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.