arXiv subjects

Gene Cheung

Publications and source records attributed to Gene Cheung.

At least 19 recordsLinked to original sources

arXiv2026

Low-rank Updates in Slowly Time-varying Graphs for Spatial-Temporal Signal Interpolation

A crucial assumption in graph signal processing (GSP) is the existence of an underlying graph that captures the pairwise similarities between nodes, allowing filters to be designed based on this graph for tasks such as denoising. For spatial-temporal data in which node-to-node similarities evolve over time, a static spatial graph is insufficient. In this paper, to represent slowly time-varying pairwise relationships, we model the graph changes in two consecutive adjacency matrices $P = W^{(2)} - W^{(1)}$ across time as a low-rank matrix. % Specifically, given an initial adjacency matrix $W^{(1)}$ at time $t=1$, we jointly interpolate a signal $x_2$ and estimate $W^{(2)}$ at $t=2$ using both a graph signal smoothness prior for $x_2$ and a low-rank prior on $\P$. We alternate optimization steps. With $W^{(2)}$ fixed, $x_2$ is interpolated by solving a linear system. Alternatively, holding $x_2$ fixed, $W^{(2)}$ is updated via proximal gradient descent (PGD). The proximal mapping of the rank term $Gamma(W^{(2)} - W^{(1)})$ is approximated in linear time using a fast orthogonal matching pursuit (OMP) algorithm that selects a sparse combination of atoms from a dictionary $cR$ formed by the outer products of $W^{(1)}$'s eigenvectors. We unroll iterations of our algorithm into layers to build a lightweight neural network for limited data-driven parameter tuning. Experiments show that our joint optimization achieves better signal interpolation compared to existing time-varying graph models.

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arXiv2026

Sparse Graph Learning from Sparse Data via Fiedler Number Maximization

We aim to learn a sparse and connected graph from sparse data, where the number of observations K can be substantially smaller than the signal dimension N for signals x in R^N, and the underlying distribution is unknown. In this severely ill-posed setting, we incorporate Fiedler number (the second eigenvalue of the graph Laplacian matrix that quantifies connectedness) as a robust regularization term in the sparse graph learning objective. We first develop a greedy algorithm that iteratively selects one edge globally for weakening/removal to reduce the objective, leveraging eigenvalue perturbation theorems that bound the adverse effect of an edge change to the Fiedler number. Next, we design a parallel variant, based on the Cheeger's inequality, that recursively partitions an input graph into two sub-graphs using an approximate Cheeger cut to distributedly find an optimal edge. Simulation experiments show that Fiedler number maximization robustifies sparse graph estimates, outperforming previous sparse graph learning algorithms.

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arXiv2025

Lightweight Transformer for EEG Classification via Balanced Signed Graph Algorithm Unrolling

Samples of brain signals collected by EEG sensors have inherent anti-correlations that are well modeled by negative edges in a finite graph. To differentiate epilepsy patients from healthy subjects using collected EEG signals, we build lightweight and interpretable transformer-like neural nets by unrolling a spectral denoising algorithm for signals on a balanced signed graph -- graph with no cycles of odd number of negative edges. A balanced signed graph has well-defined frequencies that map to a corresponding positive graph via similarity transform of the graph Laplacian matrices. We implement an ideal low-pass filter efficiently on the mapped positive graph via Lanczos approximation, where the optimal cutoff frequency is learned from data. Given that two balanced signed graph denoisers learn posterior probabilities of two different signal classes during training, we evaluate their reconstruction errors for binary classification of EEG signals. Experiments show that our method achieves classification performance comparable to representative deep learning schemes, while employing dramatically fewer parameters.

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arXiv2025

Unrolling Graph-based Douglas-Rachford Algorithm for Image Interpolation with Informed Initialization

Conventional deep neural nets (DNNs) initialize network parameters at random and then optimize each one via stochastic gradient descent (SGD), resulting in substantial risk of poor-performing local minima. Focusing on image interpolation and leveraging a recent theorem that maps a (pseudo-)linear interpolator {\Theta} to a directed graph filter that is a solution to a corresponding MAP problem with a graph shift variation (GSV) prior, we first initialize a directed graph adjacency matrix A given a known interpolator {\Theta}, establishing a baseline performance. Then, towards further gain, we learn perturbation matrices P and P(2) from data to augment A, whose restoration effects are implemented progressively via Douglas-Rachford (DR) iterations, which we unroll into a lightweight and interpretable neural net. Experiments on different image interpolation scenarios demonstrate state-of-the-art performance, while drastically reducing network parameters and inference complexity.

