Conditioning Analysis of Missing Data Estimation for Large Sensor Array

Abstract

Optimal missing data estimation algorithms including deblurring and denoising are designed to restore images captured from large CCD sensor arrays using a butting technique, where 1 to 2 columns of data are missed at the butting edge. We developed a consistency method with separable deblurring to estimate the missing data. This method converts an ill-posed restoration problem into a well-posed one by making few assumptions based on regularization theory. Under the condition that no noise is inserted, and the separable blur kernel is exactly known, the consistency method can deblur the original image and at the same time estimate the missing columns(s) exactly. However, this algorithm becomes unstable when large noise is inserted or inaccurate estimation of the blur kernel is made. Conditioning analysis is used to quantify the amount of ill condition of the blur kernel when the assumptions are relaxed to different levels, which provides a solid measurement on how stable the system will remain knowing the signal-to-noise ratio and the inaccuracy of the blur kernel estimation. Experimental results from different approaches are compared.