Estimation of the spectral reflectance of a scene is a critical problem in image processing and computer vision applications. Model-based multispectral imaging, one of the spectral reflectance estimation methods, can effectively reconstruct the full spectrum using a small number of camera shots. However, it is based on iterative optimization and, thus, is computationally too intensive. In this Letter, we modify the iterative optimization problem to a closed-form problem using nonnegative principal component analysis. The proposed method can substantially reduce the computational cost while maintaining the accuracy.