Adaptive restoration of unknown samples in discrete-time signals and digital images
Raymond N. J. Veldhuis · Radboud Repository (Radboud University) · 1988
During transmission or storage, signals can be corrupted by errors.These errors can be additive noise, but also pulse-shaped distortions, the effect of which is only noticeable during short time intervals.In the latter case, if the signal is sampled data, groups of samples will be erroneous.They can be consecutive or scattered.Very often there are indications as to which samples are distorted.In those cases one can try to restore the errors.In this thesis some restoration methods for unknown samples with known positions are presented.These restoration methods are linear, that is they try to estimate the unknown samples as linear combinations of known neighbouring samples.They are also adaptive.This means that the weighting coefficients are adapted to the local (statistical) behaviour of the signal.The methods presented in this thesis can be applied as error concealment techniques for digital audio signals, speech signals and digital images.As a basis for the restoration methods described in this thesis, a linear minimum variance estimation method is derived first.This is a general statistical method, which can be used for every signal that is a realization of a stationary stochastic process.However, it is non-adaptive, since the signal spectrum, or equivalently the autocorrelation function, has to be known in advance.It is of theoretical interest, since it provides relations between the signal spectrum and the restoration error.The estimates for the unknown samples are weighted sums of the known samples.It is also possible to obtain them as the solutions of a system of linear equations.After the discussion of the general linear minimum variance estimation method, five special cases are discussed separately.In these cases the signal spectrum can be parametrized and the systems of equations from which the estimates for the unknown samples can be χ Summary solved follow directly from the signal parameters and the known sam ples.The resulting restoration methods are made adaptive by esti mating the signal parameters from the incomplete data.In some cases iterative estimation procedures for parameters and unknown samples are developed, because the parameters and the unknown samples can not be estimated independently.The special cases discussed are sam ple restoration methods for autoregressive processes, speech signals, band-limited signals, multiple sinusoids and digital images.For all these cases results are presented in the form of graphs, tables and photographs.