Abstract
This paper proposes a statistical distortion measure for evaluating lossy compression methods of satellite images. The introduction of an adequate distortion measure is essential not only for users of satellite images but also for designers of satellite image compression methods. If the distortion measure were given, the users could know if the compressed images are reliable for their quantitative analysis and the designer could optimize their methods. The proposed distortion measure is a local Mahalanobis distance that is based on the covariance matrix of noise components in the images. The noise components are estimated from the second order spatial derivatives within a local window around the concerned pixel. Under the assumption of smooth signal components, it is shown theoretically that the local Mahalanobis distances of noise components follow the x2 distribution. In addition to this property, the local Mahalanobis distance is invariant to linear transformation of the values of multispectral bands. Then, the satellite image compression using pyramid linking segmentation is proposed where the local Mahalanobis distance is used as a similarity measure for linking. The proposed lossy compression method shows a good performance with regard to the proposed distortion measure compared with the standard lossy image compression method (JPEG) in the case of satellite images with a large number of bands such as LANDSAT TM image.