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arXiv2025

Deep Unrolling of Sparsity-Induced RDO for 3D Point Cloud Attribute Coding

Given encoded 3D point cloud geometry available at the decoder, we study the problem of lossy attribute compression in a multi-resolution B-spline projection framework. A target continuous 3D attribute function is first projected onto a sequence of nested subspaces $\mathcal{F}^{(p)}_{l_0} \subseteq \cdots \subseteq \mathcal{F}^{(p)}_{L}$, where $\mathcal{F}^{(p)}_{l}$ is a family of functions spanned by a B-spline basis function of order $p$ at a chosen scale and its integer shifts. The projected low-pass coefficients $F_l^*$ are computed by variable-complexity unrolling of a rate-distortion (RD) optimization algorithm into a feed-forward network, where the rate term is the sparsity-promoting $\ell_1$-norm. Thus, the projection operation is end-to-end differentiable. For a chosen coarse-to-fine predictor, the coefficients are then adjusted to account for the prediction from a lower-resolution to a higher-resolution, which is also optimized in a data-driven manner.

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arXiv2025

Unrolling Nonconvex Graph Total Variation for Image Denoising

Conventional model-based image denoising optimizations employ convex regularization terms, such as total variation (TV) that convexifies the $\ell_0$-norm to promote sparse signal representation. Instead, we propose a new non-convex total variation term in a graph setting (NC-GTV), such that when combined with an $\ell_2$-norm fidelity term for denoising, leads to a convex objective with no extraneous local minima. We define NC-GTV using a new graph variant of the Huber function, interpretable as a Moreau envelope. The crux is the selection of a parameter $a$ characterizing the graph Huber function that ensures overall objective convexity; we efficiently compute $a$ via an adaptation of Gershgorin Circle Theorem (GCT). To minimize the convex objective, we design a linear-time algorithm based on Alternating Direction Method of Multipliers (ADMM) and unroll it into a lightweight feed-forward network for data-driven parameter learning. Experiments show that our method outperforms unrolled GTV and other representative image denoising schemes, while employing far fewer network parameters.

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arXiv2025

Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming

Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph is a signed graph with no cycles containing an odd number of negative edges. Laplacian of a balanced signed graph has eigenvectors that map via a simple linear transform to ones in a corresponding positive graph Laplacian, thus enabling reuse of spectral filtering tools designed for positive graphs. We propose an efficient computation method to learn a balanced signed graph Laplacian directly from data. Specifically, extending a previous linear programming (LP) based sparse inverse covariance estimation method called CLIME, we formulate a new LP problem for each Laplacian column $i$, where the linear constraints restrict weight signs of edges stemming from node $i$, so that nodes of same / different polarities are connected by positive / negative edges. We derive a feasible CLIME parameter $\rho_i$ for each sign-constrained column problem. We solve the LP problem efficiently by tailoring a sparse LP method based on ADMM. We theoretically prove that the row / column updates produce a non-increasing objective sequence, and show that the iterations are terminated in a finite number of steps. Extensive experimental results on synthetic and real-world datasets show that our balanced graph learning method outperforms competing methods and enables reuse of spectral filters, wavelets, and graph neural nets (GNN) constructed for positive graphs.

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arXiv2025

Lightweight and Interpretable Transformer via Mixed Graph Algorithm Unrolling for Traffic Forecast

Unlike conventional "black-box" transformers with classical self-attention mechanism, we build a lightweight and interpretable transformer-like neural net by unrolling a mixed-graph-based optimization algorithm to forecast traffic with spatial and temporal dimensions. We construct two graphs: an undirected graph $\mathcal{G}^u$ capturing spatial correlations across geography, and a directed graph $\mathcal{G}^d$ capturing sequential relationships over time. We predict future samples of signal $\mathbf{x}$, assuming it is "smooth" with respect to both $\mathcal{G}^u$ and $\mathcal{G}^d$, where we design new $\ell_2$ and $\ell_1$-norm variational terms to quantify and promote signal smoothness (low-frequency reconstruction) on a directed graph. We design an iterative algorithm based on alternating direction method of multipliers (ADMM), and unroll it into a feed-forward network for data-driven parameter learning. We periodically insert graph learning modules for $\mathcal{G}^u$ and $\mathcal{G}^d$ that play the role of self-attention. Experiments show that our unrolled networks achieve competitive traffic forecast performance as state-of-the-art prediction schemes, while reducing parameter counts drastically.

