arXiv subjects

Hanwen Lu

Publications and source records attributed to Hanwen Lu.

5 recordsLinked to original sources

arXiv2026

Uniqueness of Extremizers and Convergence of the Euler-Lagrange Iteration for the Critical Hardy-Littlewood-Sobolev Inequality

Let $n \ge 3$, $2 \le α< n$, and $1 < p,r < \infty$ satisfy $p^{-1}+r^{-1}=1+α/n$. We prove uniqueness, up to common translations and dilations, of the normalized nonnegative extremizing pairs for the corresponding Hardy-Littlewood-Sobolev inequality. More generally, all positive finite-energy solutions of the Euler-Lagrange system belong to a single symmetry orbit. The proof compares two solutions at different relative scales. Total positivity of order two identifies the second eigenspace of an associated compact self-adjoint operator and forces each nonzero difference to change sign exactly once. The opposite orientations obtained at the two ends of the scale parameter then yield uniqueness. The same method proves radial nondegeneracy modulo dilation. We also establish strong convergence of the normalized alternating Euler-Lagrange iteration from every nonnegative, radially nonincreasing initial datum to a fixed extremizing pair, without rescaling the iterates. Square-root mass variables reduce the exclusion of several concentration profiles to a static spectral estimate and an energy-increment argument. The analysis includes sublinear exponents and the logarithmic borderline decay regimes.

math.AP↗

arXiv2026

CrossTimeEdit: A Decade-Spanning Cross-View Dataset and Reward-Guided Editing for Historical Street-View Generation

Historical street-view imagery records urban evolution, but uneven coverage leaves substantial gaps in historical records. Generating plausible past appearances requires restoring changed structures while preserving persistent scene content. We construct VIGOR-his, a decade-spanning cross-view dataset containing 43,653 location-level quadruplets across 11 cities on three continents. Its automated pipeline performs spatial pairing, consistency screening, change classification, and the generation and validation of satellite-based change descriptions and local editing instructions. Based on VIGOR-his, we propose CrossTimeEdit, a model that reformulates historical street-view generation as editing, using recent street views to constrain viewpoint and unchanged appearance and temporal satellite differences as change evidence. Starting from FLUX.2 [Klein] 4B, we train CrossTimeEdit through supervised fine-tuning (SFT) followed by online reinforcement learning (RL). We design three street-view editing criteria, namely Instruction Alignment (IA), Background Preservation (BP), and Quality and Physical Plausibility (QP), as both RL reward dimensions and evaluation metrics. We optimize this multi-reward objective using Within Group Relative Policy Optimization for flow-matching models (Flow-GRPO) with Group reward-Decoupled Normalization Policy Optimization (GDPO), which normalizes each reward dimension before aggregation. CrossTimeEdit improves overall performance across the three editing criteria by 17.12\% over the pretrained baseline and outperforms cross-view generation models in scene consistency, visual realism, and perceptual quality. The implementation code, dataset, and model weights are available at https://luhanwen67.github.io/CrossTimeEdit-release/.

cs.CV↗

arXiv2026

Algorithmic Implementation of Multi-Window STFT Phase Retrieval

STFT phase retrieval aims to reconstruct a signal from spectrogram magnitudes. While two compactly supported windows theoretically guarantee uniqueness, a complete algorithmic framework remains lacking. This paper systematically constructs numerical schemes for multi-window STFT phase retrieval. We theoretically provide a nonuniqueness counterexample for the single-window case. We then propose a two-window reconstruction algorithm based on Shannon interpolation and analytic square-root extraction. To overcome the instability of the global sign choice, we introduce a third window and a robust $K$-sign method that determines the sign locally. We also adapt SCR algorithm to the STFT setting. For the $K$-sign method, we establish deterministic stability on a finite contiguous block of frequency samples, with the contribution of the complementary tail explicitly included in the error bound. Numerical experiments validate the effectiveness of all schemes.

math.CA↗

arXiv2026

STFT Phase Retrieval with Two Window Functions

In this paper, we consider the uniqueness of STFT phase retrieval with two window functions. We show that a complex-valued locally integrable nonseparable signal is uniquely determined up to a global phase by phaseless samples of its short time Fourier transforms with respect to two well-chosen window functions over countable parallel lines or certain lattices. Moreover, we give the optimal sampling interval for STFT phase retrieval with compactly supported window functions. For periodic locally integrable signals, we obtain a uniqueness result for STFT phase retrieval with sampled values over two parallel lines whose distance is an irrational multiple of the period. And for quasi-periodic signals, we obtain a similar result.

math.CA↗

arXiv2025

Sampling Density for Gabor Phase Retrieval

Gabor phase retrieval stands for recovering a square integrable function up to a global phase from absolute values of its Gabor transform. In this paper, we study Gabor phase retrieval from discrete samples. We consider three types of sampling sequences, which include square root lattices, square root sequences on two intersecting lines and on three parallel lines respectively. In all cases we give the optimal sampling density for a sequence to do Gabor phase retrieval.

math.CA↗