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Zakariya Chaouai

Publications and source records attributed to Zakariya Chaouai.

3 recordsLinked to original sources

Universal Robustness via Median Randomized Smoothing for Real-World Super-Resolution

Most of the recent literature on image Super-Resolution (SR) can be classified into two main approaches. The first one involves learning a corruption model tailored to a specific dataset, aiming to mimic the noise and corruption in low-resolution images, such as sensor noise. However, this approach is data-specific, tends to lack adaptability, and its accuracy diminishes when faced with unseen types of image corruptions. A second and more recent approach, referred to as Robust Super-Resolution (RSR), proposes to improve real-world SR by harnessing the generalization capabilities of a model by making it robust to adversarial attacks. To delve further into this second approach, our paper explores the universality of various methods for enhancing the robustness of deep learning SR models. In other words, we inquire: "Which robustness method exhibits the highest degree of adaptability when dealing with a wide range of adversarial attacks ?". Our extensive experimentation on both synthetic and real-world images empirically demonstrates that median randomized smoothing (MRS) is more general in terms of robustness compared to adversarial learning techniques, which tend to focus on specific types of attacks. Furthermore, as expected, we also illustrate that the proposed universal robust method enables the SR model to handle standard corruptions more effectively, such as blur and Gaussian noise, and notably, corruptions naturally present in real-world images. These results support the significance of shifting the paradigm in the development of real-world SR methods towards RSR, especially via MRS.

eess.IV↗

A priori bounds and multiplicity results for slightly superlinear and sublinear elliptic p-Laplacian equations

We consider the following problem $ -Δ_{p}u= h(x,u) \mbox{ in }Ω$, $u\in W^{1,p}_{0}(Ω)$, where $Ω$ is a bounded domain in $\mathbb{R}^{N}$, $1 \frac{N}{p}$ and they are without sign condition. Firstly, we show a priori bound on solutions, then by using variational arguments, we prove the existence of at least two nonnegative solutions. One of the main difficulties is that the nonlinearity term $h(x,u)$ does not satisfy the standard Ambrosetti and Rabinowitz condition.

math.AP↗

Multiplicity of solutions for a class of elliptic problem of $p$-Laplacian type with a $p$-Gradient term

We consider the following problem $$(P) \begin{cases} -Δ_{p}u= c(x)|u|^{q-1}u+μ|\nabla u|^{p}+h(x) & \ \ \mbox{ in }Ω, u=0 & \ \ \mbox{ on } \partialΩ, \end{cases}$$ where $Ω$ is a bounded set in $\mathbb{R}^{N}$ ($N\geq 3$) with a smooth boundary, $1 0$, $μ\in \mathbb{R}^{*}$, and $c$ and $ h$ belong to $L^{k}(Ω)$ for some $k>\frac{N}{p}$. In this paper, we assume that $c\gneqq 0$ a.e. in $Ω$ and $h$ without sign condition, then we prove the existence of at least two bounded solutions under the condition that $\|c\|_{k}$ and $\|h\|_{k}$ are suitably small. For this purpose, we use the Mountain Pass theorem, on an equivalent problem to $(P)$ with variational structure. Here, the main difficulty is that the nonlinearity term considered does not satisfy Ambrosetti and Rabinowitz condition. The key idea is to replace the former condition by the \textbf{nonquadraticity condition at infinity}.

math.AP↗