Sparse projections are an effective way to reducethe exposure to radiation during X-ray CT imaging. However,reconstruction of images from sparse projection datais challenging. This paper introduces a new sparse transform,referred to as S-transform, and proposes an accurateimage reconstruction method based on the transform. TheS-transform effectively converts the ill-posed reconstructionproblem into a well-defined one by representing the imageusing a small set of transform coefficients. An algorithm isproposed that efficiently estimates the S-transform coefficientsfrom the sparse projections, thus allowing the imageto be accurately reconstructed using the inverse S-transform.The experimental results on both simulated and real imageshave consistently shown that, compared to the popular totalvariation (TV) method, the proposed method achieves comparableresults when the projections is sparse, and substantiallyimproves the quality of the reconstructed image whenthe number of the projections is relatively high. Therefore,the use of the proposed reconstruction algorithm may permitreduction of the radiation exposure without trade-off inimaging performance.