Image Reconstruction from Sparse Projections Using S-Transform

Sparse projections are an effective way to reduce the exposure to radiation during X-ray CT imaging. However, reconstruction of images from sparse projection data is challenging. This paper introduces a new sparse transform, referred to as S-transform, and proposes an accurate image reconstruction method based on the transform. The S-transform effectively converts the ill-posed reconstruction problem into a well-defined one by representing the image using a small set of transform coefficients. An algorithm is proposed that efficiently estimates the S-transform coefficients from the sparse projections, thus allowing the image to be accurately reconstructed using the inverse S-transform. The experimental results on both simulated and real images have consistently shown that, compared to the popular total variation (TV) method, the proposed method achieves comparable results when the projections is sparse, and substantially improves the quality of the reconstructed image when the number of the projections is relatively high. Therefore, the use of the proposed reconstruction algorithm may permit reduction of the radiation exposure without trade-off in imaging performance.