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To develop a rapid 31P-MRSI method with high spatiospectral resolution using low-rank tensor-based data acquisition and image reconstruction.The multidimensional image function of 31P-MRSI is represented by a low-rank tensor to capture the spatial–spectral–temporal correlations of data. A hybrid data acquisition scheme is used for sparse sampling, which consists of a set of “training” data with limited k-space coverage to capture the subspace structure of the image function, and a set of sparsely sampled “imaging” data for high-resolution image reconstruction. An explicit subspace pursuit approach is used for image reconstruction, which estimates the bases of the subspace from the “training” data and then reconstructs a high-resolution image function from the “imaging” data.We have validated the feasibility of the proposed method using phantom and in vivo studies on a 3T whole-body scanner and a 9.4T preclinical scanner. The proposed method produced high-resolution static 31P-MRSI images (i.e., 6.9 × 6.9 × 10 mm3 nominal resolution in a 15-min acquisition at 3T) and high-resolution, high-frame-rate dynamic 31P-MRSI images (i.e., 1.5 × 1.5 × 1.6 mm3 nominal resolution, 30 s/frame at 9.4T).Dynamic spatiospectral variations of 31P-MRSI signals can be efficiently represented by a low-rank tensor. Exploiting this mathematical structure for data acquisition and image reconstruction can lead to fast 31P-MRSI with high resolution, frame-rate, and SNR.