Exploring the Low-Pass Filtering Behavior in Image Super-Resolution

Deep neural networks for image super-resolution (ISR) have shown significant advantages over traditional approaches like the interpolation. However, they are often criticized as 'black boxes' compared to traditional approaches with solid mathematical foundations. In this paper, we attempt to interpret the behavior of deep neural networks in ISR using theories from the field of signal processing. First, we report an intriguing phenomenon, referred to as `the sinc phenomenon.' It occurs when an impulse input is fed to a neural network. Then, building on this observation, we propose a method named Hybrid Response Analysis (HyRA) to analyze the behavior of neural networks in ISR tasks. Specifically, HyRA decomposes a neural network into a parallel connection of a linear system and a non-linear system and demonstrates that the linear system functions as a low-pass filter while the non-linear system injects high-frequency information. Finally, to quantify the injected high-frequency information, we introduce a metric for image-to-image tasks called Frequency Spectrum Distribution Similarity (FSDS). FSDS reflects the distribution similarity of different frequency components and can capture nuances that traditional metrics may overlook. Code, videos and raw experimental results for this paper can be found in: https://github.com/RisingEntropy/LPFInISR.

Fourier-enhanced Implicit Neural Fusion Network for Multispectral and Hyperspectral Image Fusion

Recently, implicit neural representations (INR) have made significant strides in various vision-related domains, providing a novel solution for Multispectral and Hyperspectral Image Fusion (MHIF) tasks. However, INR is prone to losing high-frequency information and is confined to the lack of global perceptual capabilities. To address these issues, this paper introduces a Fourier-enhanced Implicit Neural Fusion Network (FeINFN) specifically designed for MHIF task, targeting the following phenomena: The Fourier amplitudes of the HR-HSI latent code and LR-HSI are remarkably similar; however, their phases exhibit different patterns. In FeINFN, we innovatively propose a spatial and frequency implicit fusion function (Spa-Fre IFF), helping INR capture high-frequency information and expanding the receptive field. Besides, a new decoder employing a complex Gabor wavelet activation function, called Spatial-Frequency Interactive Decoder (SFID), is invented to enhance the interaction of INR features. Especially, we further theoretically prove that the Gabor wavelet activation possesses a time-frequency tightness property that favors learning the optimal bandwidths in the decoder. Experiments on two benchmark MHIF datasets verify the state-of-the-art (SOTA) performance of the proposed method, both visually and quantitatively. Also, ablation studies demonstrate the mentioned contributions. The code will be available on Anonymous GitHub (https://anonymous.4open.science/r/FeINFN-15C9/) after possible acceptance.

Neural Shrödinger Bridge Matching for Pansharpening

Recent diffusion probabilistic models (DPM) in the field of pansharpening have been gradually gaining attention and have achieved state-of-the-art (SOTA) performance. In this paper, we identify shortcomings in directly applying DPMs to the task of pansharpening as an inverse problem: 1) initiating sampling directly from Gaussian noise neglects the low-resolution multispectral image (LRMS) as a prior; 2) low sampling efficiency often necessitates a higher number of sampling steps. We first reformulate pansharpening into the stochastic differential equation (SDE) form of an inverse problem. Building upon this, we propose a Schr\"odinger bridge matching method that addresses both issues. We design an efficient deep neural network architecture tailored for the proposed SB matching. In comparison to the well-established DL-regressive-based framework and the recent DPM framework, our method demonstrates SOTA performance with fewer sampling steps. Moreover, we discuss the relationship between SB matching and other methods based on SDEs and ordinary differential equations (ODEs), as well as its connection with optimal transport. Code will be available.

