Trying to write a signal "unsmoothing" algorithm
What you are trying to do is Contrast Enhancement. Contrast is the ratio of maximum to the minimum.

Lets consider as example that your signal's intensity is ranging from 30 to 40 but you need a range of 0 to 255 with good contrast.


Lets consider your 1D signal as I(x). First find the minimum of the signal and subtract min from the whole curve. In our example 30 is the minimum.So subtract 30 from the whole curve.The signal will be ranging from 0 to 10 now.



  J(x) = I(x) - Min(I(x))



But we want the intensity of the signal from 0 to 255. So find the ratio between the maximum value allowed(255 in our case) to maximum of your signal(our signal max is 10 now) and multiply the whole curve with that factor. Now our signal's intensity will be ranging from 0 to 255.



  K(x) = J(x)*(Max_value_allowed/Max(J(x))



At this point you should have got the spikey curve you need. But if you feel the curve is not spikey enough, contrast can be increased by applying negative slope to intensities in first half of histogram(In our case 0 to 127) and positive slope to intensities in second half  of histogram(128 to 255 in our case) which will make lower intensities much lower and the high intensities much higher.Good luck.Hope this helps you.


Added:Instead of above step3 you could also do,


  L(x) = power(K(x),n)/power(Max(K(x)),n-1)


n should be greater than 1.As n increases the spikiness also increases. In your case choosing around 2 or 3 should be enough I guess.