Abstract—Given a large sparse signal, great wishes are to reconstruct the signal precisely and accurately from lease number of measurements as possible as it could. Although this seems possible by theory, the difficulty is in built an algorithm to perform the accuracy and efficiency of reconstructing. This paper proposes a new proved method to reconstruct sparse signal depend on using new method called Least Support Matching Pursuit (LS-OMP) merge it with the theory of Partial Knowing Support (PSK) given new method called Partially Knowing of Least Support Orthogonal Matching Pursuit (PKLS-OMP). The new methods depend on the greedy algorithm to compute the support which depends on the number of iterations. So to make it faster, the PKLS-OMP adds the idea of partial knowing support of its algorithm. It shows the efficiency, simplicity, and accuracy to get back the original signal if the sampling matrix satisfies the Restricted Isometry Property (RIP). Simulation results also show that it outperforms many algorithms especially for compressible signals. Keywords—Compressed sensing, Lest Support Orthogonal Matching Pursuit, Partial Knowing Support, Restricted isometry property, signal reconstruction. I. INTRODUCTION OMPRESSED SENSING (CS) stands for a linear underdetermined problem, where the underlying sampled signal is sparse. The challenge in CS is to reconstruct this sparse signal from few measurements as possible as it could. The standard CS theorem is based on a sparse signal model and uses an underdetermined system of linear equations [1]. Linear Programming techniques are good for designing computationally CS decoders, but It show kind of complexity for many applications. So, the need for faster decoding algorithms is necessary, even if a procedure raises the measurement number. Several low complexity reconstruction methods are used today as an alternative method for linear programming recovery, which contains a collection of methods and algorithms used for testing [2]. Several algorithms exist for performing the signal reconstruction problem. Some of these include: Convex Optimization: like {Basis Pursuit (BP) and Basis Pursuit De- Noising (BPDN). Iterative Greedy Algorithms like Matching Pursuit (MP) Orthogonal Matching Pursuit (OMP), the Regularized OMP (ROMP), and compressive sampling matching pursuit CoSaMP [3]. The simple idea behind use greedy methods is to find the support for unknown signal sequentially. The support set is Israa Sh. Tawfic, PhD Student, and Sema Koc Kayhan are with the Electric and Electronic Engineering Department, Gaziantep University, Turkey (e- mail: isshakeralani@yahoo.com, skoc@gantep.edu.tr). containing of indices that are non-zero elements of a sparse vector. To evaluate the support set, iterative greedy search methods use some linear algebraic tools such as the matched filter and least square solution [2]. Greedy algorithms used at each iteration, one or several coordinates of input signal vector x which it elected depend on the maximum correlation value between the columns ofΦ and the measurement vector. The candidates will be added to the currently estimate support set of x. The pursuit algorithm repeats this procedure several times until all the coordinates arrange in the evaluated support set [2], [4]. II. BACKGROUND A. OMP Algorithm Notations: let x be a sparse signal, the arbitrary vector xx ,x …..,x , let the support set T 1,2….,N denote the set of nonzero component indices of x (i.e upx i|x 0 ), A || consists of the columns of A with indices iI, A denote the transpose of A, and A denote the pseudo- inverse {A A A }. Let us declare the standard CS problem, which achieve a signal x have a K sparse input, via the linear measurements y Φx (1) whereφ represents a random measurement (sensing) matrix, and y represent the compressed measurement signal. A K sparse signal vector consists of most K nonzero indices. With the setup of K, the task is to reconstruct x from y as x .The aim is to reconstruct sparse signal from a small number of measurements in addition to achieve good reconstruction qualification [4], [5]. Wei Dai and Parichat notes that the compressed measurement signal y is the linear combination of most K atoms (atom means a column of). One condition for sparse signal recovery is to use the Mutual Incoherence Property (MIP) [6]. The MIP requires the correlations among the column vectors Φ to be small. The coherence parameter μ of sensing matrix is defined as, μ max φ , φ (2) where φ , φ Are two columns of Φ with unit norm. For the noiseless case when Φ is a series of two square orthogonal matrices, that Israa Sh. Tawfic, Sema Koc Kayhan Partially Knowing of Least Support Orthogonal Matching Pursuit (PKLS-OMP) for Recovering Signal C International Science Index International Journal of Computer, Control, Quantum and Information Engineering Vol:8 No: 10, 2014 1720 International Scholarly and Scientific Research & Innovation 8(10), 2014 International Science Index Vol:8, No:10, 2014 internationalscienceindex.org/publication/9999597