Comparative Analysis of DFT, DCT, and DWT Transformations with ADMM and l₁-Optimization for Compressed Sensing in Meningioma Tumor MRI Image Reconstruction

In the context of modern medical imaging in MRI, it is becoming increasingly challenging to minimize the amount of time taken for scanning and data burden that is expected to be processed while still ensuring that high quality images are obtained. This study sought to compare the performances of different transforms in compressed sensing including DFT, DCT, and DWT based on conjugate ADMM and l<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf>-optimization for reconstruction of meningioma tumor MRI images. The objective of this initiative is to entail the determination of the optimal transform and optimization methodologies whose outcomes will provide the best image reconstruction quality with the lowest computational complexities. Through the use of compressed sensing, the number of measurements used was much lower than normally expected, lowering the amount of data used. It was found DWT may be preferred for non-time-sensitive applications that demand the highest quality images, DCT’s balanced attributes render it generally the best choice for the broadest range of medical imaging applications, expected to lead to a significant enhancement in the MRI diagnosis, patient comfort and the overall healthcare delivery system costs. The report outlines the method utilized for this study and the results observed using these techniques in real-world medical environments.