**Abstract:**
It is very challenging to recognize face images with illumination and expression variations in the presence of missed information, hence it turns to be an active research topic. This paper presents a greedy algorithm called Orthogonal Matching Pursuit (OMP) which can be proved theoretically and empirically that a signal with many zero entries can be recovered reliably. Existing sparse algorithms are basis pursuit, matching pursuit (MP) and Lasso. OMP differs from MP, in that the columns in MP are not orthonormal where as in OMP the column vectors are made orthonormal before start . The running time of MP is high when compared to OMP. The idea of sparse is widely used for implementing all these algorithms. The term sparse refers to a measurable property that concerns the number of non-zero entries present in a vector termed as sparsity. Recognition of a sparse image is presented here. OMP is an iterative algorithm which takes the images as the columns of a dictionary. The algorithm selects the column vector which most closely resembles a residual vector.A global optimum solution is obtained from sequence of locally optimum solutions.

**Keywords:**
sparse, sparsity, orthogonal matching pursuit, basis pursuit, matching pursuit.