Covariance Estimation From Compressive Data Partitions Using a Projected Gradient-Based Algorithm.

Area of Science:

• Signal Processing
• Statistical Inference
• Image Analysis

Background:

• Compressive covariance estimation aims to derive signal statistics from limited measurements.
• Existing methods face performance degradation at high compression rates due to ill-posed problems.
• Regularization is often needed to incorporate prior knowledge about the covariance matrix.

Purpose of the Study:

• To propose a novel algorithm for accurate covariance matrix recovery from compressive measurements.
• To address performance limitations in high compression scenarios.
• To enable robust estimation for applications like hyperspectral imaging.

Main Methods:

• A projected gradient method is employed for covariance matrix recovery.
• Compressive measurements are split into subsets and projected onto subspaces.
• Gradient filtering is integrated iteratively to minimize estimation error.
• The algorithm seeks low-rank or Toeplitz approximations of the covariance matrix.

Main Results:

• The algorithm effectively estimates hyperspectral image covariance matrices from compressive samples.
• High compression ratios (8-15%) and noisy conditions are handled effectively.
• The gradient filtering step demonstrably reduces recovery error.
• Analytical error derivation and convergence guarantees are provided.

Conclusions:

• The proposed algorithm offers a robust solution for compressive covariance estimation.
• It shows significant promise for hyperspectral imaging and other related fields.
• The method validates well with both synthetic and real-world data, including an optical implementation.