SSDiff: Spatial-spectral Integrated Diffusion Model for Remote Sensing Pansharpening

Pansharpening is a significant image fusion technique that merges the spatial content and spectral characteristics of remote sensing images to generate high-resolution multispectral images. Recently, denoising diffusion probabilistic models have been gradually applied to visual tasks, enhancing controllable image generation through low-rank adaptation (LoRA). In this paper, we introduce a spatial-spectral integrated diffusion model for the remote sensing pansharpening task, called SSDiff, which considers the pansharpening process as the fusion process of spatial and spectral components from the perspective of subspace decomposition. Specifically, SSDiff utilizes spatial and spectral branches to learn spatial details and spectral features separately, then employs a designed alternating projection fusion module (APFM) to accomplish the fusion. Furthermore, we propose a frequency modulation inter-branch module (FMIM) to modulate the frequency distribution between branches. The two components of SSDiff can perform favorably against the APFM when utilizing a LoRA-like branch-wise alternative fine-tuning method. It refines SSDiff to capture component-discriminating features more sufficiently. Finally, extensive experiments on four commonly used datasets, i.e., WorldView-3, WorldView-2, GaoFen-2, and QuickBird, demonstrate the superiority of SSDiff both visually and quantitatively. The code will be made open source after possible acceptance.

A Novel State Space Model with Local Enhancement and State Sharing for Image Fusion

In image fusion tasks, images from different sources possess distinct characteristics. This has driven the development of numerous methods to explore better ways of fusing them while preserving their respective characteristics. Mamba, as a state space model, has emerged in the field of natural language processing. Recently, many studies have attempted to extend Mamba to vision tasks. However, due to the nature of images different from casual language sequences, the limited state capacity of Mamba weakens its ability to model image information. Additionally, the sequence modeling ability of Mamba is only capable of spatial information and cannot effectively capture the rich spectral information in images. Motivated by these challenges, we customize and improve the vision Mamba network designed for the image fusion task. Specifically, we propose the local-enhanced vision Mamba block, dubbed as LEVM. The LEVM block can improve local information perception of the network and simultaneously learn local and global spatial information. Furthermore, we propose the state sharing technique to enhance spatial details and integrate spatial and spectral information. Finally, the overall network is a multi-scale structure based on vision Mamba, called LE-Mamba. Extensive experiments show the proposed methods achieve state-of-the-art results on multispectral pansharpening and multispectral and hyperspectral image fusion datasets, and demonstrate the effectiveness of the proposed approach. Code will be made available.

Content-Adaptive Non-Local Convolution for Remote Sensing Pansharpening

Currently, machine learning-based methods for remote sensing pansharpening have progressed rapidly. However, existing pansharpening methods often do not fully exploit differentiating regional information in non-local spaces, thereby limiting the effectiveness of the methods and resulting in redundant learning parameters. In this paper, we introduce a so-called content-adaptive non-local convolution (CANConv), a novel method tailored for remote sensing image pansharpening. Specifically, CANConv employs adaptive convolution, ensuring spatial adaptability, and incorporates non-local self-similarity through the similarity relationship partition (SRP) and the partition-wise adaptive convolution (PWAC) sub-modules. Furthermore, we also propose a corresponding network architecture, called CANNet, which mainly utilizes the multi-scale self-similarity. Extensive experiments demonstrate the superior performance of CANConv, compared with recent promising fusion methods. Besides, we substantiate the method's effectiveness through visualization, ablation experiments, and comparison with existing methods on multiple test sets. The source code is publicly available at https://github.com/duanyll/CANConv.

FusionMamba: Efficient Image Fusion with State Space Model

Image fusion aims to generate a high-resolution multi/hyper-spectral image by combining a high-resolution image with limited spectral information and a low-resolution image with abundant spectral data. Current deep learning (DL)-based methods for image fusion primarily rely on CNNs or Transformers to extract features and merge different types of data. While CNNs are efficient, their receptive fields are limited, restricting their capacity to capture global context. Conversely, Transformers excel at learning global information but are hindered by their quadratic complexity. Fortunately, recent advancements in the State Space Model (SSM), particularly Mamba, offer a promising solution to this issue by enabling global awareness with linear complexity. However, there have been few attempts to explore the potential of SSM in information fusion, which is a crucial ability in domains like image fusion. Therefore, we propose FusionMamba, an innovative method for efficient image fusion. Our contributions mainly focus on two aspects. Firstly, recognizing that images from different sources possess distinct properties, we incorporate Mamba blocks into two U-shaped networks, presenting a novel architecture that extracts spatial and spectral features in an efficient, independent, and hierarchical manner. Secondly, to effectively combine spatial and spectral information, we extend the Mamba block to accommodate dual inputs. This expansion leads to the creation of a new module called the FusionMamba block, which outperforms existing fusion techniques such as concatenation and cross-attention. To validate FusionMamba's effectiveness, we conduct a series of experiments on five datasets related to three image fusion tasks. The quantitative and qualitative evaluation results demonstrate that our method achieves state-of-the-art (SOTA) performance, underscoring the superiority of FusionMamba.

