The surface reflectance functions of natural and man made surfaces are invariably smooth. It is desirable to exploit this smoothness in a multispectral imaging system by using as few sensors as possible to capture and reconstruct the data. In this paper we investigate the minimum number of sensors to use, whilst also minimising reconstruction error. We do this by deriving different numbers of optimised sensors, constructed by transforming the characteristic vectors of the data, and simulating reflectance recovery with these sensors in the presence of noise. We find an upper limit to the number of optimised sensors one should use, above which the noise prevents decreases in error. For a set of Munsell reflectances, captured under educated levels of noise, we find that this limit occurs at approximately 9 sensors.