound speed to attenuation is included as a parameter. Convex optimization methods provide the basis for the reconstruction algorithm. Numerical data for inversion examples are generated by solving the discretized Lippman-Schwinger equation for the object and speckle-forming scatterers in the background. A statistical model based on the Born approximation is used for reconstruction of the object profile. Results are presented for a two dimensional problem in terms of classification performance and compared to minimum-l2-norm reconstruction. Classification using the proposed method is shown to be robust down to a signal-to-clutter ratio of less than 1 dB.

cs.CV↗