Compressed sensing MRI using an interpolation-free nonlinear diffusion model

Constraints in extended neighborhood system demand the use of a large number of interpolations in directionality-guided compressed-sensing nonlinear diffusion MR image reconstruction technique. This limits its practical application in terms of computational complexity. The proposed method aims at multifold improvement in its runtime without compromising the image quality.

Conventional approach to extended neighborhood computation requires 108 linear interpolations per pixel for 10 sets of neighborhoods. We propose a neighborhood stretching technique that systematically extends the location of neighboring pixels such that 66% to 100% fewer interpolations are required to compute the gradients along multiple directions. A spatial frequency-based deviation measure is then used to choose the most reliable edges from the set of images generated by diffusion along different directions.

The semi-interpolated and interpolation-free diffusion techniques proposed in this paper are compared with the fully interpolated diffusion-based reconstruction by reconstruing multiple multichannel in vivo datasets, undersampled using different sampling patterns at various sampling rates. Results indicate a two- to fivefold increase in reconstruction speed with a potential to generate 1 to 2 dB improvement in peak SNR measure.

The proposed method outperforms the state-of-the-art fully interpolated diffusion model and generates high-quality reconstructions for different sampling patterns and acceleration factors with a two- to fivefold increment in reconstruction speed. This makes it the most suitable candidate for edge-preserving penalties used in the compressed sensing MRI reconstruction methods.