2.2. Wald’s Protocol

Before proceeding, the images resulting from the pansharpening methods must be evaluated in terms of quantitative quality indices, as a visual inspection of the result is insufficient to determine their suitability.

The research community accepts Wald’s protocol [38,39] as establishing the essential properties of the products of image fusion algorithms where possible. These are as follows, as expressed by Aiazzi et al. [25]

Consistency: any fused image Â, once degraded to its original resolution, should be as identical as possible to the original image A

Synthesis: any image  fused by means of a high-resolution (HR) image should be as identical as possible to the ideal image AI that the corresponding sensor, if it exists, would observe at the resolution of the HR image.

The multispectral vector of images  fused by means of a high-resolution (HR) image should be as identical as possible to the multispectral vector of the ideal images AI that the corresponding sensor, if it exists, would observe at the spatial resolution of the HR image.

As the original image AI is available in our research, we can comply with Theorems 2 and 3 of Wald’s protocol.

The quality of the final products of fusion imaging must then be assured. Visual checking may be necessary, but an objective numerical comparison is compulsory. Various image fusion quality indices have been proposed to assess the quality of the fusion image procedures.