Conventional Magnetic Resonance Imagers (MRI) use a uniform main magnetic field ($$$B_{0}$$$) to polarize the sample being imaged and separately superimposed gradient fields for image encoding. Inhomogeneous $$$B_{0}$$$ fields have the potential to encode spatial information in one direction for use in novel image encoding schemes [1,2]. In this study we explore the feasibility of image reconstruction of the signal from a non-uniform rotating magnetic field and two rotating RF receivers. A Halbach magnet was used to generate a non-uniform radially-varying $$$B_{0}$$$ field, such that intended image plane was perpendicular to the axis of the magnet. The $$$B_{0}$$$ field was measured experimentally and a polynomial was fit to the data. Two separate saddle receiver coils were located $$$180^0$$$ from each other. The receiver coils were fixed relative to the magnet and both were rotated around the imaged object using a stepper motor (see Fig 1). The rotation therefore achieved spatial encoding in the angular direction primarily through the variation of the receive $$$B_{1}$$$ field relative to the object. In the experiment reported here, 32 angular positions were used and 23 transmission frequencies were used for radial encoding in the inhomogeneous $$$B_{0}$$$ field. To model the sensitivity of the receiver coils, we used the Biot Savart law to calculate the $$$B_{1}$$$ field of each receive coil for different positions in the field of view (FOV). The detected signal from object $$$x$$$, indexed by transmission frequency $$$\omega$$$ and magnet position $$$\alpha$$$ may be modeled as: $$y(\omega,\alpha)=\int\int x(r,\theta) A(\omega,\alpha;r,\theta)\: dr \: d\theta$$ where A is the encoding matrix and $$$(r,\theta) $$$ are polar coordinates. A Riemann sum approximation of Eq. (1) was used to compute the simulated signal and after rearrangement, it can be written as: $$$[y]=[A][x]$$$. The encoding matrix for each excitation, at frequency $$$\omega$$$ (for radial encoding) and rotation $$$\alpha$$$, can be calculated as $$A(\omega,\alpha)=B_{\rm{weight}}(\omega,\alpha)B_{1}(\alpha)e^{\triangle B_{0}(\omega,\alpha)\gamma\triangle T}$$ where we now discuss each term. $$$ B_{1}(\alpha)$$$ is the component of the RF receiver field perpendicular to the $$$B_{0}$$$ direction which changes relative to the imaged object at each magnet angular position and can be calculated as $$B_{1}=\sqrt{B_{1x}^{2}+B_{1y}^{2}} \sin(\phi_{B_1}-\phi_{B_0})$$ Where $$$\phi_{B_1}$$$ is the phase of $$$B_{1}$$$ field in each angular position and $$$\phi_{B_0}$$$ is the phase of $$$B_{0}$$$ field. For each excitation the slice thickness (radially) will be a sinc function which means the nuclei with the same resonant frequency will be excited completely and then others according to how far they are from the Larmor frequency will be excited. Therefore we multiply the coil sensitivity with a weighing matrix. The weighting matrix for each excitation and rotation is $$B_{\rm{weight}}(\omega,\alpha)=\mid \frac{\sin(\triangle B_{0}(\omega,\alpha))}{\triangle B_{0}(\omega,\alpha)}\mid$$ where $$$\triangle B_{0}$$$ is the difference of $$$B_{0}$$$ field from the Larmor frequency field: $$\triangle B_{0}(\omega,\alpha)=B_0(\alpha)-B_{\omega}(\omega)$$ where $$$ B_0(\alpha)$$$ is the measured $$$B_{0}$$$ field at each rotation angle and $$$ B_{\omega}(\omega)$$$ is the Larmor frequency magnetic field as determined by the transmitted frequency. The image $$$[x]$$$, from $$$[y]=[A][x]$$$, was reconstructed using a constrained least squares method with Tikhonov regularization. Let $$$M$$$ be the number of frequencies that we want to transmit at each rotation, let $$$R$$$ be the number of angular positions we want to rotate the magnet to (main magnet and the receive coils rotate together), let $$$C$$$ be the number of the receive coils and let $$$N \times N$$$ be the number of the pixels of the image. Then matrix $$$ [A]$$$ is of size of $$$MRC \times N^2$$$, $$$[y]$$$ is a vector of size of $$$MRC \times 1$$$ and, $$$[x]$$$ is a vector of size of $$$N^{2} \times 1$$$.Our results indicate the feasibility of reconstructing images from non-uniform rotating magnet. The reconstructed images from experimental data, however, include artifacts which are likely due to the high sensitivity of the reconstruction method to the assumed $$$B_{0}$$$ and $$$B_{1}$$$ field values. There were, as yet unquantified, errors associated with measuring the $$$B_{0}$$$ field. As well, the calculated $$$B_{1}$$$ field may be not be a good enough approximation to the actual field.We have made progress in the realization of a novel new approach to MRI that does not rely on active magnetic gradient fields. Improvements are expected when we have better knowledge of the $$$B_{0}$$$ and $$$B_{1}$$$ fields produced by the constructed hardware.