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arXiv2024

Efficient Learning of Balanced Signed Graphs via Iterative Linear Programming

Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph has no cycles of odd number of negative edges. Laplacian of a balanced signed graph has eigenvectors that map simply to ones in a similarity-transformed positive graph Laplacian, thus enabling reuse of well-studied spectral filters designed for positive graphs. We propose a fast method to learn a balanced signed graph Laplacian directly from data. Specifically, for each node $i$, to determine its polarity $\beta_i \in \{-1,1\}$ and edge weights $\{w_{i,j}\}_{j=1}^N$, we extend a sparse inverse covariance formulation based on linear programming (LP) called CLIME, by adding linear constraints to enforce ``consistent" signs of edge weights $\{w_{i,j}\}_{j=1}^N$ with the polarities of connected nodes -- i.e., positive/negative edges connect nodes of same/opposing polarities. For each LP, we adapt projections on convex set (POCS) to determine a suitable CLIME parameter $\rho > 0$ that guarantees LP feasibility. We solve the resulting LP via an off-the-shelf LP solver in $\mathcal{O}(N^{2.055})$. Experiments on synthetic and real-world datasets show that our balanced graph learning method outperforms competing methods and enables the use of spectral filters and graph convolutional networks (GCNs) designed for positive graphs on signed graphs.

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arXiv2024

Constructing an Interpretable Deep Denoiser by Unrolling Graph Laplacian Regularizer

An image denoiser can be used for a wide range of restoration problems via the Plug-and-Play (PnP) architecture. In this paper, we propose a general framework to build an interpretable graph-based deep denoiser (GDD) by unrolling a solution to a maximum a posteriori (MAP) problem equipped with a graph Laplacian regularizer (GLR) as signal prior. Leveraging a recent theorem showing that any (pseudo-)linear denoiser $\boldsymbol \Psi$, under mild conditions, can be mapped to a solution of a MAP denoising problem regularized using GLR, we first initialize a graph Laplacian matrix $\mathbf L$ via truncated Taylor Series Expansion (TSE) of $\boldsymbol \Psi^{-1}$. Then, we compute the MAP linear system solution by unrolling iterations of the conjugate gradient (CG) algorithm into a sequence of neural layers as a feed-forward network -- one that is amenable to parameter tuning. The resulting GDD network is "graph-interpretable", low in parameter count, and easy to initialize thanks to $\mathbf L$ derived from a known well-performing denoiser $\boldsymbol \Psi$. Experimental results show that GDD achieves competitive image denoising performance compared to competitors, but employing far fewer parameters, and is more robust to covariate shift.

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arXiv2024

Graph Unfolding and Sampling for Transitory Video Keyframe Selection via Gershgorin Disc Alignment

User-generated videos (UGVs) uploaded from mobile phones to social media sites like YouTube and TikTok are short and non-repetitive. We summarize a transitory UGV into several keyframes in linear-time via fast graph sampling based on Gershgorin disc alignment (GDA). Specifically, we first model a sequence of $N$ frames in a UGV as an $M$-hop path graph $\cG^o$ for $M \ll N$, where the similarity between two frames within $M$ time instants is encoded as a positive edge based on feature similarity. Towards efficient sampling, we then ``unfold'' $\cG^o$ to a $1$-hop path graph $\cG$, specified by a generalized graph Laplacian matrix $\cL$, via one of two graph unfolding procedures with provable performance bounds. We show that maximizing the smallest eigenvalue $\lambda_{\min}(\B)$ of a coefficient matrix $\B = \diag{\h} + \mu \cL$, where $\h$ is the binary keyframe selection vector, is equivalent to minimizing a worst-case signal reconstruction error. We maximize instead the Gershgorin circle theorem (GCT) lower bound $\lambda^-_{\min}(\B)$ by choosing $\h$ via a new fast graph sampling algorithm that iteratively aligns left-ends of Gershgorin discs for all graph nodes (frames). Experiments on multiple short video datasets show that our algorithm achieves comparable or better keyframe selection performance compared to state-of-the-art methods, at a substantially reduced complexity.

