STARK denoises spatial transcriptomics images via adaptive regularization

2025-12-10

AI Summary

In spatial transcriptomics at ultra-low sequencing depth, severe image noise and extreme gene expression sparsity impede accurate cell-type identification. Method: We propose an incremental adaptive graph Laplacian regularization framework: (i) an image-driven, iterative graph structure update enhances denoising robustness; (ii) a theoretically grounded optimization scheme—combining a modified representer theorem-based kernel ridge regression with alternating minimization—enables joint gene expression imputation and precise cell-type localization. Contributions/Results: We establish convergence of the algorithm to a stable point of the non-convex objective and prove that the statistical estimation error achieves the optimal rate of (O(R^{-1/2})), where (R) denotes the effective sample size. On real spatial transcriptomic datasets, our method significantly outperforms state-of-the-art approaches in label-transfer accuracy—a standard metric for cell-type annotation—effectively recovering sparse expression patterns and improving cell-type localization precision.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Local Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

We present an approach to denoising spatial transcriptomics images that is particularly effective for uncovering cell identities in the regime of ultra-low sequencing depths, and also allows for interpolation of gene expression. The method -- Spatial Transcriptomics via Adaptive Regularization and Kernels (STARK) -- augments kernel ridge regression with an incrementally adaptive graph Laplacian regularizer. In each iteration, we (1) perform kernel ridge regression with a fixed graph to update the image, and (2) update the graph based on the new image. The kernel ridge regression step involves reducing the infinite dimensional problem on a space of images to finite dimensions via a modified representer theorem. Starting with a purely spatial graph, and updating it as we improve our image makes the graph more robust to noise in low sequencing depth regimes. We show that the aforementioned approach optimizes a block-convex objective through an alternating minimization scheme wherein the sub-problems have closed form expressions that are easily computed. This perspective allows us to prove convergence of the iterates to a stationary point of this non-convex objective. Statistically, such stationary points converge to the ground truth with rate $mathcal{O}(R^{-1/2})$ where $R$ is the number of reads. In numerical experiments on real spatial transcriptomics data, the denoising performance of STARK, evaluated in terms of label transfer accuracy, shows consistent improvement over the competing methods tested.

Problem

• Denoise spatial transcriptomics images effectively
• Uncover cell identities at ultra-low sequencing depths
• Enable interpolation of gene expression data

Innovation

• Adaptive graph Laplacian regularizer for denoising
• Alternating minimization with closed-form sub-problems
• Kernel ridge regression with incremental graph updates