arXiv subjects

Joe-Mei Feng

Publications and source records attributed to Joe-Mei Feng.

4 recordsLinked to original sources

arXiv2026

Stability and Concentration in Nonlinear Inverse Problems with Block-Structured Parameters: Lipschitz Geometry, Identifiability, and an Application to Gaussian Splatting

We develop an operator-theoretic framework for stability and statistical concentration in nonlinear inverse problems with block-structured parameters. Under a unified set of assumptions combining blockwise Lipschitz geometry, local identifiability, and sub-Gaussian noise, we establish deterministic stability inequalities, global Lipschitz bounds for least-squares misfit functionals, and nonasymptotic concentration estimates. These results yield high-probability parameter error bounds that are intrinsic to the forward operator and independent of any specific reconstruction algorithm. As a concrete instantiation, we verify that the Gaussian Splatting rendering operator satisfies the proposed assumptions and derive explicit constants governing its Lipschitz continuity and resolution-dependent observability. This leads to a fundamental stability--resolution tradeoff, showing that estimation error is inherently constrained by the ratio between image resolution and model complexity. Overall, the analysis characterizes operator-level limits for a broad class of high-dimensional nonlinear inverse problems arising in modern imaging and differentiable rendering.

cs.CV↗

arXiv2026

The Geometric Observability Index: Influence, Fisher Information, and Weak Observability in SE(3) Pose Estimation

We introduce the Geometric Observability Index (GOI), a per-feature sensitivity measure for pose estimation on SE(3): the metric norm of the pose perturbation that a single measurement induces through the (possibly rank-deficient) Gauss-Newton curvature, restricted to the observable subspace. We prove that GOI equals the norm of the M-estimator influence function, that the underlying curvature operator coincides with the Fisher information, and that its smallest observable eigenvalue governs both the worst-case amplification of a measurement's effect and a finite-sample stability radius O(sigma/sqrt(n*lambda_min)). Operationally the theory cuts both ways. GOI is the exact per-measurement attribution, predicting the true leave-one-out pose shift with log-correlation r = 1.00; yet the influence standardized by its inlier null covariance collapses exactly to the classical chi-square residual statistic. Residual gating is thus the leverage-corrected influence test -- a first-principles explanation of its robustness -- while raw-influence gating conflates a measurement's information with its harm and is predicted to over-reject high-leverage inliers in weakly observable geometry. Controlled synthetic experiments validate every quantitative claim, and studies on five TUM RGB-D sequences (four dynamic, one static control) and two KITTI odometry sequences confirm the prediction: parity of the two criteria under well-conditioned geometry, and significant degradation of raw-influence gating at cond(H) of order 10^4. All code is released for reproducibility.

cs.CV↗

arXiv2017

Quantized Compressed Sensing for Partial Random Circulant Matrices

We provide the first analysis of a non-trivial quantization scheme for compressed sensing measurements arising from structured measurements. Specifically, our analysis studies compressed sensing matrices consisting of rows selected at random, without replacement, from a circulant matrix generated by a random subgaussian vector. We quantize the measurements using stable, possibly one-bit, Sigma-Delta schemes, and use a reconstruction method based on convex optimization. We show that the part of the reconstruction error due to quantization decays polynomially in the number of measurements. This is in line with analogous results on Sigma-Delta quantization associated with random Gaussian or subgaussian matrices, and significantly better than results associated with the widely assumed memoryless scalar quantization. Moreover, we prove that our approach is stable and robust; i.e., the reconstruction error degrades gracefully in the presence of non-quantization noise and when the underlying signal is not strictly sparse. The analysis relies on results concerning subgaussian chaos processes as well as a variation of McDiarmid's inequality.

cs.IT↗

arXiv2014

An RIP-based approach to $ΣΔ$ quantization for compressed sensing

In this paper, we provide a new approach to estimating the error of reconstruction from $ΣΔ$ quantized compressed sensing measurements. Our method is based on the restricted isometry property (RIP) of a certain projection of the measurement matrix. Our result yields simple proofs and a slight generalization of the best-known reconstruction error bounds for Gaussian and subgaussian measurement matrices.

cs.IT↗