Edge Preservation in Parameter Estimation Using Total Variation Regularization
College of Arts and Sciences
Department of Mathematics
Dr. Jodi Mead
An inverse problem is the process whereby data are used to identify unknown parameters in a system of interest. These problems arise in many important fields such as geophysics, remote sensing and medical imaging. The most mathematically appealing method for solving these problems is least squares because an analytical expression for the parameters can be found when the problem is formulated with regularization. However, many problems are ill-posed and if data have even a small amount of noise, the analytical expression may have little correlation to the true system parameters. Therefore, regularization methods other than least squares are often employed to better reflect the system of interest. In particular Total Variation (TV) regularization is commonly used to reconstruct parameters with sharp changes. We will compare least squares parameters to those found from a TV estimation algorithm and show results from benchmark problems.
Thibodeau, Jennifer, "Edge Preservation in Parameter Estimation Using Total Variation Regularization" (2019). 2019 Undergraduate Research and Scholarship Conference. 182.