An Adaptive Markov Random Field for Structured Compressive Sensing.

Area of Science:

• Signal Processing
• Machine Learning
• Information Theory

Background:

• Compressive sensing (CS) relies on exploiting intrinsic signal structures for efficient data acquisition.
• Existing CS methods often struggle to balance generality and adaptability in sparsity prior models.
• A need exists for CS priors that can capture diverse structures and adapt to individual signals.

Purpose of the Study:

• To propose a novel adaptive Markov random field (MRF) sparsity prior for compressive sensing (CS).
• To develop a unified variational optimization framework for sparse signal estimation, support, noise, and parameter estimation.
• To enhance the adaptability of sparsity priors to specific sparse signals within the CS framework.

Main Methods:

• Introduced a novel adaptive MRF sparsity prior for CS, offering both generality and adaptability.
• Developed a unified variational optimization problem for sparse signal estimation, incorporating support, noise, and parameter estimation.
• Employed an alternative minimization scheme to effectively solve the proposed optimization problem.

Main Results:

• The proposed adaptive MRF prior successfully captures a broad range of sparsity structures.
• The method demonstrates adaptability by refining prior parameters based on compressed measurements.
• Experiments show improved recovery accuracy, noise tolerance, and runtime efficiency on real-world datasets.

Conclusions:

• The novel adaptive MRF sparsity prior advances CS by providing a flexible and signal-specific modeling approach.
• The unified variational optimization framework offers a robust solution for complex sparse signal recovery problems.
• The demonstrated effectiveness on real-world data validates the practical utility of the proposed CS method.