  We propose a patch-based singular value shrinkage method for diffusion
magnetic resonance image estimation targeted at low signal to noise ratio and
accelerated acquisitions. It operates on the complex data resulting from a
sensitivity encoding reconstruction, where asymptotically optimal signal
recovery guarantees can be attained by modeling the noise propagation in the
reconstruction and subsequently simulating or calculating the limit singular
value spectrum. Simple strategies are presented to deal with phase
inconsistencies and optimize patch construction. The pertinence of our
contributions is quantitatively validated on synthetic data, an in vivo adult
example, and challenging neonatal and fetal cohorts. Our methodology is
compared with related approaches, which generally operate on magnitude-only
data and use data-based noise level estimation and singular value truncation.
Visual examples are provided to illustrate effectiveness in generating denoised
and debiased diffusion estimates with well preserved spatial and diffusion
detail.
