The objectivity of three-dimensional imaging has placed X-ray Computed Tomography (CT) into an indispensable diagnostic method in clinical and industrial applications. Despite the advances in the X-ray CT imaging, high- resolution three-dimensional reconstruction of small details in objects with large in-plane dimensions has been a fundamental challenge for the conventional X-ray CT method. An alternative scanning geometry, where X-ray source and a detector move synchronously irradiating a specimen at an inclined angle, has been proposed to address this challenge. This work presents new designs of prior (or penalty) functions developed for reconstructing the radiography data obtained under the limited angular conditions. The new prior targets reduction of shape distortion artifacts, common for laminographic reconstructions, as well as preservation of small features, such as voids, edge details, and high-density inclusions. The novel prior function designs are demonstrated on the computational phantom of a specimen scanned under tilted planar CT geometry simulating large planar dimensions of a specimen. To accommodate physical CT scanning of such specimens, a novel microfocus X-ray CT scanning device that rotates X-ray source and moves the detector synchronously while staying on the same side of the test specimen (Inclined CT), is introduced. This device allows scanning of critical areas of up to 3-meter-wide and potentially unlimited length specimens with high resolution required for identification of manufacturing and structural defects typical for modern composite structural elements used in the aerospace industry.