Figure 3.

A typical full k-space in vivo hyperpolarized [1-¹³C] pyruvate MRSI dataset, reordered as a block-Hankel matrix with size of 1000 × 30000 (via sliding window and reordering as illustrated in Fig. 2). (a) The T₂-weighted MRI depicts the field of view for the 2D 8 × 8 MRSI. (b) The first 200 singular values from the singular value decomposition of original block-Hankel matrix (red solid line) and its low-rank approximation (blue dash line) are plotted. Low-rank approximation (by Cadzow denoising on block-Hankel matrix) iteratively extracted the top 100 singular values and vectors, and was repeated 300 times. (c) Singular values and vectors from the block-Hankel matrix decomposition after low-rank approximation, showing distinct spectral, dynamic and spatial features.