Sparse Sampling for Inverse Problems with Tensors

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.

arXiv comment13 pages, 7 figures

References in corpus (12)

• Scaling up MIMO: Opportunities and Challenges with Very Large Arrays
• Tensor Decompositions for Signal Processing Applications From Two-way to Multiway Component Analysis
• Graph Convolutional Matrix Completion
• Geometric Matrix Completion with Recurrent Multi-Graph Neural Networks
• Near-Optimal Sensor Placement for Linear Inverse Problems
• Submodular Optimization with Submodular Cover and Submodular Knapsack Constraints
• Matrix Completion on Graphs
• Sensor placement by maximal projection on minimum eigenspace for linear inverse problems
• Sparse Antenna and Pulse Placement for Colocated MIMO Radar
• Sensor scheduling with time, energy and communication constraints
• Frame completions for optimally robust reconstruction
• Near-Optimal Sparse Sensing for Gaussian Detection with Correlated Observations

Cited by in corpus (8)

• Sampling Signals on Graphs: From Theory to Applications
• Fast Graph Sampling Set Selection Using Gershgorin Disc Alignment
• Low-complexity Graph Sampling with Noise and Signal Reconstruction via Neumann Series
• Faster Johnson-Lindenstrauss Transforms via Kronecker Products
• Graph Sampling for Matrix Completion Using Recurrent Gershgorin Disc Shift
• Non-Bayesian Estimation Framework for Signal Recovery on Graphs
• Sherman-Morrison-Woodbury Identity for Tensors
• Fast sensor placement by enlarging principle submatrix for large-scale linear inverse problems