Abstract
Signal extrapolation is an important task in digital signal processing for extending known signals into unknown areas. The Selective Extrapolation is a very effective algorithm to achieve this. Thereby, the extrapolation is obtained by generating a model of the signal to be extrapolated as weighted superposition of basis functions. Unfortunately, this algorithm is computationally very expensive and, up to now, efficient implementations exist only for basis function sets that emanate from discrete transforms. Within the scope of this contribution, a novel efficient solution for Selective Extrapolation is presented for utilization with arbitrary basis functions. The proposed algorithm mathematically behaves identically to the original Selective Extrapolation, but is several decades faster. Furthermore, it is able to outperform existent fast transform domain algorithms which are limited to basis function sets that belong to the corresponding transform. With that, the novel algorithm allows for an efficient use of arbitrary basis functions, even if they are only numerically defined.
Highlights
The extrapolation of signals is a very important area in digital signal processing, especially in image and video signal processing
Within the scope of this contribution, we presented Fast Selective Extrapolation for image and video signal extrapolation
The novel algorithm behaves mathematically identical to the original algorithm but is able to outspeed the original algorithm by several decades by effectively trading memory consumption versus processing time
Summary
The extrapolation of signals is a very important area in digital signal processing, especially in image and video signal processing. The three examples have in common that the used basis function sets produce significantly better subjective as well as objective results than the Fourier-based extrapolation does They have in common that for such sets no efficient transform domain implementation can exist which would be necessary for a fast implementation. Within the scope of this contribution we want to introduce a novel spatial domain solution for SE which is called Fast Selective Extrapolation (FaSE) This algorithm is able to generate a model of the signal for arbitrary basis functions in the same way as the original SE, even in the case that the basis function set does not possess any structure and the basis functions are only numerically defined or in the case that an overcomplete basis function set is regarded. Simulation results are given for proving the abilities of the novel algorithm
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