Effectively reconstructing 3D hyperspectral images (HSIs) from 2D measurements presents a significant challenge in Coded Aperture Snapshot Spectral Imaging (CASSI) systems. While recent transformers exhibit potential ...
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ISBN:
(数字)9798350368741
ISBN:
(纸本)9798350368758
Effectively reconstructing 3D hyperspectral images (HSIs) from 2D measurements presents a significant challenge in Coded Aperture Snapshot Spectral Imaging (CASSI) systems. While recent transformers exhibit potential in HSI reconstruction, they often suffer from inadequate exploration of multi-scale spatial-spectral self-similarity, leading to mean effects and information loss. Additionally, these methods struggle with insufficient modeling of the degradation inherent in the compressive imaging process. To address these issues, we propose a novel Mask-guided Multi-scale Spatial-Spectral Transformer (MMSST). Specifically, we introduce a Degradation Aware Mask Attention (DAMA) module to incorporate degradation information of the compressive imaging process. Furthermore, MMSST leverages Local-Regional SpAtial attention (LRSA) and Global-Regional SpEctral attention (GRSE) to effectively exploit multi-scale self-similarity across spatial and spectral dimensions. Extensive experimental results demonstrate the effectiveness of our MMSST.
The two-lane driven system is a type of important model to research some transport systems, and also a powerful tool to investigate properties of nonequilibrium state systems. This paper presents a driven bidirectiona...
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The two-lane driven system is a type of important model to research some transport systems, and also a powerful tool to investigate properties of nonequilibrium state systems. This paper presents a driven bidirectional two-lane model. The dynamic characteristics of the model with periodic boundary are investigated by Monte Carlo simulation, simple mean field, and cluster mean field methods, respectively. By simulations, phase separations are observed in the system with some values of model parameters. When the phase separation does not occur, cluster mean field results are in good agreement with simulation results. According to the cluster mean field analysis and simulations, a conjecture about the condition that the phase separation happens is proposed. Based on the conjecture, the phase boundary distinguishing phase separation state and homogeneous state is determined, and a corresponding phase diagram is drawn. The conjecture is validated through observing directly the spatiotemporal diagram and investigating the coarsening process of the system by simulation, and a possible mechanism causing the phase separation is also discussed. These outcomes maybe contribute to understand deeply transport systems including the congestion and efficiency of the transport, and enrich explorations of nonequilibrium state systems.
Recently, Dolbeault-Esteban-Figalli-Frank-Loss [20] established the optimal stability of the first-order Sobolev inequality with dimension-dependent constant. Subsequently, Chen-Lu-Tang [18] obtained the optimal stabi...
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Recently, Dolbeault-Esteban-Figalli-Frank-Loss [20] established the optimal stability of the first-order Sobolev inequality with dimension-dependent constant. Subsequently, Chen-Lu-Tang [18] obtained the optimal stability for the fractional Sobolev inequality of order s when 0 n2 unsolved. Furthermore, the optimal stability for Hardy-Littlewood-Soboblev (HLS) inequality still remains open although the authors in [17] have established the stability of the HLS inequality with the explicit lower bound. The purpose of this paper is to solve these problems. Our strategy is to first establish the optimal stability for the HLS inequality. The main difficulty lies in establishing the optimal local stability of HLS inequality when 1 n2 . The loss of the Hilbert structure of the distance appearing in the stability of the HLS inequality brings much challenge to establishing the desired stability. To achieve our goal, we develop a new strategy based on the H−s−decomposition instead of L n 2 +2 n s −decomposition to obtain the local stability of the HLS inequality with L n 2 +2 n s −distance. However, this kind of "new local stability" adds new difficulties to deduce the global stability from the local stability using the rearrangement flow because of the non-uniqueness and non-continuity of krk 2n for the rearrangement flow. We es-n+2s tablish the norm comparison theorem for krk 2n and "new continuity" theorem for the n+2s rearrangement flow to overcome this difficulty (see Lemma 3.1, Lemma 3.3 and Lemma 3.5). This method we develop here is particularly useful in dealing with the stability of our geometric inequalities here involving the non-Hilbertian distance. As an important application of the optimal stability of the HLS inequality together with the duality theory of the stability developed in [17], we deduce the optimal stability of the Sobolev inequality of order s when 1 ≤ s n2 with the dimension-dependent constants. As another application, we can derive the optimal stab
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