Kalman Filtering of Stationary Graph Signals

In this paper, we propose a novel definition of stationary graph signals, formulated with respect to a symmetric graph shift, such as the graph Laplacian. We show that stationary graph signals can be generated by transmitting white noise through polynomial graph channels, and that their stationarity is preserved under polynomial channel transmission. In this paper, we also investigate Kalman filtering to dynamical systems characterized by polynomial state and observation matrices. We demonstrate that Kalman filtering maintains the stationarity of graph signals, while effectively incorporating both system dynamics and noise structure. In comparison to the static inverse filtering method and naive zero-signal strategy, the Kalman filtering procedure yields more accurate and adaptive signal estimates, highlighting its robustness and versatility in graph signal processing.

Blind Deconvolution of Nonstationary Graph Signals over Shift-Invariant Channels

In this paper, we investigate blind deconvolution of nonstationary graph signals from noisy observations, transmitted through an unknown shift-invariant channel. The deconvolution process assumes that the observer has access to the covariance structure of the original graph signals. To evaluate the effectiveness of our channel estimation and blind deconvolution method, we conduct numerical experiments using a temperature dataset in the Brest region of France.

Iterative Polynomial Approximation Algorithms for Inverse Graph Filters

Chebyshev interpolation polynomials exhibit the exponential approximation property to analytic functions on a cube. Based on the Chebyshev interpolation polynomial approximation, we propose iterative polynomial approximation algorithms to implement the inverse filter with a polynomial graph filter of commutative graph shifts in a distributed manner. The proposed algorithms exhibit exponential convergence properties, and they can be implemented on distributed networks in which agents are equipped with a data processing subsystem for limited data storage and computation power, and with a one-hop communication subsystem for direct data exchange only with their adjacent agents. Our simulations show that the proposed polynomial approximation algorithms may converge faster than the Chebyshev polynomial approximation algorithm and the conventional gradient descent algorithm do.

Causal Learning for Heterogeneous Subgroups Based on Nonlinear Causal Kernel Clustering

Due to the challenge posed by multi-source and heterogeneous data collected from diverse environments, causal relationships among features can exhibit variations influenced by different time spans, regions, or strategies. This diversity makes a single causal model inadequate for accurately representing complex causal relationships in all observational data, a crucial consideration in causal learning. To address this challenge, we introduce the nonlinear Causal Kernel Clustering method designed for heterogeneous subgroup causal learning, illuminating variations in causal relationships across diverse subgroups. It comprises two primary components. First, the construction of a sample mapping function forms the basis of the subsequent nonlinear causal kernel. This function assesses the differences in potential nonlinear causal relationships in various samples, supported by our causal identifiability theory. Second, a nonlinear causal kernel is proposed for clustering heterogeneous subgroups. Experimental results showcase the exceptional performance of our method in accurately identifying heterogeneous subgroups and effectively enhancing causal learning, leading to a great reduction in prediction error.

Shift-invariant spaces, bandlimited spaces and reproducing kernel spaces with shift-invariant kernels on undirected finite graphs

In this paper, we introduce the concept of graph shift-invariant space (GSIS) on an undirected finite graph, which is the linear space of graph signals being invariant under graph shifts, and we study its bandlimiting, kernel reproducing and sampling properties. Graph bandlimited spaces have been widely applied where large datasets on networks need to be handled efficiently. In this paper, we show that every GSIS is a bandlimited space, and every bandlimited space is a principal GSIS. Functions in a reproducing kernel Hilbert space with shift-invariant kernel could be learnt with significantly low computational cost. In this paper, we demonstrate that every GSIS is a reproducing kernel Hilbert space with a shift-invariant kernel. Based on the nested Krylov structure of GSISs in the spatial domain, we propose a novel sampling and reconstruction algorithm with finite steps, with its performance tested for well-localized signals on circulant graphs and flight delay dataset of the 50 busiest airports in the USA.

