According to one aspect of the invention, there is provided a method of constructing a diagnostic image of a sample from MRI data acquired while subjecting the sample to an inhomogeneous polarizing magnetic field, the method comprising the steps of: i) deriving an estimate of the spatial map of the inhomogeneous polarizing magnetic field; ii) acquiring the MRI data; iii) processing the estimate of the spatial map with the acquired MRI data to obtain an estimate of the diagnostic image; iv) calculating an acquired data error in response to the estimates of the spatial map and the diagnostic image; v) updating the estimate of the spatial map in response to the calculated error; and repeating the steps iii) to v) to improve the estimate of the spatial map of the earlier iteration and the estimate of the diagnostic image, wherein the repetition is stopped when the calculated error of the latest iteration reaches within a tolerance range and wherein the estimate of the diagnostic image from the latest iteration becomes the diagnostic image of the sample.