Least squares support vector machine regression combined with Monte Carlo simulation based on the spatial frequency domain imaging for the detection of optical properties of pear

A spatial frequency domain imaging system to nondestructively measure wide-field optical properties of biological tissue has been developed. Optical parameters of absorption (μa) and reduced scattering coefficients (μ's) of 'Crown' pears were estimated based on spatial frequency dependent diffuse reflectance (Rd). Because of the limitation of diffusion approximation (DA), least squares support vector machine (LSSVM) regression was introduced to model the relationship between the μa, μ's and Rd that were generated by Monte Carlo (MC) simulation. To accelerate the detection speed, two spatial frequencies of fx = 0 m−1 and nonzero fx were chosen according to the correlation coefficients between the measured and simulated results of Rd of 60 liquid phantoms. The results showed that the fx of 250 m−1 presents the highest correlation. The forward LSSVR models at the two fx were trained based on a series of MC simulations with a wide range of μa, μ's and albedo, and then validated by the phantoms by comparing predicted Rd and MC simulated Rd. The validation results showed that two models were capable of describing the forward relationship with little deviation, and that both the determination coefficients were close to 1 at two fx. The μa and μ's of phantoms were predicted after an optimal searching of models. The inverse validation results showed that the mean relative errors for μa and μ's were 5.27% and 2.65% respectively. Compared with the calculation results by DA, the proposed method was capable of measuring the optical properties of tissue simulation phantoms accurately, especially when the albedo is less than 50. A case study on the inspection of pear bruises was carried out to verify the application prospect of the proposed method. Results indicated that the fresh bruise which is not obviously distinguishable by naked eyes, can be identified in μ's maps.