1 Object Composition Identification via Mediated-Reality Supplemented Radiographs Edward S. Jimenez, Member, IEEE, Laurel J. Orr, Member, IEEE, Kyle R. Thompson, Member, IEEE Abstract—This exploratory work investigates the feasibil- ity of extracting linear attenuation functions with respect to energy from a multi-channel radiograph of an object of interest composed of a homogeneous material by simulating the entire imaging system combined with a digital phantom of the object of interest and leveraging this information along with the acquired multi-channel image. This synergistic combination of information allows for improved estimates on not only the attenuation for an effective energy, but for the entire spectrum of energy that is coincident with the detector elements. Material composition identification from radiographs would have wide applications in both medicine and industry. This work will focus on industrial radiography applications and will analyse a range of materials that vary in attenuative properties. This work shows that using iterative solvers holds encouraging potential to fully solve for the linear attenuation profile for the object and material of interest when the imaging system is characterized with respect to initial source x-ray energy spectrum, scan geometry, and accurate digital phantom. I. I NTRODUCTION Full system characterization has been leveraged suc- cessfully for various estimation tasks in works [1], [2] related to SPECT imaging as well as for applications in optical testing [3]. Past work described a simplistic approach to estimate effective attenuation coefficients which reasonably estimated effective attenuation val- ues for various low-attenuation but failed for higher- attenuation materials [4]. The main cause of the break- down in this simplistic approach seemed to be mainly related to the lack of consideration to the non-linearities in the formation of the radiograph. Additionally, a more sophisticated approach to approximate attenuation infor- mation failed to consistently approximate materials due to the presence of null-spaces in the simulated imaging system [5]. II. APPROACH We represent the discretized approximation to the ini- tial energy profile of the source adjusted for attenuation through air as: I 0 (ǫ)|⇀ ε ≈ ⇀ ρ ∈ R m ,ǫ ∈ R E.S. Jimenez is at Sandia National Laboratories Software Systems R&D in Albuquerque NM 87185-0933 USA (telephone: 505-284-9690 email: esjimen@sandia.gov L.J. Orr is at Sandia National Laboratories Software Systems R&D in Albuquerque NM 87185-0932 USA (email: ljorr@sandia.gov K.R. Thompson is at Sandia National Laboratories Structural Dy- namics & X-ray Non-Destructive Evaluation in Albuquerque NM 87185-0555 USA (email: krthomp@sandia.gov where each component ρ i is approximately equal to I 0 (ε i ) and ε i is some sample point within the domain of ǫ and satisfies the following ordering: ε i-1 <ε i <ε i+1 . Therefore, the j th pixel of the radiograph may be ap- proximated as: ⇀ ρ t j      e -µ(ε1)xj e -µ(ε2)xj . . . e -µ(εN )xj      = ⇀ ρ t j ⇀ e j = I j , where x j is the length of the j th ray path from source to the j th pixel intersected with the digital phantom. Note that each ⇀ ρ j will vary slightly when accounting for attenuation through air as the path length to each pixel vary as well as variation due to path length though the object of interest. Thus, leveraging every pixel in image I , we have the following system of equations:           ⇀ ρ t 1 ⇀ 0 ... ... ⇀ 0 ⇀ 0 ⇀ ρ t 2 ⇀ 0 ... ⇀ 0 . . . ⇀ 0 . . . . . . . . . . . . . . . . . . ⇀ ρ t N-1 ⇀ 0 ⇀ 0 ... ... ⇀ 0 ⇀ ρ t N                 ⇀ e 1 ⇀ e 2 . . . ⇀ e N       = P ⇀ e = ⇀ I , where ⇀ 0 is a zero vector with the same dimensionality as vector ⇀ ρ t and P ∈ R N×Nm . Solving P ⇀ e = I can be done in a least-squares sense using any linear solver if P is full-rank; if not, iterative approaches must be used. This work extends the exploratory work in [5] where using a direct search method (DSM) as a robust and straightforward method to approximate the attenuation profile of the object of interest by leveraging a multi- channel imaging detector instead of a single-channel detector that was studied previously [4], [5]. The esti- mation method is then applied to each binned image independently. The DSM leveraged is the Nelder-Mead DSM [6], a robust gradient-free algorithm. The search method will approximate the attenuation profile for each channel as the sum of the first five Legendre Polynomials: ˆ µ(ε)= 4  i=0 c i p i (ε),