I need to perform deconvolution to obtain information about a vector b.
Let c=a*b the convolution operation (the inverse of our operation), I need to calculate b=c/a.
The vectors are afflicted by noise and so the result of deconvolution will suffer it.
I know some properties of the function b (it's monotone and b(0)=1), is there a way to make an approximate deconvolution ensuring that the resulting function b would have these properties?