SAR Interferogram Filtering via Coherence Matrix Maximization
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Solution Overview
Problem
The challenge lies in reconstructing a historical series of phase values for SAR image pixels, especially for non-permanent scatterers, where the signal-to-noise ratio varies significantly across interferograms, making it difficult to extract reliable information about optical paths and surface deformations due to temporal and geometric decorrelation.
Innovation Solution
A process involving the calculation of a coherence matrix for each pixel, followed by maximizing a functional that incorporates the moduli and phases of coherence values to derive a vector of filtered phase values, which accounts for all available interferometric data, thereby enhancing the signal-to-noise ratio and reducing noise levels.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If interferograms are obtained from SAR images for monitoring surface deformations, then information about optical path variations can be extracted, but the signal-to-noise ratio varies significantly across interferograms due to temporal and geometric decorrelation, making it difficult to obtain reliable measurements
Solution Approach 1:
The patent combines multiple interferograms into a single historical series of phase values by integrating information from all available SAR images. This merging process allows the system to leverage the total available data rather than relying on individual interferograms with varying quality, thereby improving measurement reliability and reducing the impact of temporal and geometric decorrelation on any single interferogram.
Solution Approach 2:
The patent performs preliminary filtering and integration of phase values from multiple interferograms before final analysis. By pre-processing the data to create a consolidated historical series that accounts for all available observations, the system prepares optimized input data that enhances the signal-to-noise ratio and measurement reliability before the actual deformation analysis is performed.
2Loss of information
If phase values are extracted from individual interferograms, then optical path information can be obtained, but noise levels remain high due to decorrelation effects, reducing the discernibility of interferometric fringes
Solution Approach 1:
The patent merges phase information from multiple interferograms to create a consolidated historical series. This combination allows the preservation of optical path information while simultaneously reducing noise through the integration of multiple observations, as the useful signal accumulates coherently while random noise tends to average out.
Solution Approach 2:
The patent converts the potentially harmful effect of using multiple interferograms with varying quality into a benefit by systematically integrating them. Instead of discarding lower-quality interferograms, the method uses all available data, transforming the diversity and potential noise into a strengthened signal through proper weighting and combination of the historical series.
3Quantity of substance
If multiple SAR images are processed to create interferograms, then more data is available for analysis, but the complexity of processing increases due to the need to handle varying coherence and decorrelation
Solution Approach 1:
The patent segments the processing task by calculating coherence matrices for individual pixel pairs from multiple SAR images, then processing each pixel's historical series independently. This segmentation allows the complex multi-image processing to be broken down into manageable per-pixel operations, reducing overall processing complexity while still utilizing all available data.
Solution Approach 2:
The patent changes the processing approach by transitioning from individual interferogram analysis to historical series analysis. By modifying the fundamental parameter of how data is organized and processed - from pairwise interferograms to multi-temporal phase series - the system efficiently handles the increased data volume without proportionally increasing processing complexity.
Data Source
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AI summary
A process for filtering interferograms obtained from SAR images, acquired on the same area by synthetic aperture radars, comprising the following steps: a) acquiring a series of N radar images (Al.. AN) by means of a SAR sensor on a same area with acquisition geometries such as to allow re- sampling of the data on a common grid; b) after re-sampling on a common grid, selecting a pixel from the common grid; c) calculating the coherence matrix of the selected pixel, that is estimating the complex coherence values for each possible pair of available images; d) maximizing, with respect of the source vector ?, here an unknown element, the functional: (formula) being R the operator which extracts the real part of a complex number, ? nm the modulus of the element (n,m) of the coherence matrix, k a positive real number, f nm the phase of the element (n,m) of the coherence matrix, ?n and ?m the elements n and m of the unknown vector ?. Given that only phase differences appear in the functional T, the values of the unknown factor are estimated less an additive constant, which can be fixed by setting for example ?1=0, and the phase values ?n thus obtained constitute the vector of the filtered phase values.