Your question contains the answer: salt and pepper corruption is about texture. It's about isolated dots. If it were 1D, what would you do? This amounts to detecting a comb shape added to a smooth shape. Then let me phrase it again very pictorially: the salt and pepper is about "a brush" on a fairly smooth head. What do you do? You use a maximum likelihood method (or a ML algo, who cares?) and find the most likely "brush". If the brush is "brushy" enough, you have a salt and pepper case (you define the thresholds) otherwise, you neglect the brush or salt and pepper found, because it's not significant to be trusted.
The first generation of digital mobile phones was using this in 1D, more or less for the voice codec (the actual algorithm was the Kroon Deprettere algorithm called Regular Pulse Excitation -Linear Prediction, or in short RPE-LTP, now the comb we mentioned above is adujsted as the RPE part of the RPE-LTP algorithm; it works well, very well)
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