Low-dropout current source

I'm looking for an LDO based current source to bias a shunt regulator. There isn't much headroom in the application so I need to make a circuit which works as a high-impedance current generator with even small voltages across it.That means both low reference voltage and low dropout voltage for an LDO.

My goal is to power the current generator + shunt series circuit with down to 4.5VDC and have the shunt output close to 4V. The current will be in the 100-400mA range.

Thanks,

Borge