A simple error estimation method for linear-regression-based thermal sharpening techniques with the consideration of scale difference

Thermal remote sensing imagery is helpful for land cover classification and related analysis.Unfortunately,the spatial resolution of thermal infrared(TIR)band is generally coarser than that of visual near-infrared band,which limits its more precise applications.Various thermal sharpening(TSP)techniques have been developed for improving the spatial resolution of the imagery of TIR band or land surface temperature(LST).However,there is no research on the theoretical estimation of TSP error till now,which implies that the error in sharpened LST imagery is unknown and the further analysis might be not reliable.In this paper,an error estimation method based on classical linear regression theory for the linear-regression-based TSP techniques was firstly introduced.However,the scale difference between the coarse resolution and fine resolution is not considered in this method.Therefore,we further developed an improved error estimation method with the consideration of the scale difference,which employs a novel term named equivalent random sample size to reflect the scale difference.A simulation study of modified TsHARP(a typical TSP technique)shows that the improved method estimated the TSP error more accurately than classical regression theory.Especially,the phenomena that TSP error increases with the increasing resolution gap between the initial and target resolutions can be successfully predicted by the proposed method.