Wavelet Image Processing

Linear system theory plays an important role in wavelet theory. A signal or function can often be better described, analyzed, or compressed if it is transformed into another domain using a linear transform such as the Fourier transform or a wavelet transform. Linear transformations of discrete signals can be expressed in linear algebraic forms, where the signals are considered as vectors and the transformations as matrix–vector multiplications. The wavelet series expansion is analogous to the Fourier series, in that both methods represent continuous-time signals with a series of discrete coefficients. A set of basis functions is formed by scaling and translating the basic wavelet, but the scaling and translation take only discrete values.