2,765 research outputs found
Sparse Sampling for Inverse Problems with Tensors
We consider the problem of designing sparse sampling strategies for
multidomain signals, which can be represented using tensors that admit a known
multilinear decomposition. We leverage the multidomain structure of tensor
signals and propose to acquire samples using a Kronecker-structured sensing
function, thereby circumventing the curse of dimensionality. For designing such
sensing functions, we develop low-complexity greedy algorithms based on
submodular optimization methods to compute near-optimal sampling sets. We
present several numerical examples, ranging from multi-antenna communications
to graph signal processing, to validate the developed theory.Comment: 13 pages, 7 figure
A Probabilistic Interpretation of Sampling Theory of Graph Signals
We give a probabilistic interpretation of sampling theory of graph signals.
To do this, we first define a generative model for the data using a pairwise
Gaussian random field (GRF) which depends on the graph. We show that, under
certain conditions, reconstructing a graph signal from a subset of its samples
by least squares is equivalent to performing MAP inference on an approximation
of this GRF which has a low rank covariance matrix. We then show that a
sampling set of given size with the largest associated cut-off frequency, which
is optimal from a sampling theoretic point of view, minimizes the worst case
predictive covariance of the MAP estimate on the GRF. This interpretation also
gives an intuitive explanation for the superior performance of the sampling
theoretic approach to active semi-supervised classification.Comment: 5 pages, 2 figures, To appear in International Conference on
Acoustics, Speech, and Signal Processing (ICASSP) 201
- …