Abstract
Restoration algorithms of signals and images on the basis of their generalized spectra in bases of orthogonal polynomials and functions at absence and presence of random distortions have been examined. It is shown that in absence of hindrances the number of coefficients of the generalized spectrum of a restored signal (image) is determined by the desired approximation error at use of one or another metrics of functional space. If hindrances take place then there is an optimum number of coefficients of the generalized spectrum for signal (image) restoration. Working data of the proposed algorithms for various types of useful signals have been illustrated.
Highlights
One of the methods of increasing throughput of multimedia data transmission, receiving and processing systems is optimization and improvement of coding procedures of a signal source and redundancy reduction
The optimum number of restored modes Kopt corresponding to the minimum restoration error μ(K) of a useful signal sM(x) is determined by the relation z2K ϭ 1 for the considered example Kopt ϭ 4 (Fig. 1c)
It was shown that the number of coefficients of the generalized spectrum of a restored deterministic signal is defined by the desired approximation error at use of one or another metrics of functional space
Summary
One of the methods of increasing throughput of multimedia data transmission, receiving and processing systems is optimization and improvement of coding (decoding) procedures of a signal source and redundancy reduction. Within the scope of this approach various linear orthogonal transforms are applied: a) discrete cosine transform and its updatings; b) wavelet-transform; c) discontinuous piecewise constant function basis expansion (such as Walsh, Haar, S-transformation, etc.), all of them are not flawless [2] It causes need of new basic function search. It is obvious that new algorithms of signal and image compression should be optimized in respect of computational burden reduction, complexity of hardware implementation and in statistical sense taking into account probabilistic nature of hindrances, messages and performance measures. This problem is so severe under image transmission and processing as images have sufficiently great information capacity. In the present work it is shown that, as in [3, 4], the application of orthogonal polynomials or functions connected with them allows to receive effective, practically realizable procedures of signal and image restoration including presence of random distortions
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