"JOURNAL OF RADIO ELECTRONICS" (Zhurnal Radioelektroniki ISSN 1684-1719, N 7, 2016

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Using Fourier spectrum for retouching and restoration missing parts of the image which were deformed by instrumental function

A.V. Kokoshkin, V.A. Korotkov, K.V. Korotkov, E.P. Novichihin

Kotel’nikov Institute of Radio Engineering and Electronics RAS, Fryazino Branch


The paper is received on June 29, 2016

Abstract.  The work proposed and investigated the method of interpolation sequentially calculating the Fourier spectrum which allows you to retouch and restore the missing (shaded) parts of the image. The distortion of the images  of the objects can be described in terms of convolution equations [1.2] with the appropriate instrumental function (IF). Image restoration is complicated by the need to determine the type of IF and its parameters. Different objects presented in the image may be distorted by different IF. Furthermore, objects may overshade each other. A number of studies considered the possibility of the restoration is partially shaded images [3-5]. We used replacement (retouching) shading objects for an image obtained by linear interpolation [3-5]. On the reconstructed image  the artifacts caused by retouching are appeared. If the shape of the shading object is different from  rectangle, the difficulty in applying linear interpolation increases.

A number of studies [6-13] considered the possibility of retouching the missing parts of the image using wavelets, different types of interpolation (bilinear, spline, trigonometric, polynomial). Using these techniques for retouching shading objects to further restoration of the image distorted by IF, is possible. However, the  arbitrary shape of the shading object and the appearance of additional artifacts caused by such retouching, limit the applicability of these methods.

The following conclusions can be drawn from this study:

1. Interpolation Method of Sequential Computation of the Fourier spectrum (IMSCS) allows you to retouch missing (shaded) part of the image.

2. Unlike IMSCS, linear interpolation can be used in any form of a missing parts of the image.

3. Restoring images, which were distorted by IF and retouched with help of  IMSCS makes artifacts less noticed in  comparision with the results of the linear interpolation.

4. Retouching and IMSCS image restoration can give good results even with a large part  of the missing image (see. Figure 6, 9 and 10).

Key words: interpolation, retouching and restoration of images, Fourier spectrum.


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