From Accession to Exemption: A Brief History of the Development of Alaska Property Exemption Laws

This Article examines the historical development of Alaska\u27s debtor protections from their beginnings in the period of initial federal administration to the present. The current Alaska statutes protecting certain property of debtors from their creditors descended from policies first enacted by Congress. Although federal authority began in 1867 with the area\u27s acquisition from Russia, Congress did not provide for governmental administration in Alaska until 1884, which act also provided Alaska its first debtor protection statutes. Extension of the federal Homestead Act to Alaska in 1898 brought the first protections for settlers\u27 homesteads from their creditors. By 1912 and the creation of the territorial government, Congress had set the basic structure of debtor protection in Alaska. Unlike those states which insisted historically on placing certain debtor protections within their constitutions, public policy in Alaska has deemed statutory structures adequate to protect a debtor\u27s interests

High-order regularized regression in Electrical Impedance Tomography

We present a novel approach for the inverse problem in electrical impedance tomography based on regularized quadratic regression. Our contribution introduces a new formulation for the forward model in the form of a nonlinear integral transform, that maps changes in the electrical properties of a domain to their respective variations in boundary data. Using perturbation theory the transform is approximated to yield a high-order misfit unction which is then used to derive a regularized inverse problem. In particular, we consider the nonlinear problem to second-order accuracy, hence our approximation method improves upon the local linearization of the forward mapping. The inverse problem is approached using Newton's iterative algorithm and results from simulated experiments are presented. With a moderate increase in computational complexity, the method yields superior results compared to those of regularized linear regression and can be implemented to address the nonlinear inverse problem

Exploiting Structural Complexity for Robust and Rapid Hyperspectral Imaging

This paper presents several strategies for spectral de-noising of hyperspectral images and hypercube reconstruction from a limited number of tomographic measurements. In particular we show that the non-noisy spectral data, when stacked across the spectral dimension, exhibits low-rank. On the other hand, under the same representation, the spectral noise exhibits a banded structure. Motivated by this we show that the de-noised spectral data and the unknown spectral noise and the respective bands can be simultaneously estimated through the use of a low-rank and simultaneous sparse minimization operation without prior knowledge of the noisy bands. This result is novel for for hyperspectral imaging applications. In addition, we show that imaging for the Computed Tomography Imaging Systems (CTIS) can be improved under limited angle tomography by using low-rank penalization. For both of these cases we exploit the recent results in the theory of low-rank matrix completion using nuclear norm minimization