Abstract: Methods are disclosed for calculating a fat fraction corrected for noise bias of one or more voxels of interest using a magnetic resonance imaging (MRI) system. A plurality of image data sets are obtained each corresponding to NMR k-space data acquired using a pulse sequence with an individual associated echo time tn. A system of linear equations is formed relating image signal values to a desired decomposed calculated data vector having a component such as a water and fat combination having zero mean noise, or having a real fat component and a real water component. A fat fraction is calculated from at least one component of the decomposed calculated data vector. In another embodiment, the system of linear equations is normalized and can directly estimate a fat fraction or a water fraction having reduced noise bias.

Abstract: A method for producing images of a subject containing M spin species using a magnetic resonance imaging (MRI) system includes obtaining N k-space data matrices from N k-space data sets acquired with the MRI system using a pulse sequence with an individual associated echo time. The k-space data matrices each include corresponding data at the same plurality of k-space locations and time stamps are tracked for each k-space location. For each k-space location, a set of linear equations in k-space is solved. The set of linear equations relates corresponding data from the N k-space data matrices, echo times and time stamps to desired calculated k-space data. Calculated data in k-space which is corrected for chemical shift is produced corresponding to each k-space location and aggregated to obtain a k-space calculated data set. The k-space calculated data set is transformed to image space to obtain a corresponding image.

Abstract: Metabolite images are produced with an MRI system using a priori information about the resonant peaks of the metabolites and their relative sizes to reduce the amount of NMR data needed for proper spectral resolution. With the a priori information the acquired NMR signal is modeled. Using this model and NMR data acquired at a plurality of echo times (TE), the metabolite at each image pixel is calculated.

Abstract: A combined toroid/shunt device for detecting residual current in an electrical installation comprising a plurality of conductors such as a live conductor (2) and a neutral conductor (3) is described. The device comprises a toroid means (1, 4) for detecting an AC residual current within a first range and a plurality of resistive shunts (6a) to (6d) for connection in respective ones of the plurality of conductors. A current detection means (5, 7, 13) responsive to current flowing in each of said shunts for detecting a DC residual current and/or an AC residual current within a second range is described. The first range of AC residual current is an AC residual current resulting from earth leakage or cross-leakage between conductors up to a saturation level at which the toroid or electronic means associated means therewith becomes saturated. The second range includes an AC residual current of said saturation level.