Core Concepts
The author proposes an iterative holography approach for quantitative passive imaging, addressing challenges in correlation data processing and providing convergence through iteration.
Abstract
The content discusses the application of iterative holography in helioseismology for quantitative passive imaging. It introduces the concept of forward and backward propagators to improve image reconstruction without directly computing correlations. The paper highlights challenges in correlation data handling and presents an algorithmic approach to enhance the accuracy of inverse problem solutions.
Key points include:
- Passive imaging aims to reconstruct coefficients in a wave equation from observed correlations.
- Challenges include high dimensionality and poor signal-to-noise ratios in correlation data.
- The proposed method works on primary data implicitly using correlation information for quantitative estimates.
- Helioseismic holography serves as motivation, extending to nonlinear problems for better reconstructions.
- Traditional approaches reduce correlations, losing information, while the new method uses full correlation data iteratively.
The study emphasizes the importance of avoiding direct computation of correlations and implementing iterative regularization methods for accurate image reconstruction.
Stats
Very large data sets of high-resolution solar Doppler images have been recorded over 25 years.
Correlations are reduced to observable quantities like travel times or amplitudes due to storage limitations.
The forward operator mapping parameters to covariance is crucial for inverse problem solutions.