The findings in this paper have significant implications for practical despeckling algorithms, particularly in fields such as synthetic aperture radar (SAR), ultrasound imaging, and digital holography. The theoretical insights regarding the minimax estimation error provide a benchmark for evaluating the performance of existing despeckling techniques. By establishing that the minimax risk for estimating a ( \\beta )-Hölder continuous function in the presence of both speckle and additive noise decays at the same rate as that for additive noise alone, practitioners can better understand the limitations and capabilities of their algorithms.
To leverage these insights, developers of despeckling algorithms can focus on designing methods that achieve the established minimax rates. This could involve optimizing existing algorithms or developing new ones that specifically target the characteristics of speckle noise. For instance, incorporating adaptive filtering techniques that account for the local smoothness of the underlying function could enhance performance. Additionally, the results can guide the selection of parameters in despeckling algorithms, ensuring that they are tuned to achieve optimal performance in terms of the minimax risk.