X-rays have been valuable to a large number of fields including Science, Medicine, and Security. Yet, the availability of a compact high-spectral brilliance X-ray sources is limited. A technique to produce X-rays with spectral brilliance B ∼ 10 12 photons.(mm-mrd) −2 .(0.1% BW) −1 .s −1 is discussed. The method is based on the generation and acceleration of a low-emittance field-emitted electron bunches. The bunches are then focused on a diamond crystal thereby producing channeling radiation. In this paper, after presenting the overarching concept, we discuss the generation, acceleration and transport of the low-emittance bunches with parameters consistent with the production of high-brilliance X-rays through channeling radiation. We especially consider the example of the Advanced Superconducting Test Accelerator (ASTA) currently in construction at Fermilab where a proof-of-principle experiment is in preparation.