Continuum topological derivative - a novel application tool for denoising CT and MRI medical images
Authors: Muthukrishnan Viswanath , Jaipurkar Sandeep , Damodaran Nedumaran 
Published: July 2024

Abstract
Background
CT and MRI modalities are important diagnostics tools for exploring the anatomical and tissue properties, respectively of the human beings. Several advancements like HRCT, FLAIR and Propeller have advantages in diagnosing the diseases very accurately, but still have enough space for improvements due to the presence of inherent and instrument noises. In the case of CT and MRI, the quantum mottle and the Gaussian and Rayleigh noises, respectively are still present in their advanced modalities of imaging. This paper addresses the denoising problem with continuum topological derivative technique and proved its trustworthiness based on the comparative study with other traditional filtration methods such as spatial, adaptive, frequency and transformation techniques using measures like visual inspection and performance metrics.

Methods
This research study focuses on identifying a novel method for denoising by testing different filters on HRCT (High-Resolution Computed Tomography) and MR (Magnetic Resonance) images. The images were acquired from the Image Art Radiological Scan Centre using the SOMATOM CT and SIGNA Explorer (operating at 1.5 Tesla) machines. To compare the performance of the proposed CTD (Continuum Topological Derivative) method, various filters were tested on both HRCT and MR images. The filters tested for comparison were Gaussian (2D convolution operator), Wiener (deconvolution operator), Laplacian and Laplacian diagonal (2nd order partial differential operator), Average, Minimum, and Median (ordinary spatial operators), PMAD (Anisotropic diffusion operator), Kuan (statistical operator), Frost (exponential convolution operator), and HAAR Wavelet (time–frequency operator). The purpose of the study was to evaluate the effectiveness of the CTD method in removing noise compared to the other filters. The performance metrics were analyzed to assess the diligence of noise removal achieved by the CTD method. The primary outcome of the study was the removal of quantum mottle noise in HRCT images, while the secondary outcome focused on removing Gaussian (foreground) and Rayleigh (background) noise in MR images. The study aimed to observe the dynamics of noise removal by examining the values of the performance metrics.
In summary, this study aimed to assess the denoising ability of various filters in HRCT and MR images, with the CTD method being the proposed approach. The study evaluated the performance of each filter using specific metrics and compared the results to determine the effectiveness of the CTD method in removing noise from the images.

Results
Based on the calculated performance metric values, it has been observed that the CTD method successfully removed quantum mottle noise in HRCT images and Gaussian as well as Rayleigh noise in MRI. This can be evidenced by the PSNR (Peak Signal-to-Noise Ratio) metric, which consistently exhibited values ranging from 50 to 65 for all the tested images. Additionally, the CTD method demonstrated remarkably low residual values, typically on the order of e−09, which is a distinctive characteristic across all the images. Furthermore, the performance metrics of the CTD method consistently outperformed those of the other tested methods. Consequently, the results of this study have significant implications for the quality, structural similarity, and contrast of HRCT and MR images, enabling clinicians to obtain finer details for diagnostic purposes.

Conclusion
Continuum topological derivative algorithm is found to be constructive in removing prominent noises in both CT and MRI images and can serve as a potential tool for recognition of anatomical details in case of diseased and normal ones. The results obtained from this research work are highly inspiring and offer great promise in obtaining accurate diagnostic information for critical cases such as Thoracic Cavity Carina, Brain SPI Globe Lens 4th Ventricle, Brain-Middle Cerebral Artery, Brain-Middle Cerebral Artery and neoplastic lesions. These findings lay the foundation for implementing the proposed CTD technique in routine clinical diagnosis.