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Fractal interpolation functions are used to construct a compactly supported continuous, orthogonal wavelet basis spanning L 2 (IR). The wavelets share many of the properties normally associated with spline wavelets in particular linear phase.

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We consider an extension of the 1-D concept of analytical wavelet to n-D which is by construction compatible with rotations. This extension, called a monogenic wavelet, yields a decomposition of the wavelet coefficients into amplitude, phase, and phase direction. The monogenic wavelet is based on the hypercomplex monogenic signal which is defined using Riesz transforms and perfectly isotropic wavelets frames. Employing the new concept of Clifford frames, we can show that the monogenic wavelet generates a wavelet frame. Furthermore, this approach yields wavelet frames that are steerable with respect to direction. Applications to descreening and contrast enhancement illustrate the versatility of this approach to image analysis and reconstruction.

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In the context of general iterated function systems (IFSs), we introduce bilinear fractal interpolants as the fixed points of certain Read-Bajraktarević operators. By exhibiting a generalized "taxi-cab" metric, we show that the graph of a bilinear fractal interpolant is the attractor of an underlying contractive bilinear IFS. We present an explicit formula for the box-counting dimension of the graph of a bilinear fractal interpolant in the case of equally spaced data points.