Reconstruction of a Analog Image Using Maximum Likelihood and Interpolation by Atomic Functions According to the Aperture of the Photosensitive Element of the Sensor

The purpose of research is develop a method for efficient processing of an optical image on a digital computer.

Methodology. Two sequentially applied methods are presented for representing a digital image as continuously approaching the original signal values. The quantized light intensity is considered as grouped data. The maximum likelihood method on grouped data allows you to get the best estimate of the original analog value of the light intensity for each photosensitive element of the sensor. The light intensity measured by each photosensitive element is considered as a double integral of the original optical signal over the area defined by the element aperture. Interpolation by atomic functions can use the integrated data to obtain an approximation to the original optical signal.

Results. An urgent problem in vision systems is the loss of information when converting an optical signal into a digital form. Therefore, the problem of efficient digital image processing is relevant. It is necessary to develop a method, to investigate it by conducting statistical modeling, to draw conclusions. In order to evaluate the effectiveness of the developed method, statistical modeling was carried out, after which a comparative analysis of the results obtained for the developed method and the method of moments was carried out. On the whole, the results of the experiment agree with the theoretical calculations.

Conclusion. The use of interpolation, an interpolation polynomial, which is obtained as a result of the proposed method for representing an optical image, allows you to obtain additional information about the optical signal and the optical system used. In turn, this makes it possible to reduce the requirements for expensive optical equipment and reduce material costs or increase the quality characteristics of the resulting optical image without increasing the performance of the imaging equipment.

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