I would try to increase the dynamic range of the image by means of histogram techniques.

http://web.cs.wpi.edu/~emmanuel/courses/cs545/S14/slides/lecture02.pdf

If your image is noisy, the first step is to reduce the noise. Standard means are averaging or médian filter though other algorithms apply as well. The image will not be the same as you will loose some details, but this is the only way to reduce noise.

After this step you can proceed with contrast enhancement techniques - whether histogram driven or something else.

What you seem to have missed: noise is just an overlay over your image - with high frequency content. When enhancing contrast, the noise is enhanced too. And the contrast enhancement you are trying acts like a high-pass filter - favoring the higher frequencies. 

As Huma suggested I would also like to see an image to see what type of noise you are dealing with.  Keep in mind that the noise can be either 'part' of the pixel's dn or it can be the 'entire' dn value; that is, can you remove the noise and see the non-noise information at that pixel or is the pixel 'just' noise and the best you can do is identify it and remove it or sub due it's effect.  Salt and pepper type noise is usually all noise and has to be removed and replaced with the surrounding average (window size depends on the amount of smoothing you want).  By identifying and smoothing 'ONLY' the noise pixels it keeps the rest of the image (most of the image) from being smoothed as well.

Pat

Perhaps you can change the formula to reduce the noisy effect.

e.g.

change  C=(L-M)/(L+M)  to implement median filter. Replace L(Largest?) to second or third maximum. Replace M(mean?) to  second or third minimum.

Of course, filtering the original image is another solution.

To my opinion, the first step should be analysis of noise properties in original image(s) - additive or signal-dependent, white or correlated. After this, it will become more clear what filter to apply. Better to apply filtering to original images, not to somehow pre-processed. 

Salt and pepper noise  can be removed with a median filter. Matlab uses medfilt2 function to do it.. 

there is a "mean shift" segmentation filter implemented in OTB which could help you computing the mean of the image while keeping the edge. Anisotropic filtering is also a solution if you need smoother edge transitions.