Purpose: Address the shortcomings of edge-preserving filters to preserve the complex nature of edges, by adapting the direction of diffusion to the local variations in intensity function on a subpixel level, thereby achieving a reconstruction accuracy superior to that of data-driven learning-based approaches.
Theory and methods: Rate of diffusion for edges is found to vary in accordance with their gradient direction. Therefore, the edge preservation is strongly dependent on the direction in which the gradient is computed. Since the directionality of edges varies at different regions of the image, the proposed technique computes the gradients in all possible angular directions and uses a spatial-frequency-based deviation measure to choose the most reliable edges from the images diffused along different directions.
Results: The proposed method is compared with the state-of-the-art data-driven learning-based techniques of block matching and 3D filtering (BM3D), patch-based nonlocal operator (PANO), and dictionary learning MRI (DLMRI). Best results are obtained when directionality of edges is estimated from a prior optimized k-space and shows an improvement in peak signal-to-noise ratio (PSNR) measures by a factor of 2.36 dB, 1.92 dB, and 1.59 dB over BM3D, PANO, and dictionary learning MRI, respectively.
Conclusion: The proposed technique prevents the emphasis of false edges and better captures the structural details by a locally varying directionality-guided diffusion to make the error lower than that of the state-of-the-art reconstruction techniques. In addition, a highly parallelizable form of the proposed model promises a significant gain in the reconstruction speed for practical implementations.
Keywords: compressed sensing; gradient direction; learned reconstruction; non-linear diffusion; total variation.
© 2019 International Society for Magnetic Resonance in Medicine.