Face detection is an important and challenging task in many computer vision applications. Signal processing using sparse framework has seen much interest in various areas in the recent past. In this paper, we propose a sparse framework based methodology to model a human face using very few training faces. We propose to use SIFT, LBP and RGB based feature vectors to model and detect the face in the sparse framework. The proposed algorithm is based on dictionary learning and uses a sparse framework. The approach adopted is patch based and uses a small number of training faces to train a prototype/basis dictionary. We perform extensive simulation to study the effect of patch size, number of dictionary atoms, number of training faces and sparsity constraint on the face detection accuracy. We study the effect of the choice of different types of feature vectors on detection accuracy and perform a comparative study.