Mathematics behind a Class of Image Restoration Algorithms

The restoration techniques are usually oriented toward modeling the type of degradation in order to infer the inverse process for recovering the given image. This approach usually involves the option for a criterion to numerically evaluate the quality of the resulted image and consequently the restoration process can be expressed in terms of an optimization problem. Most of the approaches are essentially based on additional hypothesis concerning the statistical properties of images. However, in real life applications, there is no enough information to support a certain particular image model, and consequently model-free developments have to be used instead. In our approaches the problem of image denoising/restoration is viewed as an information transmission/processing system, where the signal representing a certain clean image is transmitted through a noisy channel and only a noise-corrupted version is available. The aim is to recover the available signal as much as possible by using different noise removal techniques that is to build an accurate approximation of the initial image. Unfortunately, a series of image qualities, as for instance clarity, brightness, contrast, are affected by the noise removal techniques and consequently there is a need to partially restore them on the basis of information extracted exclusively from data. Following a brief description of the image restoration framework provided in the introductory part, a PCA-based methodology is presented in the second section of the paper. The basics of a new informational-based development for image restoration purposes and scatter matrix-based methods are given in the next two sections. The final section contains concluding remarks and suggestions for further work.