Ripple-free local bases by design

In some applications, a local or "parts based" representation is preferable to global basis functions, such as those used in Fourier and principal component analysis. In applications that require human understanding and editing of the data, it is also desirable that the basis functions be in some sense as "simple" as possible. This means, for example, that the basis functions should not have Gabor-like ripples if such ripples are not a prominent feature of the data to be represented. The paper introduces a direct local basis construction. Specifically, we show that local bases result from maximizing an appropriate redefinition of pairwise orthogonality while maintaining the ability to represent the data. The resulting basis functions are competitive with (and for some applications superior to) those obtained from existing algorithms, and the construction does not require that the basis coefficients be statistically non-Gaussian or independent, as would be the case with an independent component analysis approach.