Title: Inverse problems in image restoration: from basic principles to current deep-learning trends
Authors: Filip Šroubek, Jan Flusser and Barbara Zitová
Various types of degradation such as noise, blur, aliasing and geometric deformation are present in digital images and hamper further processing of images. The degradation results in smoothing high-frequency details, which makes the image analysis problematic. Heavy degradation may corrupt images to such an extent, that neither automatic analysis nor visual interpretation of the content are possible. Degradation often conveys valuable information both about the measuring device and the measured object. For example, motion blur gives us hints about the camera and/or object motion.
Two major approaches to handling degradation exist: restoration and invariants. They are more complementary rather than concurrent; each of them is appropriate for different tasks and employs different mathematical methods and algorithms.
Image restoration is one of the oldest areas of image processing. It appeared as early as in 1960's and 1970's in the work of the pioneers A. Rosenfeld, H. Andrews, B. Hunt, and others. In the last ten years, this area has received new impulses and has undergone a quick development. We have witnessed the appearance of multichannel techniques, blind techniques, and superresolution enhancement resolved by means of variational calculus in very high-dimensional spaces and recently also by deep learning (DL). A common point of all these methods is that they suppress or even remove the degradation from the input image and produce an image of a high visual quality. However, image restoration methods are often ill-posed and computationally expensive.
On the contrary, the invariant approach, proposed originally in 1995, works directly with the degraded data without any preprocessing. Degraded image is described by features, which are invariant with respect to noise, convolution and/or geometric deformation. Image analysis is then performed in the feature space. This approach is suitable for object recognition, template matching, and other tasks where we want to recognize/localize objects rather than to completely restore the image. The mathematics behind it is based on projection operators and moment invariants.
In this tutorial, we focus on both approaches. We start with modelling all types of degradation, analyzing their sources and providing recommendation to avoid them in practical applications. In the image restoration part of the tutorial, we review traditional as well as modern techniques for tackling problems of denosing, superresolution, image rectification and blind deconvolution in various forms. In the invariant part, we show invariants to noise, blur and geometric transformations. The tutorial is enriched with numerous demonstrations and practical examples. The content of the tutorial originates from speakers’ 20-year experience in image restoration, deconvolution, invariants, and related fields.
Outline:
There is no specific required knowledge of the tutorial participants except standard undergraduate courses of image processing and pattern recognition. The tutorial is self-contained and consists of four parts: modeling degradation, image restoration, invariants to degradation, and applications.
1) Modeling degradation
2) Image restoration
3) Invariants
4) Applications
Tutorial slides are available here.