Objective Numerical Evaluation of Diffuse, Optically Reconstructed Images Using Structural Similarity Index

Diffuse optical tomography is emerging as a non-invasive optical modality used to evaluate tissue information by obtaining the optical properties’ distribution. Two procedures are performed to produce reconstructed absorption and reduced scattering images, which provide structural information that can be used to locate inclusions within tissues with the assistance of a known light intensity around the boundary. These methods are referred to as a forward problem and an inverse solution. Once the reconstructed image is obtained, a subjective measurement is used as the conventional way to assess the image. Hence, in this study, we developed an algorithm designed to numerically assess reconstructed images to identify inclusions using the structural similarity (SSIM) index. We compared four SSIM algorithms with 168 simulated reconstructed images involving the same inclusion position with different contrast ratios and inclusion sizes. A multiscale, improved SSIM containing a sharpness parameter (MS-ISSIM-S) was proposed to represent the potential evaluation compared with the human visible perception. The results indicated that the proposed MS-ISSIM-S is suitable for human visual perception by demonstrating a reduction of similarity score related to various contrasts with a similar size of inclusion; thus, this metric is promising for the objective numerical assessment of diffuse, optically reconstructed images.

New measures of sharpness for symmetric powder diffraction peak profiles

New measures of sharpness for symmetric powder diffraction peak profiles are proposed. The sharpness parameter is defined through the \nuth-order moment of the Fourier transform of the profile function. Analytical expressions for the sharpness parameter for empirical model profile functions, namely the Gaussian, logistic distribution, hyperbolic secant, Lorentzian, Voigt, Pearson VII and pseudo-Voigt functions, and theoretical size-broadening profiles with statistical size distribution are presented. Theoretical diffraction profiles with complicated formulae can be approximated by empirical model functions assuming equivalent values of the sharpness parameter. The concept of the sharpness parameter provides a simple way to define an approximation for a theoretical diffraction peak profile with empirical model functions.