Double-density and dual-tree based methods for image super resolution

When several low-resolution images are taken of the same scene, they often contain aliasing and differing subpixel shifts causing different focuses of the scene. Super-resolution imaging is a technique that can be used to construct high-resolution imagery from these low-resolution images. By combining images, high frequency components are amplified while removing blurring and artifacting. Super-resolution reconstruction techniques include methods such as the Non-Uniform Interpolation Approach, which is low resource and allows for real-time applications, or the Frequency Domain Approach. These methods make use of aliasing in low-resolution images as well as the shifting property of the Fourier transform. Problems arise with both approaches, such as limited types of blurred images that can be used or creating non-optimal reconstructions. Many methods of super-resolution imaging use the Fourier transformation or wavelets but the field is still evolving for other wavelet techniques such as the Dual-Tree Discrete Wavelet Transform (DTDWT) or the Double-Density Discrete Wavelet Transform (DDDWT). In this paper, we propose a super-resolution method using these wavelet transformations for use in generating higher resolution imagery. We evaluate the performance and validity of our algorithm using several metrics, including Spearman Rank Order Correlation Coefficient (SROCC), Pearson's Linear Correlation Coefficient (PLCC), Structural Similarity Index Metric (SSIM), Root Mean Square Error (RMSE), and PeakSignal-Noise Ratio (PSNR). Initial results are promising, indicating that extensions of the wavelet transformations produce a more robust high resolution image when compared to traditional methods.