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Sparse projection has been shown to be highly effective in several domains, including image denoising and scene / object classification. However, practical application to large scale problems such as video analysis requires efficient versions of sparse projection algorithms such as Orthogonal Matching Pursuit (OMP). In particular, random projection based locality sensitive hashing (LSH) has been proposed for OMP. In this paper, we propose a novel technique called Comparison Hadamard random projection (CHRP) for further improving the efficiency of LSH within OMP. CHRP combines two techniques:(1) The Fast Johnson-Lindenstrauss Transform (FJLT) which uses a randomized Hadamard transform and sparse projection matrix for LSH, and (2) Achlioptas' random projection that uses only addition and comparison operations. Our approach provides the robustness of FJLT while completely avoiding multiplications. We empirically validate CHRP's efficacy by performing a suite of experiments for image denoising, scene classification, and video categorization. Our experiments indicate that CHRP significantly speeds-up OMP with negligible loss in classification accuracy.