Spectral characterization is often performed based on the set of measured spectral color signals and corresponding scalar sensor responses. Most methods attempt to reconstruct the sensor sensitivities at a discrete set of specific wavelengths or as a linear combination of basis functions. This paper describes a general method for estimating spectra using a direct regression of the discrete data with a continuous function by means of nonlinear optimization of its parameters. A priori information such as positivity and smoothness constraints and other assumed physical properties of the sensor are incorporated in the estimation process by an appropriate choice of the function. Results are provided for a simple neural network approximator which can be used for modeling of a wide variety of spectral functions. The proposed method is compared with quadratic programming, pseudoinverse, principal eigenvectors, and direct physical measurements.