How can I lowpass filter by only reducing peak data?
There is indeed a 2D version for your attempt #2 - it is similar in theory, but it cannot be decomposed into two 1D operations. Please read about "2D grayscale morphological filtering". It is faster than curve fitting.


http://opencv.willowgarage.com/documentation/image_filtering.html
http://en.wikipedia.org/wiki/Dilation_(morphology)


Median filtering might also be useful if you are trying to remove speckles. A more advanced form of median filtering is "ordinal filtering".

In all cases, requirement #1 can be met trivially by taking the pixelwise minimum between the output and the input. It is an important quality criteria, but it will not limit the choice of algorithms.



Gaussian filtering (and a number of other useful filters) can be decomposed (first from 2D to 1D operations, then via Fourier transform), but there are many other useful image processing techniques that are not decomposable, which make them slow but does not diminish their usefulness.