Blood oxygen level dependent (BOLD) functional MRI (fMRI) imaging is the most common way of imaging neuronal activity in humans using MRI. The BOLD contrast is directly related to changes in vascular physiology associated with neuronal activity and can be directly linked to changes in cerebral blood volume, blood flow and metabolic rate of oxygen. Conventional BOLD imaging is done by reconstructing [special characters omitted]-weighted images. [special characters omitted]-weighted images are unitless and even though they measure the magnitude of the BOLD contrast they are still nonquantifiable in terms of the vascular physiology. An alternative approach is to reconstruct [special characters omitted] maps which are quantifiable and can be directly linked to the vascular changes during activation. However, conventional [special characters omitted] mapping involves long readouts and generally ignores relaxation and off-resonance during readout.

Since fMRI data is usually acquired over a course of several minutes, where the same image volume is collected multiple times, it is important for the time series of each pixel to only reflect changes due to neuronal activity. However, BOLD imaging suffers from temporal drift/fluctuations and subject motion which can confound the findings. Conventionally, a field map is collected at the start of the fMRI study to correct for off-resonance, ignoring any possible changes in it due to either drift or motion. Here we propose a new fast and motion robust [special characters omitted] iterative reconstruction that jointly reconstructs initial magnetization and field maps along with the [special characters omitted] changes, for all time frames in fMRI. To accelerate the algorithm we propose to linearize the MR signal model, enabling the use of fast regularized iterative reconstruction methods. The regularizer was designed to account for the different resolution properties of both [special characters omitted] and field maps and provide uniform spatial resolution.