Optimal sampling with prior information of the image geometry in microfluidic MRI.

Recent advances in MRI acquisition for microscopic flows enable unprecedented sensitivity and speed in a portable NMR/MRI microfluidic analysis platform. However, the application of MRI to microfluidics usually suffers from prolonged acquisition times owing to the combination of the required high resolution and wide field of view necessary to resolve details within microfluidic channels. When prior knowledge of the image geometry is available as a binarized image, such as for microfluidic MRI, it is possible to reduce sampling requirements by incorporating this information into the reconstruction algorithm. The current approach to the design of the partial weighted random sampling schemes is to bias toward the high signal energy portions of the binarized image geometry after Fourier transformation (i.e. in its k-space representation). Although this sampling prescription is frequently effective, it can be far from optimal in certain limiting cases, such as for a 1D channel, or more generally yield inefficient sampling schemes at low degrees of sub-sampling. This work explores the tradeoff between signal acquisition and incoherent sampling on image reconstruction quality given prior knowledge of the image geometry for weighted random sampling schemes, finding that optimal distribution is not robustly determined by maximizing the acquired signal but from interpreting its marginal change with respect to the sub-sampling rate. We develop a corresponding sampling design methodology that deterministically yields a near optimal sampling distribution for image reconstructions incorporating knowledge of the image geometry. The technique robustly identifies optimal weighted random sampling schemes and provides improved reconstruction fidelity for multiple 1D and 2D images, when compared to prior techniques for sampling optimization given knowledge of the image geometry.

Quantitative measurements of injections into porous media with contrast based MRI.

Porous flow occurs in a wide range of materials and applies to many commercially relevant applications such as oil recovery, chemical reactors and contaminant transport in soils. Typically, breakthrough and pressure curves of column floods are used in the laboratory characterization of these materials. These characterization methods lack the detail to easily and unambiguously resolve flow mechanisms with similar effects at the core scale that can dominate at the aquifer or oil field scale, as well as the effects of geometry that control the flow at interfaces as in a perforated well or the inlet of an improperly designed column. Non-invasive imaging techniques such as MRI have been shown to provide a far more detailed characterization of the properties of the solid matrix and flow, but usually focus on the intrinsic flow properties of porous media or matching a numerical model to a complex flow system. We show that these MRI techniques, utilizing paramagnetic tagging in combination with a carefully controlled and ideal flow system, can quantitatively characterize the effects of geometry and intrinsic flow properties for a point injection into a core. The use of a carefully controlled and 'idealized' system is essential to be able to isolate and match predicted effects from geometry and extract subtle flow processes omitted in the model that would be hidden in a more heterogeneous system. This approach provides not only a tool to understand the behavior of intentional boundary effects, but also one to diagnose the unintentional ones that often degrade the data from routine column flood measurements.