CMT: Cross Modulation Transformer with Hybrid Loss for Pansharpening

Pansharpening aims to enhance remote sensing image (RSI) quality by merging high-resolution panchromatic (PAN) with multispectral (MS) images. However, prior techniques struggled to optimally fuse PAN and MS images for enhanced spatial and spectral information, due to a lack of a systematic framework capable of effectively coordinating their individual strengths. In response, we present the Cross Modulation Transformer (CMT), a pioneering method that modifies the attention mechanism. This approach utilizes a robust modulation technique from signal processing, integrating it into the attention mechanism's calculations. It dynamically tunes the weights of the carrier's value (V) matrix according to the modulator's features, thus resolving historical challenges and achieving a seamless integration of spatial and spectral attributes. Furthermore, considering that RSI exhibits large-scale features and edge details along with local textures, we crafted a hybrid loss function that combines Fourier and wavelet transforms to effectively capture these characteristics, thereby enhancing both spatial and spectral accuracy in pansharpening. Extensive experiments demonstrate our framework's superior performance over existing state-of-the-art methods. The code will be publicly available to encourage further research.

APLA: Additional Perturbation for Latent Noise with Adversarial Training Enables Consistency

Diffusion models have exhibited promising progress in video generation. However, they often struggle to retain consistent details within local regions across frames. One underlying cause is that traditional diffusion models approximate Gaussian noise distribution by utilizing predictive noise, without fully accounting for the impact of inherent information within the input itself. Additionally, these models emphasize the distinction between predictions and references, neglecting information intrinsic to the videos. To address this limitation, inspired by the self-attention mechanism, we propose a novel text-to-video (T2V) generation network structure based on diffusion models, dubbed Additional Perturbation for Latent noise with Adversarial training (APLA). Our approach only necessitates a single video as input and builds upon pre-trained stable diffusion networks. Notably, we introduce an additional compact network, known as the Video Generation Transformer (VGT). This auxiliary component is designed to extract perturbations from the inherent information contained within the input, thereby refining inconsistent pixels during temporal predictions. We leverage a hybrid architecture of transformers and convolutions to compensate for temporal intricacies, enhancing consistency between different frames within the video. Experiments demonstrate a noticeable improvement in the consistency of the generated videos both qualitatively and quantitatively.

A Theoretically Guaranteed Quaternion Weighted Schatten p-norm Minimization Method for Color Image Restoration

Inspired by the fact that the matrix formulated by nonlocal similar patches in a natural image is of low rank, the rank approximation issue have been extensively investigated over the past decades, among which weighted nuclear norm minimization (WNNM) and weighted Schatten $p$-norm minimization (WSNM) are two prevailing methods have shown great superiority in various image restoration (IR) problems. Due to the physical characteristic of color images, color image restoration (CIR) is often a much more difficult task than its grayscale image counterpart. However, when applied to CIR, the traditional WNNM/WSNM method only processes three color channels individually and fails to consider their cross-channel correlations. Very recently, a quaternion-based WNNM approach (QWNNM) has been developed to mitigate this issue, which is capable of representing the color image as a whole in the quaternion domain and preserving the inherent correlation among the three color channels. Despite its empirical success, unfortunately, the convergence behavior of QWNNM has not been strictly studied yet. In this paper, on the one side, we extend the WSNM into quaternion domain and correspondingly propose a novel quaternion-based WSNM model (QWSNM) for tackling the CIR problems. Extensive experiments on two representative CIR tasks, including color image denoising and deblurring, demonstrate that the proposed QWSNM method performs favorably against many state-of-the-art alternatives, in both quantitative and qualitative evaluations. On the other side, more importantly, we preliminarily provide a theoretical convergence analysis, that is, by modifying the quaternion alternating direction method of multipliers (QADMM) through a simple continuation strategy, we theoretically prove that both the solution sequences generated by the QWNNM and QWSNM have fixed-point convergence guarantees.