A method for highly accelerated projection imaging ("EtaAlphaRhoI") is provided. In this method, conventional linear gradients are used to obtain coil sensitivity-weighted projections of the object being imaged. Only a relatively small number of projections, such as sixteen or less, of the object are required to reconstruct a two-dimensional image of the object, unlike conventional projection imaging techniques. The relationship between the voxel values of the imaged object and the coil sensitivity- weighted projections is formulated as a linear system of equations and the reconstructed images are obtained by solving this matrix equation. This method advantageously allows higher acceleration rates compared to echo planar imaging ("EpsilonRhoI") with SENSE or GRAPPA acceleration. Moreover, the method does not require any additional or specialized hardware because hardware in conventional MRI scanners is adequate to implement the method.