Method for increasing the spatial resolution of a multispectral image from a panchromatic image

1. A method for increasing a spatial resolution of a multispectral (MS) image using a panchromatic (PAN) image having a spatial resolution greater than the spatial resolution of the MS image, the MS image comprising pixels representative of a MS reflectance of a scene, the PAN image comprising pixels representative of a PAN reflectance of said scene, comprising, for at least a portion of said scene:

obtaining a set of values of parameters of a scene model, said scene model simulating a reflectance of the portion of said scene in bands of wavelengths corresponding to the MS image and to the PAN image to respectively provide simulated MS reflectance and simulated PAN reflectance, according to hypotheses associated with parameters on the portion of said scene, said set of values of parameters being obtained according to a resemblance between the simulated MS reflectance and the MS reflectance for the portion of said scene;

determining a relative variation in the simulated MS reflectance with respect to the simulated PAN reflectance near said set of values of parameters;

estimating a difference between the PAN reflectance and a reflectance of a PAN image with reduced spatial resolution, the difference being referred to as a high spatial resolution PAN modulation; and

determining an MS image with increased spatial resolution, by adding to the MS reflectance a correction corresponding to a product of said high spatial resolution PAN modulation and said relative variation.

2. The method of claim 1 , wherein in estimating said high spatial resolution PAN modulation, the PAN image with reduced spatial resolution has a spatial resolution corresponding to the spatial resolution of the MS image.

3. The method of claim 1 , wherein, for the portion of said scene, obtaining said set of values of parameters comprises an optimized parameterisation of said scene model with respect to the resemblance between the simulated MS reflectance and the MS reflectance.

4. The method of claim 1 , wherein the determination of the MS image with increased spatial resolution comprises:

a spatial oversampling of the MS image so as to obtain an oversampled MS image;

low-pass filtering of the PAN image so as to obtain a PAN image with reduced spatial resolution; and

correction of the oversampled MS image in the portion of said scene according to said relative variation and said high spatial resolution PAN modulation.

5. The method of claim 1 , wherein the determination of said relative variation in the simulated MS reflectance with respect to the simulated PAN reflectance comprises:

determining a gradient of values of parameters of said scene model with respect to the simulated PAN reflectance near a reference simulated PAN reflectance corresponding to said set of values of parameters;

determining a variation in the simulated MS reflectance according to values of parameters near said set of values of parameters; and

composing said variation in the simulated MS reflectance and said gradient of values of parameters, providing said relative variation in the simulated MS reflectance with respect to the simulated PAN reflectance.

6. The method of claim 5 , wherein, for the portion of said scene, the determination of said gradient comprises an optimized parameterisation of said scene model with respect to a resemblance between the simulated PAN reflectance and a vicinity of the reference simulated PAN reflectance.

7. The method of claim 6 , wherein said optimized parameterisation comprises, for the portion of said scene considered, an optimization of a cost function comprising:

a reflectance function representative of a resemblance between the vicinity of the reference simulated PAN reflectance and the simulated PAN reflectance for the values of parameters considered; and

a function of a priori knowledge representative of a resemblance between the values of parameters considered and an a priori knowledge of parameters of the scene model.

8. The method of claim 7 , wherein the a priori knowledge of the parameters of the scene model is a function of said set of values of parameters.

9. The method of claim 1 , wherein the portion of said scene corresponds to a pixel and said relative variation is determined for each pixel.

10. The method of claim 1 , wherein pixels being classified into groups of pixels and the portion of said scene corresponding to one of said groups of pixels, said relative variation is determined for each group of pixels.

11. The method of claim 10 , wherein said relative variation of a group of pixels is determined according to a median value or an average value of the MS reflectances of the group of pixels considered.

12. The method of claim 1 , wherein the scene model comprises a model of reflectance on the ground and an atmospheric model.

13. The method of claim 1 , further comprising a previous conversion of the values of the pixels of the MS image and the values of the PAN image respectively into values of MS reflectance and values of PAN reflectance on the ground or at a top of the atmosphere.

14. A computer program product recorded on a non-transitory media executable by a processor, comprising a set of program code instructions to implement a method for increasing spatial resolution of claim 1 .

15. An image processing system to process image by increasing a spatial resolution of a multispectral (MS) image using a panchromatic (PAN) image having a spatial resolution greater than the spatial resolution of the MS image, the MS image comprising pixels representative of a MS reflectance of a scene, the PAN image comprising pixels representative of a PAN reflectance of said scene, the image processing system comprises at least one processor configured, for at least a portion of said scene, to:

obtain a set of values of parameters of a scene model, said scene model simulating a reflectance of the portion of said scene in bands of wavelengths corresponding to the MS image and to the PAN image to respectively provide simulated MS reflectance and simulated PAN reflectance, according to hypotheses associated with parameters on the portion of said scene, said set of values of parameters being obtained according to a resemblance between the simulated MS reflectance and the MS reflectance for the portion of said scene;

determine a relative variation in the simulated MS reflectance with respect to the simulated PAN reflectance near said set of values of parameters;

estimate a difference between the PAN reflectance and a reflectance of a PAN image with reduced spatial resolution, the difference being referred to a high spatial resolution PAN modulation;

determine an MS image with increased spatial resolution, by adding to the MS reflectance a correction corresponding to a product of said high spatial resolution PAN modulation and said relative variation; and

wherein said at least one processor is configured to implement the method for increasing the spatial resolution of claim 1 .