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

Abstract

Sub-pixel registration is a crucial step for applications such as super-resolution in remote sensing, motion compensation in magnetic resonance imaging, and non-destructive 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 subpixel 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 is sparse. Index Terms Subpixel Registration Wavelet Decomposition Haar Wavelets Image PyramidsRecently, there has been a trend in various imaging modalities and applications such as non-destructive testing and Magnetic Resonance Imaging (MRI) to adopt wavelet-encoded imaging [81], [82] and sparse sensing [83]- [85], with the aim of achieving better resolution, reduced distortions, higher SNR, and quick acquisition time, which are crucial for these applications. Subpixel registration is an integral step of various applications involving these wavelet-encoded compressive imaging technologies. Therefore, in this paper, our goal is to obtain a wavelet domain sub-pixel registration method that can achieve highly accurate results from a sparse set of wavelet coefficients. We make the following major contributions towards this goal: (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 Haar wavelet coefficients, (iii) Using the derived expressions, we propose a multiscale 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, due to signal energy localization in a sparse set of wavelet coefficients. Extensive experiments are used to validate our method both on simulated and real data under various scenarios. II. RELATED WORKThe earliest methods related to our work are based on image pyramids, with the aim of reducing computational time and avoiding local extrema. Examples ...

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