During operation, the system may apply an external magnetic field and an RF pulse sequence or mechanical stimulus to the sample. The system can then measure at least a component of magnetization or mechanical parameters, such as elasticity associated with the sample, such as the MR signal of one or more types of nuclei of the sample or the elasticity of the sample. Moreover, the system may at least calculate the predicted components of the magnetization for the voxels associated with the sample based on the measured component of the magnetization, the forward model, the external magnetic field and the RF pulse sequence. Next, the system can solve the inverse problem by iteratively changing the parameters associated with the voxel in the forward model until the difference between the predicted component of the magnetization and the measured component of the magnetization is less than a predefined value have. It is noted that the calculation may be performed concurrently with the measurement, and may not include performing a Fourier transform.
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