Exploiting Block-sparsity for Hyperspectral Kronecker Compressive Sensing: a Tensor-based Bayesian Method.

Area of Science:

• Signal Processing
• Data Science
• Machine Learning

Background:

• Bayesian methods are increasingly used for compressive sensing (CS) signal recovery.
• Existing Bayesian CS methods are limited in tensor-based applications like hyperspectral Kronecker compressive sensing (HKCS) due to single-dimension sparsity exploitation.

Purpose of the Study:

• To propose a novel Bayesian model for HKCS that overcomes the limitations of existing methods.
• To exploit multi-dimensional block-sparsity for efficient information redundancy elimination in HKCS.

Main Methods:

• Developed a novel Bayesian model for HKCS incorporating multi-dimensional block-sparsity.
• Employed Laplace prior distributions for sparse coefficients and their coupling.
• Designed a tensor-based Bayesian reconstruction algorithm with decoupled hyperparameters.

Main Results:

• The proposed method achieves more accurate signal reconstruction in HKCS compared to existing Bayesian techniques.
• The algorithm operates at a satisfactory speed, demonstrating practical applicability.
• Validated the effectiveness of exploiting multi-dimensional block-sparsity for enhanced recovery.

Conclusions:

• The novel Bayesian model effectively addresses limitations in HKCS by leveraging multi-dimensional block-sparsity.
• The developed reconstruction algorithm offers improved accuracy and efficiency.
• The method shows potential for broader applications in multi-dimensional CS and block-sparse data recovery.