This paper proposes a sparse representation of an
image using discrete functions. A function is defined
as the product of a Kronecker delta function and a step
function. Based on the sparse representation, we have developed
a novel and effective method for reconstructing an image from
limited-angle projections. The method first estimates the parameters
of the sparse representation from the incomplete projection
data, and then directly calculates the image to be reconstructed.
Experiments have shown that the proposed method can effectively
recover the missing data and reconstruct images more accurately
than the total-variation (TV) regularized reconstruction method.