A New Look at Image Fusion Methods from a Bayesian Perspective

Abstract

Component substitution (CS) and multi-resolution analysis (MRA) are the two basic categories in the extended general image fusion (EGIF) framework for fusing panchromatic (Pan) and multispectral (MS) images. Despite of the method diversity, there are some unaddressed questions and contradictory conclusions about fusion. For example, is the spatial enhancement of CS methods better than MRA methods? Is spatial enhancement and spectral preservation competitive? How to achieve spectral consistency defined by Wald et al. in 1997? In their definition any synthetic image should be as identical as possible to the original image once degraded to its original resolution. To answer these questions, this research first finds out that all the CS and MRA methods can be derived from the Bayesian fusion method by adjusting a weight parameter to balance contributions from the spatial injection and spectral preservation models. The spectral preservation model assumes a Gaussian distribution of the desired high-resolution MS images, with the up-sampled low-resolution MS images comprising the mean value. The spatial injection model assumes a linear correlation between Pan and MS images. Thus the spatial enhancement depends on the weight parameter but is irrelevant of which category (i.e., MRA or CS) the method belongs to. This paper then adds a spectral consistency model in the Bayesian fusion framework to guarantee Wald's spectral consistency with OPEN ACCESSRemote Sens. 2015, 7 6829 regard to arbitrary sensor point spread function. Although the spectral preservation in the EGIF methods is competitive to spatial enhancement, the Wald's spectral consistency property is complementary with spatial enhancement. We conducted experiments on satellite images acquired by the QuickBird and WorldView-2 satellites to confirm our analysis, and found that the performance of the traditional EGIF methods improved significantly after adding the spectral consistency model.

Water Bodies’ Mapping from Sentinel-2 Imagery with Modified Normalized Difference Water Index at 10-m Spatial Resolution Produced by Sharpening the SWIR Band

“…B1 60 443 20 B2 10 490 65 B3 10 560 35 B4 10 665 30 B5 20 705 15 B6 20 740 15 B7 20 783 20 B8 10 842 115 B8A 20 865 20 B9 60 945 20 B10 60 1375 30 B11 20 1610 90 B12 20 2190 180 An alternative and advisable way to enhance the performance of water bodies' mapping using the Sentinel-2 imagery is to produce MNDWI at the 10-m resolution by downscaling the SWIR band (Band 11) from 20 m to 10 m. Obviously, the key issue is how to increase the spatial resolution of the SWIR band accurately. In general, spatial interpolation [30,31] and image fusion [32,33] (e.g., pan-sharpening [34]) are the two most popular kinds of methods applied to increase the spatial resolution of remote sensing imagery. The spatial interpolation method is always applied to coarse spatial resolution images directly and does not use any additional datasets.…”

Landsat 15-m Panchromatic-Assisted Downscaling (LPAD) of the 30-m Reflective Wavelength Bands to Sentinel-2 20-m Resolution

“…Downscaling using panchromatic bands has been studied for several decades and the detailed critical surveys can be found in [40][41][42]. Such methods are often grouped into component substitution (CS) and multiresolution analysis (MRA) methods [36,41,43,44].…”

Pan-Sharpening Approaches Based on Unmixing of Multispectral Remote Sensing Imagery

“…F is a total variation in (Palsson et al 2014), ERM3 is applied only on high frequency components of signal and F is a spectral correlation dependent regularization (Aly and Sharma 2015). Moreover, the methods can be formulated using a Bayesian (Fasbender et al 2008, Zhang et al 2012, Zhang and Huang 2015 or sparsity regularization frameworks (Li and Yang 2011, Zhu and Bamler 2013, Vicinanza et al 2015. Further, unmixing models can be included into the cost function definition as, e.g.…”

“…In recent review (Pohl and van Genderen 2015), which is an update of the old review (Pohl and van Genderen 1998), methods are divided into five groups: CS, numerical and statistical image fusion, modulation-based techniques, multi-resolution approaches and hybrid techniques. In (Zhang and Huang 2015) a new look at image fusion methods from a Bayesian perspective is presented, which shows that CS and MRA based methods are special cases of Bayesian based method under Gaussian model assumption.…”