In this paper, we propose a novel method for beam hardening correction in polychromatic transmission tomography. A
family of polynomials is firstly determined in a training phase, which forms a complete set in the sense of X-ray physics
of medical diagnostic imaging. In particular, every polynomial in the set is indexed by a beam hardening factor, i.e.
effective atomic number, which is further assigned to specific X-ray penetrating path. In order to successfully accomplish
the assignation in an imaging phase, another polynomial is adopted to formulize the mapping relationship between the
index of polynomial family and the area density ratio of bone tissue. Here, the area density ratio of bone tissue is
calculated after the pre reconstructed image being segmented into soft tissue and bone regions. The mapping polynomial
is iteratively approximated by a dedicated HL Consistency (HLC) based nonlinear algorithm. The characteristics of this
method include that the polynomial family can cover the variations of both high potential and effective filter of X-ray
tube, the beam hardening correction in the imaging phase can adapt the content variations of objects being imaged, and
the correction effect is also sophisticated even bowtie filter exists. Performance analysis and related computer simulation
show that our HLC based correction is much robust than traditional bone correction to the variants of scale factor lambda0.