Least Squares Time-Series Synchronization in Image Acquisition Systems

Area of Science:

• Signal Processing
• Image Reconstruction
• Data Analysis

Background:

• Image acquisition systems use sensor arrays generating time series data.
• Real-world data is often corrupted by noise and time shifts, complicating image estimation.
• Existing methods may lack closed-form solutions for these complex scenarios.

Purpose of the Study:

• To develop and analyze practical image estimation methods for time series data affected by noise and time shifts.
• To introduce a data model suitable for least squares (LS) estimation in this context.
• To evaluate the performance of proposed methods using real and simulated data from infrared photometers.

Main Methods:

• Formulation of the image estimation problem using a least squares (LS) approach.
• Development of practical estimation techniques leveraging separable nonlinear LS and alternating LS.
• Application and validation of methods on data from the Herschel satellite's infrared photometer.

Main Results:

• The standard LS estimate for this problem does not have a closed-form solution.
• Proposed separable nonlinear LS and alternating LS methods offer practical solutions.
• Analysis of accuracy and computational complexity of the developed estimation techniques.

Conclusions:

• Novel LS-based methods effectively address image estimation challenges in noisy, time-shifted sensor data.
• The proposed techniques demonstrate practical applicability, validated on astronomical instrument data.
• Further investigation into accuracy and computational efficiency provides valuable insights for system design.