Abstract
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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.