ON AN EFFICIENT SPARSE REPRESENTATION OF OBJECTS OF GENERAL SHAPE VIA CONTINUOUS EXTENSION AND WAVELET APPROXIMATION
Naoki Saito, Zhihua Zhang · International Journal of Wavelets Multiresolution and Information Processing · 2010
In this paper, we discuss the continuous extension and wavelet approximation of the detected object on a general domain Ω of ℝ2. We first extend continuously the image to a square T such that it vanishes on the boundary ∂T. On T∖Ω, the extension has a simple and clear representation which is determined by the equation of the boundary ∂Ω. We expand the extension into wavelet series on ℝ2. Since the extension tools are polynomials, by the moment theorem, we know that the sequence of wavelet coefficients obtained by us is sparse. Therefore, we can approximate and analyze the internal information of the object very well even if we only store a few wavelet coefficients.