Registration of images subject to non-linear warping has numerous practical applications. We present an algorithm based on double multiresolution structure of warp and image spaces. Tuning a so-called scale parameter controls the coarseness of the grid by which the deformation is described and also the amount of implicit regularization. The application of our algorithm deals with undoing unidirectional non-linear geometrical distortion of echo-planar images (EPI) caused by local magnetic field inhomogeneities induced mainly by the subject presence. The unwarping is based on registering the EPI images with corresponding undistorted anatomical MRI images. We present evaluation of our method using a wavelet-based random Sobolev-type deformation generator as well as other experimental examples.