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Imaging Reconstruction – Exploiting Spatiotemporal Correlations for Dynamic Imaging

What are spatiotemporal correlations? Strictly speaking, in statistical terms, a correlation refers to the linear relationship between two variables. For example, if Y is plotted against X, and the points fall on a line, then X and Y are correlated (Fig. 1). Extending to higher dimensions, if X and Y are vectors, the presence of a correlation means that Y can be predicted from X through a linear transformation. In the MRI field, the term “spatiotemporal correlations” is often used more loosely. Generally, it means that by knowing some data points (e.g. some pixels, or k-space points), we can determine the value of other data points that may be at different spatial locations, different k-space positions and/or different time points. The simple, linear relationship remains important, because many important reconstruction algorithms are linear or approximately linear.