An improved PDE-constrained optimization fluid registration for image multi-frame super resolution

Abstract

The main idea of multi-frame super resolution (SR) algorithms is to recover a single high-resolution image from a sequence of low resolution ones of the same object. The success of the SR approaches is often related to a well registration and restoration steps. Therefore, we propose a new approach based on a partial differential equation (PDE)-constrained optimization fluid image registration and we use a fourth order PDE to treat both the registration and restoration steps that guarantee the success of SR algorithms. Since the registration step is usually a variational ill-posed model, a mathematical study is needed to check the existence of the solution to the regularized problem. Thus, we prove the existence and of the well posed fluid image registration and assure also the existence of the used second order PDE in the restoration step. The results show that the proposed method is competitive with the existing methods.

Enhancing deblurring through optimal controlled bilevel with nonlocal weighted model

“…Proof. By taking a minimizing sequence (X j ) j∈N for (23) and considering X j (x) to be the image at pixel position x, then there exist three non-negative constants denoted by M 1 , M 2 and M 3 verifying:…”

“…For instance, Tikhonov regularization [34] is commonly used and can be implemented as a one-step filter using Fourier transform in the case of image deconvolution. However, this approach often amplifies high frequencies where noise is prominent, leading to suboptimal results, and Total Variation (TV) is widely applied in various image processing applications, such as blind deconvolution [3,25], inpainting [11], and super-resolution [29,23], due to its ability to preserve edges. However, total variation based methods often fail to retain fine structures, intricate details, and textures present in the original image [26,27].…”

Learning nonlocal weights for second-order nonlocal super-resolution

“…It restricts the inter-frame motion to be translational because the discrete Fourier transform assumes uniformly spaced samples, another drawback is that the considered prior knowledge is frequently difficult to express in the frequency domain. • The spatial domain on the other hand, which is discussed in [29,20,28] makes it possible to integrate priors on the image.…”