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Based on the recent mathematical findings on solving the linear inverse problems with sparsity constraints by Daubechiesx et al., here we adapt a simultaneous algebraic reconstruction technique (SART) for image reconstruction from a limited number of projections subject to a sparsity constraint in terms of an invertible compression transform. The algorithm is implemented with an exemplary Haar wavelet transform and tested with a modified Shepp-Logan phantom. Our preliminary results demonstrate that the sparsity constraint helps effectively improve the quality of reconstructed images and reduce the number of necessary projections.