Modeling nonstationary lens blur using eigen blur kernels for restoration

Images acquired through a lens show nonstationary blur due to defocus and optical aberrations. This paper presents a method for accurately modeling nonstationary lens blur using eigen blur kernels obtained from samples of blur kernels through principal component analysis. Pixelwise variant nonstationary lens blur is expressed as a linear combination of stationary blur by eigen blur kernels. Operations that represent nonstationary blur can be implemented efficiently using the discrete Fourier transform. The proposed method provides a more accurate and efficient approach to modeling nonstationary blur compared with a widely used method called the efficient filter flow, which assumes stationarity within image regions. The proposed eigen blur kernel-based modeling is applied to total variation restoration of nonstationary lens blur. Accurate and efficient modeling of blur leads to improved restoration performance. The proposed method can be applied to model various nonstationary degradations of image acquisition processes, where degradation information is available only at some sparse pixel locations. (C) 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreemen

Two-dimensional signal processing with application to image restoration

A recursive technique for modeling and estimating a two-dimensional signal contaminated by noise is presented. A two-dimensional signal is assumed to be an undistorted picture, where the noise introduces the distortion. Both the signal and the noise are assumed to be wide-sense stationary processes with known statistics. Thus, to estimate the two-dimensional signal is to enhance the picture. The picture representing the two-dimensional signal is converted to one dimension by scanning the image horizontally one line at a time. The scanner output becomes a nonstationary random process due to the periodic nature of the scanner operation. Procedures to obtain a dynamical model corresponding to the autocorrelation function of the scanner output are derived. Utilizing the model, a discrete Kalman estimator is designed to enhance the image

A comparison of SAR image speckle filters

High quality images of Earth produced by synthetic aperture radar (SAR) systems have become increasingly available, however, SAR images are difficult to interpret. Speckle reduction remains one of the major issues in SAR imaging process, although speckle has been extensively studied for decades. Many reconstruction filters have been proposed and they can be classified into two categories: multilook and/or minimum mean-square error (MMSE) despeckling using the speckle model; and maximum a posteriori (MAP) or maximum likihood (ML) despeckling using the product model. The most well known Lee, Kuan, and Frost filters belong to first category. These filters are based on conventional techniques that were originally derived for stationary signals, such as MMSE. In the second category, filters are based on the product model, such as the MAP Gaussian filter and the Gamma filter, and require knowledge of the a priori probability density function. These filters force speckle to have nonstationary Gaussian or gamma distributed intensity mean. The speckle filtering is mainly Bayesian model fitting that optimizes the MAP criteria. Scene reconstruction is performed using an inversion of the ascending chain. An objective measure is required to compare the technical merits of these filters, and Shi et al. presented a comparison 15 years ago. In this paper, a brief introduction of speckle, product, and filter models is summarized. A review of some most widely used SAR image speckle filters is given. And stationary speckle filters, like Lee, Kuan, and Frost filters, and nonstationary speckle filters like Gamma MAP filter are studied. Despeckling results on stationary and nonstationary SAR image of these speckle filters are presented. © 2009 Copyright SPIE - The International Society for Optical Engineering.published_or_final_versio