以遞迴濾波器進行影像還原

Abstract

傳統的線性影像還原技巧要求還原時，必須先知道部份點模糊函數 (point-spread function, PSF) 的資訊。然而，在實際應用上，點模糊函數為未知函數，透過退化影像的觀察，整個問題包含同時辨析出原始影像與點模糊函數。這樣的影像還原過程歸類為隱蔽性影像反迴旋積分法 (blind image deconvolution)。 本論文介紹一種新的隱蔽性影像反迴旋積分技巧，針對在不知道關於原始影像或點模糊函數的明確資訊下，對於線性退化影像的還原。這個方法稱為非負最小矩形限制遞迴反濾波演算法 (the non-negativity and support constraints recursive inverse filtering, NAS-RIF)。這個技巧的適用條件為，在影像中，包含所觀察物體的最小框架為固定矩形，且為均勻背景。除了原始影像灰階值為非負外，需要的資訊還包括原始影像中，包含所觀察物體的最小矩形之範圍。而影像還原取決於，對模糊影像進行遞迴濾波，使凸成本函數 (convex cost function) 降低。在實現演算法時，我們著重在兩方面的分析：第一方面為模糊的過程或模糊函數的特徵，第二方面為初始參數的設定。當反退化函數的維度很大時，此演算法利用小維度濾波器所得的影像還原效果有限。此外，利用適當的初始參數進行影像還原，比起原演算法所提的初始參數設定，其遞迴次數將可以有效的減少。

Classical linear image restoration techniques assume that the linear shift invariant blur, also known as the point-spread function (PSF), is partially known prior to restoration. In many practical situations, however, the PSF is unknown and the problem of image restoration involves simultaneously identifying both the true image and PSF from the degraded observation. Such a process is referred to as the blind deconvolution. This thesis introduces a novel blind deconvolution technique for the restoration of linearly degraded images without explicit knowledge of either the original image or the point spread function. The method is called the non-negativity and support constraints recursive inverse filtering (NAS-RIF) algorithm. The technique applies to situations in which the scene consists of a finite support object against a uniform background. The information required includes the non-negativity of the true image and the supporting region of the original object. The procedure involves recursive filtering of the blurred image to minimize a convex cost function. We focus on the study of two factors in implementing the technique: one is the blurring process or characteristics of the point-spread function, and the other is the initialization of the filter parameters. When the size of the inverse of the degraded function is large, the performance of the introduced algorithm by the small sized FIR filter will be limited. Besides, with proper initial condition, the recursive cycles will be reduced. English Abstract Acknowledgement Contents List of Figures List of Tables Chapter 1 INTRODUCTION 1.1 Background 1.2 Motivation 1.3 Outline of this Thesis Chapter 2 BLINE IMAGE DECONVOLUTION 2.1 Preface 2.2 Brief Introduction of Existing Approaches 2.3 Problem Formulation Chapter 3 THE NONNEGATIVITY AND SUPPORT CONSTRAINTS RECURSIVE INVERSE FILTERING (NAS-RIF) 3.1 Nonparametric Deterministic Image Restoration 3.2 The NAS-RIF Algorithm Chapter 4 EXPERIMENT AND RESULTS 4.1 Characteristics of Typical Images and Point-Spread Functions for Simulations 4.2 Image Restoration Results 4.3 Analysis and Discussion Chapter 5 CONCLUSIONS Reference Appendix A Appendix B