You're doing it without knowing you're doing it. You're mapping every possible input voltage to an output current.Im not sure I understand how to do this so I think I may need to simplify my requirements further.
One way to process the input signal would be to use a dual op-amp, one in inverting mode and one non-inverting. Both could be set to the gain required to boost the input noise signal from whatever it is, say 1V p-p, up to the rail voltage, say 9V p-p. Bias the noise input and opamp reference voltages to one half the rail voltage. The two outputs would then drive the constant current circuit.