# Sub-Pixel Registration of Wavelet-Encoded Images

## TL;DR

This paper introduces a novel wavelet domain sub-pixel registration method that accurately aligns images directly from sparse wavelet coefficients, enhancing super-resolution and imaging applications.

## Contribution

The paper presents a new approach for direct wavelet domain registration that decouples parameters and works effectively with sparse coefficients, improving accuracy and efficiency.

## Key findings

- Outperforms state-of-the-art methods on simulated data
- Maintains high accuracy with sparse wavelet coefficients
- Effective for real-world imaging applications

## 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.