A computer that determines coefficients in a representation of coil sensitivities and MR information associated with a sample is described. During operation, the computer may acquire MR signals associated with a sample from the measurement device. Then, the computer may access a predetermined set of coil magnetic field basis vectors, where weighted superpositions of the predetermined set of coil magnetic field basis vectors using the coefficients represent coil sensitivities of coils in the measurement device, and where the predetermined coil magnetic field basis vectors are solutions to Maxwell's equations. Next, the computer may solve a nonlinear optimization problem for the MR information associated with the sample and the coefficients using the MR signals and the predetermined set of coil magnetic field basis vectors.
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