Different ROI imaging configurations. (a) Global scan where the entire object is located inside the FOV (standard configuration and the image reconstruction is exact). (b) The FOV contains two regions (shaded) located outside a roughly estimated OS (μ) where exact reconstruction is assured for the ROI (Ω) that is defined as a union of parallel vertical Hilbert lines that connect shaded regions without intersection with the remaining regions of the object (Noo et al., 2004). (c) The FOV contains a single region (shaded) outside the OS (μ) and solution exactness for ROI (Ω) is assured (Defrise et al., 2006). (d) The FOV is located completely inside the OS (μ) where the exact OS is estimated and reconstruction of ROI (Ω) is exact (Rashed et al., 2009). (e) Local tomography is exact if a sub-region (ω) inside the ROI (Ω) is known and a rough OS (μ) is defined (Kudo et al., 2008). (f) The local tomography problem to be investigated in this paper with ROI (Ω) is located completely inside the object and both OS (μ) and sub-region (ω) are estimated for exact ROI reconstruction.