Process for filtering interferograms obtained from SAR images acquired on the same area

• US 8,711,029 B2
• Filed: 07/02/2010
• Issued: 04/29/2014
• Est. Priority Date: 07/08/2009
• Status: Active Grant

• Current Assignee: Politecnico di Milano, Tele-Rilevamento Europa- TRE SRL
• Original Assignee: Politecnico di Milano, Tele-Rilevamento Europa- TRE SRL
• Inventors: Ferretti, Alessandro, Fumagalli, Alfio, De Zan, Francesco, Rucci, Alessio, Novali, Fabrizio, Tebaldini, Stefano
• Primary Examiner(s): Sotomayor, John B
• Application Number:
  US13/259,295
• Publication Number:
  US 20120019410A1
• Time in Patent Office: 1,397 Days
• Field of Search: 342/25.R, 342 25 A- 25 F
• US Class Current: 342/25.C
• CPC Class Codes: G01S 13/9023 combined with interferometric techniques
• CPC Class Codes: G01S 13/904 SAR modes
• CPC Class Codes: G06T 2207/10044 Radar image

Abstract

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 θ, here an unknown element, the functional: (formula) being R the operator which extracts the real part of a complex number, γ_nm the modulus of the element (n,m) of the coherence matrix, k a positive real number, φ_nm the phase of the element (n,m) of the coherence matrix, θn and θm the elements n and m of the unknown vector θ. 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 θ₁=0, and the phase values θ_n thus obtained constitute the vector of the filtered phase values.

$\begin{array}{cc}T=\left\{\sum _{n=1}^N\sum _{m=1}^N{\gamma }_{nm}^k·e^{{\mathrm{i\varphi }}_{nm}}{e}^{-i\left({\theta }_n-{\theta }_m\right)}\right\}& \left(I\right)\end{array}$

Claims

1. A process for filtering interferograms obtained from SAR images, acquired on the same area by synthetic aperture radars, the process 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 common grid;

b) after re-sampling on common grid, selecting a pixel from the common grid;

c) calculating, using a microprocessor, 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 θ

, here unknown element, the functional;

2. The process according to claim 1, wherein the additive constant is fixed by setting θ

₁=0.

3. The process according to claim 1, wherein every element of the coherence matrix is evaluated by means of the equation:

4. The process according to claim 1, wherein the N elements of the source vector θ

are linked by a polynomial relation, referable to the following form;

θ

_n=g(t_n, B_n)

being t_n the acquisition time of the n-th image with respect to the first acquisition, B_n the normal baseline of the n-th image still with respect to the first acquisition, the functional being maximized with respect to the coefficients of the polynomial g.

5. The process according to claim 1, wherein the N elements of the source vector θ

are linked by a linear relation, referable to the following form;

θ

_n=C_v·

v·

t_n+C_h·

h·

B_n

being C_v and C_h known parameters depending on the acquisition geometry and on the utilized sensor, t_n the acquisition time of the n-th image with respect to the first acquisition, B_n the normal baseline of the n-th image still with respect to the first acquisition, in the optimization process, with also t_n and B_n known, being estimated only the values v and h, linked respectively to the average displacement speed and to the elevation of the object which occupies the selected pixel.

6. The process according to claim 1, wherein the N images acquired by means of a SAR are acquired at different times.

7. The process according to claim 1, wherein the N images acquired by means of a SAR are acquired with different sight angles.

8. A computer comprising a memory and a microprocessor suitable to exchange data with the memory, the memory including an applicative software which is installed in the memory and is running, and the software being suitable to implement a process for filtering interferograms obtained from SAR images, acquired on the same area by synthetic aperture radars, the process including 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 common grid;

b) after re-sampling on 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 θ

, here unknown element, the functional;

9. A computer comprising a memory and a microprocessor suitable to exchange data with the memory, the memory including an applicative software which is installed in the memory and is running, and the software being suitable to implement a process for filtering interferograms obtained from SAR images, acquired on the same area by synthetic aperture radars, the process including 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 common grid;

b) after re-sampling on 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 θ

, here unknown element, the functional;

10. A computer comprising a memory and a microprocessor suitable to exchange data with the memory, the memory including an applicative software which is installed in the memory and is running, and the software being suitable to implement a process for filtering interferograms obtained from SAR images, acquired on the same area by synthetic aperture radars, the process including 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 common grid;

b) after re-sampling on 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 θ

, here unknown element, the functional;

11. A computer comprising a memory and a microprocessor suitable to exchange data with the memory, the memory including an applicative software which is installed in the memory and is running, and the software being suitable to implement a process for filtering interferograms obtained from SAR images, acquired on the same area by synthetic aperture radars, the process including 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 common grid;

b) after re-sampling on 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 θ

, here unknown element, the functional;

12. A computer comprising a memory and a microprocessor suitable to exchange data with the memory, the memory including an applicative software which is installed in the memory and is running, and the software being suitable to implement a process for filtering interferograms obtained from SAR images, acquired on the same area by synthetic aperture radars, the process including 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 common grid;

b) after re-sampling on 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 θ

, here unknown element, the functional;

13. A computer comprising a memory and a microprocessor suitable to exchange data with the memory, the memory including an applicative software which is installed in the memory and is running, and the software being suitable to implement a process for filtering interferograms obtained from SAR images, acquired on the same area by synthetic aperture radars, the process including 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 common grid;

b) after re-sampling on 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 θ

, here unknown element, the functional;

14. A computer comprising a memory and a microprocessor suitable to exchange data with the memory, the memory including an applicative software which is installed in the memory and is running, and the software being suitable to implement a process for filtering interferograms obtained from SAR images, acquired on the same area by synthetic aperture radars, the process including 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 common grid;

b) after re-sampling on 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 θ

, here unknown element, the functional;