This paper studies the removal of salt-and-pepper noise from images using median filter (MF) and simple three-layer autoencoder (AE) within recursive threshold algorithm. The performance of denoising is assessed with two metrics: the standard Structural Similarity Index SSIMImg of restored and clean images and a newly applied metric SSIMMap - the SSIM of entropy maps of these images computed via 2D Sample Entropy in sliding windows. We shown that SSIMMap is more sensitive to blur and local intensity transitions and complements SSIMImg. Experiments on low- and high-resolution grayscales images demonstrate that recursive threshold MF robustly restores images even under strong noise (50-60 %), whereas simple AE is only capable of restoring images with low levels of noise (<30 %). We propose two scalable schemes: (i) 2MF, which uses two MFs with different window sizes and a final thresholding step, effective for highlighting sharp local details at low resolution; and (ii) MFs-AE, which aggregates features from multiple MFs via an AE and is beneficial for restoring the overall scene structure at higher resolution. Owing to its simplicity and computational efficiency, MF remains preferable for deployment on resource-constrained platforms (edge/IoT), whereas AE underperforms without prior denoising. The results also validate the practical value of SSIMMap for objective blur assessment and denoising parameter tuning.

We also provide examples where biased estimators outperform their unbiased counterparts or where unbiased versions are simply not available. Finally, we demonstrate the effectiveness of our framework through experimental results that validate our theoretical findings.

We also provide examples where biased estimators outperform their unbiased counterparts or where unbiased versions are simply not available. Finally, we demonstrate the effectiveness of our framework through experimental results that validate our theoretical findings.

In this paper, we consider non-smooth stochastic convex optimization with two function evaluations per round under infinite noise variance.