Periodic splines and the fast Fourier transform
Computational Mathematics and Mathematical Physics
Adapted wave form analysis, wavelet-packets and applications
ICIAM 91 Proceedings of the second international conference on Industrial and applied mathematics
Adapted wavelet analysis from theory to software
Adapted wavelet analysis from theory to software
A Technique for the Numerical Solution of Certain Integral Equations of the First Kind
Journal of the ACM (JACM)
A Wavelet Packet Algorithm for Classification and Detectionof Moving Vehicles
Multidimensional Systems and Signal Processing
Wavelet-based acoustic detection of moving vehicles
Multidimensional Systems and Signal Processing
Signal Processing
ForWaRD: Fourier-wavelet regularized deconvolution for ill-conditioned systems
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
An EM algorithm for wavelet-based image restoration
IEEE Transactions on Image Processing
A Fast Thresholded Landweber Algorithm for Wavelet-Regularized Multidimensional Deconvolution
IEEE Transactions on Image Processing
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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.