Sparse Sampling for Inverse Problems with Tensors

TL;DR

This paper introduces a tensor-based approach for designing sparse sampling strategies in multidomain signals, utilizing Kronecker-structured sensing functions and greedy algorithms to efficiently handle high-dimensional data.

Contribution

It proposes a novel tensor-based sampling method with low-complexity greedy algorithms for near-optimal sparse sampling in multidomain signals.

Findings

Effective sampling strategies for tensor signals demonstrated in numerical examples.

Reduced computational complexity compared to traditional methods.

Validated approach across applications like multi-antenna communications and graph signal processing.

Abstract

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.