A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
| Hi-index | 0.00 |
The discrete wavelet transform decomposes a discrete time signal into an approximation sequence and a detail sequence at each level of resolution. The approximation at any resolution is the projection of the signal onto the orthogonal space spanned by the translates of an analysing scaling function. The choice of scaling function can have a large impact on the error in the approximation at a given resolution. However, finding the optimum scaling function is challenging. The optimization problem has constraints, the cost function is not an explicit function of the scaling function coefficients, and many local minima may exist. A systematic method for generating scaling functions is developed. This method insures that a scaling function will be found that is close to the optimum. The resulting scaling functions can be used by themselves or serve as starting point for further optimization.