Because tomographic reconstructions are ill-conditioned, algorithms that incorporate additional knowledge about the imaging volume generally have improved image quality. This is particularly true when measurements are noisy or have missing data. This paper presents a general framework for inclusion of the attenuation contributions of specific component objects known to be in the field-of-view as part of the reconstruction. Components such as surgical devices and tools may be modeled explicitly as being part of the attenuating volume but are inexactly known with respect to their locations poses, and possible deformations. The proposed reconstruction framework, referred to as Known-Component Reconstruction (KCR), is based on this novel parameterization of the object, a likelihood-based objective function, and alternating optimizations between registration and image parameters to jointly estimate the both the underlying attenuation and unknown registrations. A deformable KCR (dKCR) approach is introduced that adopts a control pointbased warping operator to accommodate shape mismatches between the component model and the physical component, thereby allowing for a more general class of inexactly known components. The KCR and dKCR approaches are applied to low-dose cone-beam CT data with spine fixation hardware present in the imaging volume. Such data is particularly challenging due to photon starvation effects in projection data behind the metallic components. The proposed algorithms are compared with traditional filtered-backprojection and penalized-likelihood reconstructions and found to provide substantially improved image quality. Whereas traditional approaches exhibit significant artifacts that complicate detection of breaches or fractures near metal, the KCR framework tends to provide good visualization of anatomy right up to the boundary of surgical devices.