In recent years, miniature spectrometers have been found to be useful in many applications to resolve spectrum signatures of materials. In this paper, algorithms are proposed to realize a miniature spectrometer using a low-cost filter-array spectrum sensor. Conventionally, the filter-array spectrum sensor can be modeled as an overdetermined problem, and the spectrum can be reconstructed by solving a set of linear equations. In this paper, we instead model the spectrum reconstruction process as an underdetermined problem, and bring up the concept of template-selection by sparse representation. l1 − norm minimization is introduced to achieve a high reconstruction resolution. Both simulation and experimental results show that a superior quality of spectrum reconstruction can be made possible from the presented underdetermined approach.