Errors of neural networks

Approach to the approximation of the transfer characteristic and correlation response of Fourier holography scheme

“…1), the transfer characteristic (1) with power-law spectra of reference images recorded on a hologram in a limited frequency range determined by the dynamic range of the EC HRS can often be approximated by exponential functions, since a) frequency-contrast characteristics of information input paths, both optical and electronic, usually decrease with increasing frequency [1], i.e. information input paths play the role of additional low-frequency filters ( LFF); b) spatial limitation of the size of the processed information by the aperture of the frame window leads to a weakening of the zero and low-frequency components of the spectrum as a result of the convolution of the spectrum with the Fourier transform of the aperture -" low spatial" frequencies; c) EC HRS, represented by the dependence of the diffraction efficiency on exposure, usually have a sigmoidal form in the area of the direct (increasing) dependence [5][6][7], which causes additional bandpass filtering on the hologramattenuation of the transfer characteristic (1) relative to the reference spectrum in the ranges of both low and high spatial frequencies [4,[8][9][10]; d) additional filtering is also due to the form factor of the hologram [11], which is especially relevant for Fourier holograms and their special caseholographic matched filters, which in reality are matched only in a limited range spatial frequencies, determined both by the dynamic range of the EC HRS, and the conditions for recording the hologramby choosing the frequency of equality of the local amplitudes of the spectrum and the plane reference beam [4,[8][9][10]. In this case, the limited dynamic range of the EC HRS, which usually does not exceed two orders of magnitude, even in the case of a low-frequency hologram, as a rule, results, if not in a rejection, then in a very strong attenuation of zero and extremely low spatial frequencies.…”

“…A number of papers are devoted to the search for a convenient and adequate model for approximating the response of the 4 f -scheme; we mention [4,[8][9][10] as applied to the correlation processing of images. In these studies, convenient and practically sufficient for the problem of recognition by the criterion of the magnitude of the signalto-noise ratio [12] simplified approximation models were used.…”

“…A number of papers are devoted to the search for a convenient and adequate model for approximating the response of the 4 f -scheme; we mention [4,[8][9][10] as applied to the correlation processing of images. In these studies, convenient and practically sufficient for the problem of recognition by the criterion of the magnitude of the signalto-noise ratio [12] simplified approximation models were used. For example, in [8] the transfer characteristic (1) is approximated by a triangular -function, and in the analytical description of the correlation response (2) only one parameterits frequency ( -function) of the maximum, which in the first approximation corresponds to the frequency of equality of the local intensities of the spectrum of the reference image and the plane reference beam when recording the hologram.…”

“…In these studies, convenient and practically sufficient for the problem of recognition by the criterion of the magnitude of the signalto-noise ratio [12] simplified approximation models were used. For example, in [8] the transfer characteristic (1) is approximated by a triangular -function, and in the analytical description of the correlation response (2) only one parameterits frequency ( -function) of the maximum, which in the first approximation corresponds to the frequency of equality of the local intensities of the spectrum of the reference image and the plane reference beam when recording the hologram. This approach turned out to be effective in the framework of the problem of recognizing images subjected to affine transformations relative to the reference ones.…”

“…But for a number of real recognition conditions, for example, in the presence of projective distortions of the recognizable image relative to the reference one, a simple and convenient model [8] turned out to be insufficienta complete description of both spectra and holograms was required [13], which requires significant computational resources. The complication of problems solved by the Fourier holography method [14][15][16][17][18][19][20][21][22], including computer [16][17][18][19], and the corresponding complication of algorithms also actualizes the issue of adequate, visual and, which is important for practical real-time applications [16][17][18][19] of computationally inexpensive approximation.…”