The Denoising menu includes various routines that allow to both denoise and regularize 1D and 2D data. Except for the well-known wavelet shrinkage, all other methods are based on a manipulation of the Hölder regularity of the input signal. The basic idea is as follows: it is intuitively clear that any signal that has at least some amount of regularity will undergo a decrease of its Hölder exponents when noise is added. Denoting X the original signal, B the noise, and Y the observations, we shall have that, in general, the estimated exponents of Y are "in between" those of X and B (this is not true of the theoretical exponents). A plausible denoising procedure is then to look for a signal Z which would minimize the risk subject to the constraint that its regularity is close the one of X. Usually, of course, the regularity of X is not known. We will thus be content with imposing equalities of the form: regularity of Z = regularity of Y + shift, or: regularity of Z = (regularity of Y)(1 + shift), where "shift" is some positive parameter. The same approach makes senses in a regularization framework: one then seeks a signal Z close to Y and with prescribed regularity. For various reasons, it is much easier to consider regularity in the sense of local Hölder exponents than pointwise ones. To allow for simple algorithms, the method is wavelet-based, i.e. we estimate regularity with the help of wavelet coefficients. These are modified and the updated coefficients are used to reconstruct the smoothed signal (an alternative algorithm based on the use of genetic algorithms will hopefully be implemented in future releases of Fraclab).
In the current implementation of the denoising/regularization algorithms, you may deal with both 1D and 2D signals, in a transparent way: Just input your signal, and Fraclab will recognize its type.