  In spectral CT reconstruction, the basis materials decomposition involves
solving a large-scale nonlinear system of integral equations, which is highly
ill-posed mathematically. This paper proposes a model that parameterizes the
attenuation coefficients of the object using a neural field representation,
thereby avoiding the complex calculations of pixel-driven projection
coefficient matrices during the discretization process of line integrals. It
introduces a lightweight discretization method for line integrals based on a
ray-driven neural field, enhancing the accuracy of the integral approximation
during the discretization process. The basis materials are represented as
continuous vector-valued implicit functions to establish a neural field
parameterization model for the basis materials. The auto-differentiation
framework of deep learning is then used to solve the implicit continuous
function of the neural base-material fields. This method is not limited by the
spatial resolution of reconstructed images, and the network has compact and
regular properties. Experimental validation shows that our method performs
exceptionally well in addressing the spectral CT reconstruction. Additionally,
it fulfils the requirements for the generation of high-resolution
reconstruction images.
