Processing of Multidimensional Signals by Professor Alexandre Smirnov (auth.)

By Professor Alexandre Smirnov (auth.)

In this e-book indications or photographs defined through capabilities whose variety of arguments varies from one to 5 are thought of. This arguments will be time, spatial dimensions, or wavelength in a polychromatic sign. The ebook discusses the fundamentals of mathematical types of signs, their changes in technical pre-processing platforms, and standards of the structures caliber. The types are used for the answer of useful projects of approach research, dimension and optimization, and sign recovery. a number of examples are given.

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K, I: = 1, ... , L, can be transformed into vector [F*m] or vector [F**m], m : = 1, ... , KL, by means of scanning of lines or columns: [F*m] = [FU, ... , FIL, F21, ... , F2L, .... , FKI, ... , FKL], [F**m] = [FU, ... , FKI, F12, ... , FK2, .... , FIL, ... 2) Both vectors can be inversely transformed into the same matrix, or rearranged, for example, in three-dimensional array [Fkij], k: = 1, ... = I, ... , I, j : = 1, ... , J, IJ = L (such rearrangement can be useful, ifthe vector should be recorded in a threedimensional memory).

As a rule, correcting of distortions results in the image quality improvement, but the enhancement techniques not necessary provide minimization of the norm of image difference. These techniques include such image transformations which can result in increasing of distortion of a specific type. One of the methods of enhancement is non-linear transformation of the gray (half-tone) scale of image intensity within fixed range [Fmin, Fmax]. Other method is coloring (reproduction ofblack-and-white image in pseudo-colors).

3 Discrete and Digital Signals 45 Here the value nn detennines the number of binary digits in the rounded value Fklmn(2). The binary number Fklmn(2) coincides with its natural binary code. The decimal number Fklmn(lO) can be translated into the decimal-binary code F(2-1O), for example, in such a way: each decimal digit is represented by fourdigit binary number. Example: The number in the decimal calculus is F(10) = 1·100 + 9·10 + 3·1 = 193 The same number in the binary calculus is F(2) = F(lO) = 1·128 + 1·64 + 0·32 + 0·16 + 0·8 + 0·4 + 0·2 + 1·1 = 11000001 The number F(lO) = 193 can be represented in the decimal-binary code as F(2-1O) = 0001 10010011.

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