Computation of mass-density images from x-ray refraction-angle images

In this paper, we investigate the possibility of computing quantitatively accurate images of mass density variations in soft tissue. This is a challenging task, because density variations in soft tissue, such as the breast, can be very subtle. Beginning from an image of refraction angle created by either diffraction-enhanced imaging (DEI) or multiple-image radiography (MIR), we estimate the mass-density image using a constrained least squares (CLS) method. The CLS algorithm yields accurate density estimates while effectively suppressing noise. Our method improves on an analytical method proposed by Hasnah et al (2005 Med. Phys. 32 549-52), which can produce significant artefacts when even a modest level of noise is present. We present a quantitative evaluation study to determine the accuracy with which mass density can be determined in the presence of noise. Based on computer simulations, we find that the mass-density estimation error can be as low as a few per cent for typical density variations found in the breast. Example images computed from less-noisy real data are also shown to illustrate the feasibility of the technique. We anticipate that density imaging may have application in assessment of water content of cartilage resulting from osteoarthritis, in evaluation of bone density, and in mammographic interpretation.