Computer vision tasks for intelligent aerospace missions: An overview

Computer vision tasks are crucial for aerospace missions as they help spacecraft to understand and interpret the space environment, such as estimating position and orientation, reconstructing 3D models, and recognizing objects, which have been extensively studied to successfully carry out the missions. However, traditional methods like Kalman Filtering, Structure from Motion, and Multi-View Stereo are not robust enough to handle harsh conditions, leading to unreliable results. In recent years, deep learning (DL)-based perception technologies have shown great potential and outperformed traditional methods, especially in terms of their robustness to changing environments. To further advance DL-based aerospace perception, various frameworks, datasets, and strategies have been proposed, indicating significant potential for future applications. In this survey, we aim to explore the promising techniques used in perception tasks and emphasize the importance of DL-based aerospace perception. We begin by providing an overview of aerospace perception, including classical space programs developed in recent years, commonly used sensors, and traditional perception methods. Subsequently, we delve into three fundamental perception tasks in aerospace missions: pose estimation, 3D reconstruction, and recognition, as they are basic and crucial for subsequent decision-making and control. Finally, we discuss the limitations and possibilities in current research and provide an outlook on future developments, including the challenges of working with limited datasets, the need for improved algorithms, and the potential benefits of multi-source information fusion.

Scalable Networked Feature Selection with Randomized Algorithm for Robot Navigation

We address the problem of sparse selection of visual features for localizing a team of robots navigating an unknown environment, where robots can exchange relative position measurements with neighbors. We select a set of the most informative features by anticipating their importance in robots localization by simulating trajectories of robots over a prediction horizon. Through theoretical proofs, we establish a crucial connection between graph Laplacian and the importance of features. We show that strong network connectivity translates to uniformity in feature importance, which enables uniform random sampling of features and reduces the overall computational complexity. We leverage a scalable randomized algorithm for sparse sums of positive semidefinite matrices to efficiently select the set of the most informative features and significantly improve the probabilistic performance bounds. Finally, we support our findings with extensive simulations.

Barron Space for Graph Convolution Neural Networks

Graph convolutional neural network (GCNN) operates on graph domain and it has achieved a superior performance to accomplish a wide range of tasks. In this paper, we introduce a Barron space of functions on a compact domain of graph signals. We prove that the proposed Barron space is a reproducing kernel Banach space, it can be decomposed into the union of a family of reproducing kernel Hilbert spaces with neuron kernels, and it could be dense in the space of continuous functions on the domain. Approximation property is one of the main principles to design neural networks. In this paper, we show that outputs of GCNNs are contained in the Barron space and functions in the Barron space can be well approximated by outputs of some GCNNs in the integrated square and uniform measurements. We also estimate the Rademacher complexity of functions with bounded Barron norm and conclude that functions in the Barron space could be learnt from their random samples efficiently.

GasMono: Geometry-Aided Self-Supervised Monocular Depth Estimation for Indoor Scenes

This paper tackles the challenges of self-supervised monocular depth estimation in indoor scenes caused by large rotation between frames and low texture. We ease the learning process by obtaining coarse camera poses from monocular sequences through multi-view geometry to deal with the former. However, we found that limited by the scale ambiguity across different scenes in the training dataset, a na\"ive introduction of geometric coarse poses cannot play a positive role in performance improvement, which is counter-intuitive. To address this problem, we propose to refine those poses during training through rotation and translation/scale optimization. To soften the effect of the low texture, we combine the global reasoning of vision transformers with an overfitting-aware, iterative self-distillation mechanism, providing more accurate depth guidance coming from the network itself. Experiments on NYUv2, ScanNet, 7scenes, and KITTI datasets support the effectiveness of each component in our framework, which sets a new state-of-the-art for indoor self-supervised monocular depth estimation, as well as outstanding generalization ability. Code and models are available at https://github.com/zxcqlf/GasMono

IBAFormer: Intra-batch Attention Transformer for Domain Generalized Semantic Segmentation

Domain generalized semantic segmentation (DGSS) is a critical yet challenging task, where the model is trained only on source data without access to any target data. Despite the proposal of numerous DGSS strategies, the generalization capability remains limited in CNN architectures. Though some Transformer-based segmentation models show promising performance, they primarily focus on capturing intra-sample attentive relationships, disregarding inter-sample correlations which can potentially benefit DGSS. To this end, we enhance the attention modules in Transformer networks for improving DGSS by incorporating information from other independent samples in the same batch, enriching contextual information, and diversifying the training data for each attention block. Specifically, we propose two alternative intra-batch attention mechanisms, namely mean-based intra-batch attention (MIBA) and element-wise intra-batch attention (EIBA), to capture correlations between different samples, enhancing feature representation and generalization capabilities. Building upon intra-batch attention, we introduce IBAFormer, which integrates self-attention modules with the proposed intra-batch attention for DGSS. Extensive experiments demonstrate that IBAFormer achieves SOTA performance in DGSS, and ablation studies further confirm the effectiveness of each introduced component.