Block Based Deconvolution Algorithm Using Spline Wavelet Packets
Averbuch, A., Zheludev, V., Neittaanmäki, P., & Koren, J. (2010). Block Based Deconvolution Algorithm Using Spline Wavelet Packets. Journal of Mathematical Imaging and Vision, 38 (3), 197-225. doi:10.1007/s10851-010-0224-4
Published inJournal of Mathematical Imaging and Vision
© Springer Science+Business Media, LLC 2010
This paper presents robust algorithms to deconvolve discrete noised signals and images. The idea behind the algorithms is to solve the convolution equation separately in different frequency bands. This is achieved by using spline wavelet packets. The solutions are derived as linear combinations of the wavelet packets that minimize some parameterized quadratic functionals. Parameters choice, which is performed automatically, determines the trade-off between the solution regularity and the initial data approximation. This technique, which id called Spline Harmonic Analysis, provides a unified computational scheme for the design of orthonormal spline wavelet packets, fast implementation of the algorithm and an explicit representation of the solutions. The presented algorithms provide stable solutions that accurately approximate the original objects.
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