TABLE OF CONTENTS To recover a sharp image from its blurry observation is the problem known as image deblurring. Like denoising, it frequently arises in imaging sciences and technologies, including optical, medical, and astronomical applications, and is often a crucial step towards successful detection of important patterns such as abnormal tissues or the surface details of some distant planets.
Mathematically, image deblurring is intimately connected to backward diffusion processes (e.g., inverting the heat equation), which are notoriously unstable. As inverse problem solvers, deblurring models therefore crucially depend upon proper regularizers or conditioners that help secure stability, often at the necessary cost of losing certain high frequency details of the ideal images. Such regularization techniques can result in the existence or uniqueness of deblurred images.
In this chapter, we present the physics foundations of some common types of blurs, classify deblurring problems, and develop both mathematical analysis on several deblurring models and their associated computational methods.
There are three major categories of blurs according to their physical background: optical, mechanical, and medium-induced.
Optical blur is also often called out-of-focus blur and is due to the deviation of an imaging plane from the focus of an optical lens. For instance, for a nearsighted eye, the retina falls slightly behind the focus of the pupil lens. On the other hand, when capturing an outdoor scene with many objects in notably different ranges, the lens of a digital camera can only focus...