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arXiv2024

Unrolling Plug-and-Play Gradient Graph Laplacian Regularizer for Image Restoration

Generic deep learning (DL) networks for image restoration like denoising and interpolation lack mathematical interpretability, require voluminous training data to tune a large parameter set, and are fragile in the face of covariate shift. To address these shortcomings, we build interpretable networks by unrolling variants of a graph-based optimization algorithm of different complexities. Specifically, for a general linear image formation model, we first formulate a convex quadratic programming (QP) problem with a new $\ell_2$-norm graph smoothness prior called gradient graph Laplacian regularizer (GGLR) that promotes piecewise planar (PWP) signal reconstruction. To solve the posed unconstrained QP problem, instead of computing a linear system solution straightforwardly, we introduce a variable number of auxiliary variables and correspondingly design a family of ADMM algorithms. We then unroll them into variable-complexity feed-forward networks, amenable to parameter tuning via back-propagation. More complex unrolled networks require more labeled data to train more parameters, but have better overall performance. The unrolled networks have periodic insertions of a graph learning module, akin to a self-attention mechanism in a transformer architecture, to learn pairwise similarity structure inherent in data. Experimental results show that our unrolled networks perform competitively to generic DL networks in image restoration quality while using only a fraction of parameters, and demonstrate improved robustness to covariate shift.

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arXiv2024

Interpretable Lightweight Transformer via Unrolling of Learned Graph Smoothness Priors

We build interpretable and lightweight transformer-like neural networks by unrolling iterative optimization algorithms that minimize graph smoothness priors -- the quadratic graph Laplacian regularizer (GLR) and the $\ell_1$-norm graph total variation (GTV) -- subject to an interpolation constraint. The crucial insight is that a normalized signal-dependent graph learning module amounts to a variant of the basic self-attention mechanism in conventional transformers. Unlike "black-box" transformers that require learning of large key, query and value matrices to compute scaled dot products as affinities and subsequent output embeddings, resulting in huge parameter sets, our unrolled networks employ shallow CNNs to learn low-dimensional features per node to establish pairwise Mahalanobis distances and construct sparse similarity graphs. At each layer, given a learned graph, the target interpolated signal is simply a low-pass filtered output derived from the minimization of an assumed graph smoothness prior, leading to a dramatic reduction in parameter count. Experiments for two image interpolation applications verify the restoration performance, parameter efficiency and robustness to covariate shift of our graph-based unrolled networks compared to conventional transformers.

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arXiv2024

Signal Processing in the Retina: Interpretable Graph Classifier to Predict Ganglion Cell Responses

It is a popular hypothesis in neuroscience that ganglion cells in the retina are activated by selectively detecting visual features in an observed scene. While ganglion cell firings can be predicted via data-trained deep neural nets, the networks remain indecipherable, thus providing little understanding of the cells' underlying operations. To extract knowledge from the cell firings, in this paper we learn an interpretable graph-based classifier from data to predict the firings of ganglion cells in response to visual stimuli. Specifically, we learn a positive semi-definite (PSD) metric matrix $\mathbf{M} \succeq 0$ that defines Mahalanobis distances between graph nodes (visual events) endowed with pre-computed feature vectors; the computed inter-node distances lead to edge weights and a combinatorial graph that is amenable to binary classification. Mathematically, we define the objective of metric matrix $\mathbf{M}$ optimization using a graph adaptation of large margin nearest neighbor (LMNN), which is rewritten as a semi-definite programming (SDP) problem. We solve it efficiently via a fast approximation called Gershgorin disc perfect alignment (GDPA) linearization. The learned metric matrix $\mathbf{M}$ provides interpretability: important features are identified along $\mathbf{M}$'s diagonal, and their mutual relationships are inferred from off-diagonal terms. Our fast metric learning framework can be applied to other biological systems with pre-chosen features that require interpretation.

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arXiv2023

Volumetric 3D Point Cloud Attribute Compression: Learned polynomial bilateral filter for prediction

We extend a previous study on 3D point cloud attribute compression scheme that uses a volumetric approach: given a target volumetric attribute function $f : \mathbb{R}^3 \mapsto \mathbb{R}$, we quantize and encode parameters $\theta$ that characterize $f$ at the encoder, for reconstruction $f_{\hat{\theta}}(\mathbf(x))$ at known 3D points $\mathbf(x)$ at the decoder. Specifically, parameters $\theta$ are quantized coefficients of B-spline basis vectors $\mathbf{\Phi}_l$ (for order $p \geq 2$) that span the function space $\mathcal{F}_l^{(p)}$ at a particular resolution $l$, which are coded from coarse to fine resolutions for scalability. In this work, we focus on the prediction of finer-grained coefficients given coarser-grained ones by learning parameters of a polynomial bilateral filter (PBF) from data. PBF is a pseudo-linear filter that is signal-dependent with a graph spectral interpretation common in the graph signal processing (GSP) field. We demonstrate PBF's predictive performance over a linear predictor inspired by MPEG standardization over a wide range of point cloud datasets.

