Estimating the Transfer Functions of Optical Imaging Systems from Their Degraded Images by Optimization and Global Search Algorithms

Optical imaging is among the safest and most highly impactful biomedical imaging modalities. Aberration in optical imaging systems leads to distorted images. This distortion is almost nonlinear and hence affects the relative size, intensity and appearance of image details. Image aberration has many types, with some or all of them able to be imposed on the image based on the quality of the imaging system and/or surrounding conditions. Many approaches have been introduced to remove or minimize aberration from optical images. If the transfer function of an imaging system and the function of the noise added during the imaging process are known, then an ideal image can be obtained from the image produced by this system. The point spread function (PSF) of an optical imaging system is the image it produces for a point object. PSF is the observable form of the transfer function. The transfer function itself is the exit pupil function or typically the system aberration. The nonlinearity and multiplicity of the aberration imposed on the image, together with the added noise, make it difficult to obtain the transfer function from the degraded images. In this work, optimization and global search techniques are utilized in an iterative image restoration algorithm to estimate the transfer function and restore the image. The proposed technique updates an initially suggested solution of transfer function by optimizing the aberration coefficients. The final solution of the transfer function and hence the PSF is reached when the optimum restored image is obtained. The proposed algorithm is validated by a set of 12 images degraded by different combinations of aberration patterns. Many statistical metrics are used to assess the performance of the proposed algorithm, resulting in a 100% success rate with SSIM equals 1 and a MAE range from 0 to 1×10−8.