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Compressive sensing (CS) has emerged as an efficient signal compression and recovery technique, that exploits the sparsity of a signal in a transform domain to perform sampling and stable recovery. The existing image compression methods have complex coding techniques involved and are also vulnerable to errors. In this paper, we propose a novel image compression and recovery scheme based on compressive sensing principles. This is an alternative paradigm to conventional image coding and is robust in nature. To obtain a sparse representation of the input, discrete wavelet transform is used and random complex Hadamard transform is used for obtaining CS measurements. At the decoder, sparse reconstruction is carried out using compressive sampling matching pursuit (CoSaMP) algorithm. We show that, the proposed CS method for image sampling and reconstruction is efficient in terms of complexity, quality and is comparable with some of the existing CS techniques. We also demonstrate that our method uses considerably less number of random measurements.