Efficient and Nearly Lossless 3D MRI Reconstruction via Hyper-Sparse Encoding and QR Factorization

Medical images often permit latent low-dimensional representations, enabling data-sparse representation. We propose a novel method originating from fluid dynamics, which is based on pivoted-QR factorization(piQURe), for sparse representation and reconstruction of medical images. With 315 publicly available samples provided by DLBS, this method encodes original 3D MRI data of size 128 \(\,\times \,\) 128 \(\,\times \,\) 80 in a vector of 315 points ( \(0.024\%\) ), enabling nearly lossless reconstruction with the highest normalized error of \(10^{-10}\) in 0.137 s on a regular workstation. Our approach is applicable in both the spatial and frequency domains and performs excellently on medical image data sets containing heterogeneous lesions. Deep learning classification experiments on brain MRI images in Kaggle datasets for tumor detection confirm that errors due to reconstruction and additive noise have little effect on model training, with p-values between 0.731 and 0.956 from DeLong tests on ROC curves. The piQURe algorithm facilitates encrypted data transmission and protects data during artificial intelligence model training with negligible impact on classification performance.