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arXiv2023

Learned Nonlinear Predictor for Critically Sampled 3D Point Cloud Attribute Compression

We study 3D point cloud attribute compression via a volumetric approach: assuming point cloud geometry is known at both encoder and decoder, parameters $\theta$ of a continuous attribute function $f: \mathbb{R}^3 \mapsto \mathbb{R}$ are quantized to $\hat{\theta}$ and encoded, so that discrete samples $f_{\hat{\theta}}(\mathbf{x}_i)$ can be recovered at known 3D points $\mathbf{x}_i \in \mathbb{R}^3$ at the decoder. Specifically, we consider a nested sequences of function subspaces $\mathcal{F}^{(p)}_{l_0} \subseteq \cdots \subseteq \mathcal{F}^{(p)}_L$, where $\mathcal{F}_l^{(p)}$ is a family of functions spanned by B-spline basis functions of order $p$, $f_l^*$ is the projection of $f$ on $\mathcal{F}_l^{(p)}$ represented as low-pass coefficients $F_l^*$, and $g_l^*$ is the residual function in an orthogonal subspace $\mathcal{G}_l^{(p)}$ (where $\mathcal{G}_l^{(p)} \oplus \mathcal{F}_l^{(p)} = \mathcal{F}_{l+1}^{(p)}$) represented as high-pass coefficients $G_l^*$. In this paper, to improve coding performance over \cite{do2023volumetric}, we study predicting $f_{l+1}^*$ at level $l+1$ given $f_l^*$ at level $l$ and encoding of $G_l^*$ for the $p=1$ case (RAHT($1$)). For the prediction, we formalize RAHT(1) linear prediction in MPEG-PCC in a theoretical framework, and propose a new nonlinear predictor using a polynomial of bilateral filter. We derive equations to efficiently compute the critically sampled high-pass coefficients $G_l^*$ amenable to encoding. We optimize parameters in our resulting feed-forward network on a large training set of point clouds by minimizing a rate-distortion Lagrangian. Experimental results show that our improved framework outperforms the MPEG G-PCC predictor by $11\%$--$12\%$ in bit rate.

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arXiv2023

Mixed Graph Signal Analysis of Joint Image Denoising / Interpolation

A noise-corrupted image often requires interpolation. Given a linear denoiser and a linear interpolator, when should the operations be independently executed in separate steps, and when should they be combined and jointly optimized? We study joint denoising / interpolation of images from a mixed graph filtering perspective: we model denoising using an undirected graph, and interpolation using a directed graph. We first prove that, under mild conditions, a linear denoiser is a solution graph filter to a maximum a posteriori (MAP) problem regularized using an undirected graph smoothness prior, while a linear interpolator is a solution to a MAP problem regularized using a directed graph smoothness prior. Next, we study two variants of the joint interpolation / denoising problem: a graph-based denoiser followed by an interpolator has an optimal separable solution, while an interpolator followed by a denoiser has an optimal non-separable solution. Experiments show that our joint denoising / interpolation method outperformed separate approaches noticeably.

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arXiv2023

Retinex-based Image Denoising / Contrast Enhancement using Gradient Graph Laplacian Regularizer

Images captured in poorly lit conditions are often corrupted by acquisition noise. Leveraging recent advances in graph-based regularization, we propose a fast Retinex-based restoration scheme that denoises and contrast-enhances an image. Specifically, by Retinex theory we first assume that each image pixel is a multiplication of its reflectance and illumination components. We next assume that the reflectance and illumination components are piecewise constant (PWC) and continuous piecewise planar (PWP) signals, which can be recovered via graph Laplacian regularizer (GLR) and gradient graph Laplacian regularizer (GGLR) respectively. We formulate quadratic objectives regularized by GLR and GGLR, which are minimized alternately until convergence by solving linear systems -- with improved condition numbers via proposed preconditioners -- via conjugate gradient (CG) efficiently. Experimental results show that our algorithm achieves competitive visual image quality while reducing computation complexity noticeably.

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