GPU Computing based fast discrete wavelet transform for l₁-regularized SPIRiT reconstruction

Parallel imaging is a technique to shorten the acquisition time by reducing the data size in phase encoding direction. Compressed Sensing is a technique to improve the performance of parallel imaging based reconstruction methods such as l₁-regularized SPIRiT by adding the regularization term, which leads to frequent calculations of Discrete Wavelet Transform (DWT) with high time cost. However, clinical practice of MRI scan requires fast or real-time reconstruction with high image quality. In this paper, by taking advantage of the properties of parallel imaging and GPU computing, we develop a fast three-dimensional DWT for parallel imaging based reconstruction methods such as l₁-regularized SPIRiT. Computational results show that fast DWT in l₁-regularized SPIRiT MRI reconstruction is approximately three times faster than the conventional DWT. Computational results also show that fast DWT for reconstructing an 80 × 150 × 32 × 80 Cardiac MRI dataset by l₁-regularized SPIRiT is approximately 20 per cent faster than l₁-regularized SPIRiT of the conventional DWT.