We extend Schoenberg's B-splines to all fractional degrees α > − 2 . These splines are constructed using linear combinations of the integer shifts of the power functions x+ α (one-sided) or x * α (symmetric); in each case, they are αHölder continuous for α > 0. They satisfy most of the properties of the traditional B-splines; in particular, the Riesz basis condition and the two-scale relation, ...

This paper presents a method for effectively detecting patterns and clusters in high dimensional time-dependent functional data. It is based on waveletbased similarity measures since wavelets are ideal for identifying highly discriminant local time and scale features. We consider the contribution of each scale to the global energy, in the orthogonal wavelet transform of each input function to g...

Ruttimann et al. have proposed to use the wavelet transform for the detection and localization of activation patterns in functional magnetic resonance imaging (fMRI). Their main idea was to apply a statistical test in the wavelet domain to detect the coefficients that are significantly different from zero. Here, we improve the original method in the case of non-stationary Gaussian noise by repl...

In structural health monitoring (SHM) of civil structures, data compression is often needed to reduce the cost of data transfer and storage, because of the large volumes of sensor data generated from the monitoring system. The traditional framework for data compression is to first sample the full signal and, then to compress it. Recently, a new data compression method named compressive sampling...

With respect to space-time tensor-product wavelet bases, parabolic initial boundary value problems are equivalently formulated as bi-infinite matrix problems. Adaptive wavelet methods are shown to yield sequences of approximate solutions which converge at the optimal rate. In case the spatial domain is of product type, the use of spatial tensor product wavelet bases is proved to overcome the so...