The minimum number of scanning windows required for effective maximum likelihood estimation of image texture parameters and additive noise variance

In this paper, we dealt with the problem of noise variance estimation from additive mixture of the noise and an underlying image texture. Assuming fBm-model for image texture, the number M
_e
[H, SNR) of SWs has been obtained such that statistical efficiency e of the previously designed ML noise variance estimator is close to a predefined level e = 0.9 . The value Me defines a boundary between asymptotic and non-asymptotic modes of the ML estimator with respect to image fragment size (number of SWs available). For fixed SNR , M
_e
takes minimum values for smooth textures (H close to 0.8) and increases fast as H approaches 0. As a function of SNR , M
_e
has minimum at approximately SNR = 1.5 and increases fast as SNR deviates from this value. These results are useful for establishing the area of applicability of noise variance estimators and to assure the quality of estimates obtained from an image texture of a given size, roughness and SNR.