Abstract
The wavelet is an effective tool for representing an irregular or discontinuous function (or signal and image), which uses a linear combination of two types of basis functions: a scaling function and a wavelet function. The pair is also called a "wavelet", and some types of wavelet have already been developed. Thresholding is the most common method of noise reduction for wavelets. With this method, coefficients, which represent the observed data, are compared with a "threshold" value, and are replaced with zero if their absolute values are less than the threshold. This replacement removes noise since it disregards small changes in the data. However, estimates obtained by thresholding depend on the type of wavelet. Therefore, we need to adopt a specific wavelet according to the observed data. We consider a numerical criterion, AIC (Akaike Information Criterion), and adopt the wavelet that corresponds to the least AIC. We illustrate our method with figures and simulations.
