Extracting Super-resolution Details Directly from a Diffraction-Blurred Image or Part of Its Frequency Spectrum

It is usually believed that the low frequency part of a signal’s Fourier spectrum represents its profile, while the high frequency part represents its details. Conventional light microscopes filter out the high frequency parts of image signals, so that people cannot see the details of the samples (objects being imaged) in the blurred images. However, we find that in a certain “resolvable condition”, a signal’s low frequency and high frequency parts not only represent profile and details respectively. Actually, any one of them also contains the full information (including both profile and details) of the sample’s structure. Therefore, for samples with spatial frequency beyond diffraction-limit, even if the image’s high frequency part is filtered out by the microscope, it is still possible to extract the full information from the low frequency part. On the basis of the above findings, we propose the technique of Deconvolution Super-resolution (DeSu-re), including two methods. One method extracts the full information of the sample’s structure directly from the diffraction-blurred image, while the other extracts it directly from part of the observed image’s spectrum (e.g., low frequency part). Both theoretical analysis and simulation experiment support the above findings, and also verify the effectiveness of the proposed methods.Edward Y. Sheffield is a pen name of Yaohua Xie (Yaohua.Xie@hotmail.com, fjpnxyh2000@163.com, http://orcid.org/0000-0001-6780-3156