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PURPOSE: To present and validate a new method that formalizes a direct link between k-space and wavelet domains to apply separate undersampling and reconstruction for high- and low-spatial-frequency k-space data. THEORY AND METHODS: High- and low-spatial-frequency regions are defined in k-space based on the separation of wavelet subbands, and the conventional compressed sensing problem is transformed into one of localized k-space estimation. To better exploit wavelet-domain sparsity, compressed sensing can be used for high-spatial-frequency regions, whereas parallel imaging can be used for low-spatial-frequency regions. Fourier undersampling is also customized to better accommodate each reconstruction method: random undersampling for compressed sensing and regular undersampling for parallel imaging. RESULTS: Examples using the proposed method demonstrate successful reconstruction of both low-spatial-frequency content and fine structures in high-resolution three-dimensional breast imaging with a net acceleration of 11-12. CONCLUSION: The proposed method improves the reconstruction accuracy of high-spatial-frequency signal content and avoids incoherent artifacts in low-spatial-frequency regions. This new formulation also reduces the reconstruction time due to the smaller problem size.
Sung et al. (Thu,) studied this question.