One of the key factors affecting functional MRI image reconstruction is field inhomogeneity. It is desirable to estimate both the distortion-free MRI image and field map simultaneously, thus compensating for image distortions caused by the field inhomogeneity. To solve this problem, which is called Joint Estimation problem, we propose a new non-iterative approach using Harmonic Retrieval (HR) methods. This connection establishes an elegant framework to solve the Joint Estimation problem through a sequence of one dimensional HR problems in which efficient solutions are available. We also derive the condition on the smoothness of the field map in order for HR techniques to recover the image with high SNR. Experimental results with the proposed method show significant improvements in MRI image reconstruction compared to methods that do not correct for field inhomogeneity.