29 research outputs found
Spectrum-Adapted Tight Graph Wavelet and Vertex-Frequency Frames
We consider the problem of designing spectral graph filters for the
construction of dictionaries of atoms that can be used to efficiently represent
signals residing on weighted graphs. While the filters used in previous
spectral graph wavelet constructions are only adapted to the length of the
spectrum, the filters proposed in this paper are adapted to the distribution of
graph Laplacian eigenvalues, and therefore lead to atoms with better
discriminatory power. Our approach is to first characterize a family of systems
of uniformly translated kernels in the graph spectral domain that give rise to
tight frames of atoms generated via generalized translation on the graph. We
then warp the uniform translates with a function that approximates the
cumulative spectral density function of the graph Laplacian eigenvalues. We use
this approach to construct computationally efficient, spectrum-adapted, tight
vertex-frequency and graph wavelet frames. We give numerous examples of the
resulting spectrum-adapted graph filters, and also present an illustrative
example of vertex-frequency analysis using the proposed construction
Inpainting of long audio segments with similarity graphs
We present a novel method for the compensation of long duration data loss in
audio signals, in particular music. The concealment of such signal defects is
based on a graph that encodes signal structure in terms of time-persistent
spectral similarity. A suitable candidate segment for the substitution of the
lost content is proposed by an intuitive optimization scheme and smoothly
inserted into the gap, i.e. the lost or distorted signal region. Extensive
listening tests show that the proposed algorithm provides highly promising
results when applied to a variety of real-world music signals