In-band sub-pixel registration of wavelet-encoded images from sparse coefficients

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Sub-pixel registration is a crucial step for applications such as super-resolution in remote sensing, motion compensation in magnetic resonance imaging, and nondestructive testing in manufacturing, to name a few. Recently, these technologies have been trending towards wavelet-encoded imaging and sparse/compressive sensing. The former plays a crucial role in reducing imaging artifacts, while the latter significantly increases the acquisition speed. In view of these new emerging needs for applications of wavelet-encoded imaging, we propose a sub-pixel registration method that can achieve direct wavelet domain registration from a sparse set of coefficients. We make the following contributions: (i) We devise a method of decoupling scale, rotation, and translation parameters in the Haar wavelet domain, (ii) we derive explicit mathematical expressions that define in-band sub-pixel registration in terms of wavelet coefficients, (iii) using the derived expressions, we propose an approach to achieve in-band sub-pixel registration, avoiding back and forth transformations. (iv) Our solution remains highly accurate even when a sparse set of coefficients are used, which is due to localization of signals in a sparse set of wavelet coefficients. We demonstrate the accuracy of our method, and show that it outperforms the state of the art on simulated and real data, even when the data are sparse.