Optimal Estimation of Deterioration From Diagnostic Image Sequence

Abstract

Abstract-This paper considers estimation of pixel-wise monotonic increasing (or decreasing) data from a time series of noisy blurred images. The motivation comes from estimation of mechanical structure damage that accumulates irreversibly over time. We formulate a Maximum A posteriory Probablity (MAP) estimation problem and find a solution by direct numerical optimization of a log-likelihood index. Spatial continuity of the damage is modeled using a Markov Random Field (MRF). The MRF prior includes the temporal monotonicity constraints. We tune the MRF prior, using a spatial frequency domain loopshaping technique to achieve a tradeoff between noise rejection and signal restoration properties of the estimate.The MAP optimization is a large-scale Quadratic Programming (QP) problem that could have more than a million of decision variables and constraints. We describe and implement an efficient interior-point method for solving such optimization problem. The method uses a preconditioned conjugate gradient method to compute the search step. The developed QP solver relies on the special structure of the problem and can solve the problems of this size in a few tens of minutes, on a PC.The application example in the paper describes structural damage images obtained using a Structural Health Monitoring (SHM) system. The damage signal is distorted by environmental temperature that varies for each acquired image in the series. The solution for the experimental data is demonstrated to provide an excellent estimate of the damage accumulation trend while rejecting the spatial and temporal noise.Index Terms-Optimal estimation, spatio-temporal filtering, regularization, interior-point method, isotonic regression, Markov Random Field.

An Interior-Point Method for Large-Scale -Regularized Least Squares

“…As an example, the problem of finding monotone trends in a Gaussian setting can be cast as a problem of this form [49], [21]. As another example, the problem of estimating accumulating damage trend from a series of structural health monitoring (SHM) images can be formulated as a problem of the form in which the variables are 3-D (a time series of images) [22].…”

ADMM for Penalized Quantile Regression in Big Data

“…In many fields, assumptions of parameters or prior knowledge in applications can be formulated in terms of linear equalities or inequalities on β. These problems can be found in estimating mechanical structure damage from images [10], portfolio selection [6] and shape-restricted nonparametric regression [22]. In this paper, we consider linearly constrained quantile regression with a general lasso penalty (LCG-QR) as follows.…”

Geometry and Degrees of Freedom of Linearly Constrained Generalized Lasso

“…We refer to the estimate of as an lcg‐lasso solution and the corresponding fit as an lcg‐lasso fit. Examples of linearly constrained generalized lasso include estimating mechanical structure damage from images (Gorinevsky et al, ), portfolio selection (Fan et al, ) and shape‐restricted non‐parametric regression (Wang & Ghosh, ). In these applications, prior knowledge is formulated in terms of linear equality or linear inequality constraints on the parameters.…”