RAO TRANSFORM: Deblurring of Medical Images with Shift-Variant Blur

Preliminary report on the performance comparison of Rao Transform to State-of-the-Art methods in over 40 different cases of medical imaging modalities.

BACKGROUND

Rao Transform was invented in 2004 (US Patent No. 7,558,709 B2) by this author for shiftvariant deblurring of images and other applications. It was applied to deblur photographic images and published in 2008 (ICPR2008) but it did not become known to researchers in medical image processing and other areas like microscopy and astronomy. This author did not become aware of the application and advantages of Rao Transform for deblurring medical images perhaps due to a lack of publicly shared databases of medical images. Since Nov. 2025, this author has begun to use AI chatbots like Grok.com to investigate the performance of Rao Transform (RT) on many medical and non-medical image deblurring tasks, specifically the hard problem of Shift-Variant Deblurring. Grok.com did not know about the Rao Transform technique, and it was given the ICPR2008 paper by this author and his students to learn about it. Using the technique in the paper, and based on the prompts given by this author, Grok compared the performance of RT with the state of the art (SOTA) techniques for shift-variant deblurring of images in many areas like medical imaging, microscopy, and astronomy. Test images from online public research databases were used by Grok to evaluate the methods for accuracy and speed. In the preliminary results produced by Grok, Rao Transform outperformed all the SOTA techniques by a surprisingly huge margin both in accuracy of deblurred images as well as the computational speed in processing. AI/Chatbot systems like Grok are known to hallucinate, lie, act sycophantic, and make mistakes, but the results here are so surprising and important for clinical diagnosis based on medical images that they deserve further investigation. Therefore, these results and the comparison methods were examined briefly by this author, and one of the cases related to MRI was examined in some detail. The methods and programs used by Grok were mostly reasonable but there were some approximations and assumptions, and in some cases actual errors. However, there is enough evidence to believe that after these approximations, assumptions, and errors, are fixed, Rao Transform will outperform SOTA methods in many cases. Therefore, this author has begun detailed and thorough investigations in this direction. It is expected that the Rao Transform technique will provide more accurate and faster results for deblurring medical images related to MRI, X-ray CT, Ultrasound, PET, SPECT, etc. It is clear from initial experience that AI systems like Grok will assist and accelerate these research efforts greatly.

Warning: This report is a compilation of raw unedited responses from Grok.com to prompts by this author. The information here is useful but it is preliminary, very approximate, and has some errors. The purpose of this report is to demonstrate that the information in this report, however much inaccurate it may be, strongly demands us to investigate the application of Rao Transform to some important practical applications considered here.