Image Restoration (unblur image) and Blur Recognition

Blur is a form of bandwidth reduction of an ideal image due to the imperfect image formation process. It can be caused by relative motion between the camera and the original scene, or by an optical system that is out of focus. When aerial photographs are produced for remote sensing purposes, blur is introduced by atmospheric turbulence, aberrations in the optical system, and relative motion between the camera and the ground. Such blurring is not confined to optical images, for example electron micrographs are corrupted by spherical aberrations of the electron lenses, and CT scans suffer from X-ray scatter.

Today there are different techniques available for solving the restoration (unblur) problem including Fourier domain techniques, regularization methods, recursive and iterative filters.

A problem is that without a priori knowledge of at least approximate parameters of the blur (its mathematical model), these filters show poor results. If an incorrect blur model is chosen, the image after filtering will be distorted rather than restored. All of the known filters attempt to build a model of blur (blur recognition): blurring function and its point spread function. More complicated filters also try to make some assumptions about the ideal image and even create some approximation of it.

Today a lot of different algorithms for blur recognition, identification and recognition, identification of its parameters exist, for example the maximum likelihood blur estimation or regularization approach. The common disadvantages of these algorithms are their computing complexity and relatively high level of misidentification, especially for noisy images and for the blur parameters estimation task.

We utilize an original solution of the problem. Blur Recognition on the Neural Network based on Multi-Valued Neurons. As previously mentioned, to restore the blurred image (unblur), it is very important to know the type of blur and parameters of the corresponding distorting operator.

To identify a blur and its parameters we analyze specific distortions of the Fourier spectrum amplitude, which are implied by each particular blur.

To do this, we use a neural network based on multi-valued neurons (MVN). It is used both for the blur recognition (identification) of the distorting operator and for the identification of the corresponding distorting blur operator parameters. The multi-valued neurons have a lot of wonderful properties. The main advantages are the high functionality and simplicity of learning.

This solution ensures more than 90% successful blur recognition even for the noisy images. The corresponding blur parameters can be correctly identified in 85%-90% cases.

After a type of blur and its parameters are recognised the image can be restored using several kinds of methods. A high level of blur and blur parameter identification ensures a good quality of restoration (unblur). All solutions are implemented in the software system. Currently this system supports identification and deblurring of Gaussian, Defocus, 1D Motion and Rectangular blurs.

Examples

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Blurred (blur is natural, not artificial)	Deblurred