7.2. Quotient Space Approximation and Second-Generation Wavelets

Since the quotient space approximation is a multi-resolution analysis method, it is closely related to wavelets analysis. Now, we discuss their connection.

7.2.1. Second-Generation Wavelets Analysis

We can see the wavelet transform (WT) as a decomposition of a signal f(x) onto a set of basis functions called wavelets to obtain a series expansion of the signal. So far there are two kinds of WT, the first-generation wavelets (Mallat, 1989; Rioul and Vetterli, 1991; Unser and Blu, 2003) and the second-generation wavelets (Sweldens, 1998). In the first-generation wavelets, the basis functions are obtained from a single mother wavelet by dilations and translations. Then, the signal f(

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