Kronecker compressive sensing

Area of Science:

• Signal Processing
• Applied Mathematics
• Multidimensional Data Analysis

Background:

• Compressive Sensing (CS) traditionally focuses on 1-D signals and 2-D images.
• Acquiring multidimensional signals with CS is challenging due to higher dimensionality.
• Existing methods for multidimensional CS lack efficient sparsifying bases and measurement protocols.

Purpose of the Study:

• To introduce Kronecker product matrices for advanced Compressive Sensing (CS) in multidimensional signal processing.
• To utilize Kronecker products as sparsifying bases that capture inter-dimensional signal structure.
• To apply Kronecker products for representing measurement protocols in distributed CS settings.

Main Methods:

• Formulation of a CS framework using Kronecker product matrices.
• Development of analytical bounds for sparse approximation of multidimensional signals.
• Derivation of performance bounds for CS recovery in multidimensional and distributed scenarios.

Main Results:

• Kronecker product matrices effectively serve as sparsifying bases for multidimensional signals.
• The proposed method enables joint modeling of structure across all signal dimensions.
• Analytical bounds for sparse approximation and CS recovery performance were derived.
• A framework for evaluating novel distributed measurement schemes was established.

Conclusions:

• Kronecker product matrices offer a powerful tool for multidimensional Compressive Sensing.
• This approach enhances the modeling of signal structure and measurement protocols.
• The findings provide theoretical guarantees and practical evaluation methods for advanced CS applications.