Now a days application of sparse representation are widely spreading in many fields such as face recognition. For this usage, defining a dictionary and choosing a proper recovery algorithm plays an important role for the method accuracy. In this paper, two type of dictionaries based on input face images, the method named SRC, and input extracted features, the method named MKD-SRC, are constructed. SRC fails for partial face recognition whereas MKD-SRC overcomes the problem. Three extension of MKD-SRC are introduced and their performance for comparison are presented. For recommending proper recovery algorithm, in this paper, we focus on three greedy algorithms, called MP, OMP, CoSaMP and another called Homotopy. Three standard data sets named AR, Extended Yale-B and Essex University are used to asses which recovery algorithm has an efficient response for proposed methods. The preferred recovery algorithm was chosen based on achieved accuracy and run time.