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Dan Ma

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Computer Vision math.FA physics.med-ph eess.IV Machine Learning math.AP math.MG Networking and Internet Architecture quant-ph

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preprint2026arXiv

Which Face and Whose Identity? Solving the Dual Challenge of Deepfake Proactive Forensics in Multi-Face Scenarios

Unlike single-face forgeries, deepfakes in complex multi-person interaction scenarios (such as group photos and multi-person meetings) more closely reflect real-world threats. Although existing proactive forensics solutions demonstrate good performance, they heavily rely on a "single-face" setting, making it difficult to effectively address the problems of deepfake localization and source tracing in complex multi-person environments. To address this challenge, we propose the Deep Attributable Watermarking Framework (DAWF). This framework adopts a novel multi-face encoder-decoder architecture that bypasses the cumbersome offline pre-processing steps of traditional forensics, facilitating efficient in-network parallel watermark embedding and cross-face collaborative processing. Crucially, we propose a selective regional supervision loss. This innovative mechanism guides the decoder to focus exclusively on the facial regions tampered with by deepfakes. Leveraging this mechanism alongside the embedded identity payloads, DAWF realizes the "which + who" goal, answering the dual questions of which facial region was forged and who was forged. Extensive experiments on challenging multi-face datasets show that DAWF achieves excellent deepfake localization and traceability in complex multi-person scenes.

preprint2022arXiv

Automated Design of Pulse Sequences for Magnetic Resonance Fingerprinting using Physics-Inspired Optimization

Magnetic Resonance Fingerprinting (MRF) is a method to extract quantitative tissue properties such as T1 and T2 relaxation rates from arbitrary pulse sequences using conventional magnetic resonance imaging hardware. MRF pulse sequences have thousands of tunable parameters which can be chosen to maximize precision and minimize scan time. Here we perform de novo automated design of MRF pulse sequences by applying physics-inspired optimization heuristics. Our experimental data suggests systematic errors dominate over random errors in MRF scans under clinically-relevant conditions of high undersampling. Thus, in contrast to prior optimization efforts, which focused on statistical error models, we use a cost function based on explicit first-principles simulation of systematic errors arising from Fourier undersampling and phase variation. The resulting pulse sequences display features qualitatively different from previously used MRF pulse sequences and achieve fourfold shorter scan time than prior human-designed sequences of equivalent precision in T1 and T2. Furthermore, the optimization algorithm has discovered the existence of MRF pulse sequences with intrinsic robustness against shading artifacts due to phase variation.

preprint2020arXiv

Game of Learning Bloch Equation Simulations for MR Fingerprinting

Purpose: This work proposes a novel approach to efficiently generate MR fingerprints for MR fingerprinting (MRF) problems based on the unsupervised deep learning model generative adversarial networks (GAN). Methods: The GAN model is adopted and modified for better convergence and performance, resulting in an MRF specific model named GAN-MRF. The GAN-MRF model is trained, validated, and tested using different MRF fingerprints simulated from the Bloch equations with certain MRF sequence. The performance and robustness of the model are further tested by using in vivo data collected on a 3 Tesla scanner from a healthy volunteer together with MRF dictionaries with different sizes. T1, T2 maps are generated and compared quantitatively. Results: The validation and testing curves for the GAN-MRF model show no evidence of high bias or high variance problems. The sample MRF fingerprints generated from the trained GAN-MRF model agree well with the benchmark fingerprints simulated from the Bloch equations. The in vivo T1, T2 maps generated from the GAN-MRF fingerprints are in good agreement with those generated from the Bloch simulated fingerprints, showing good performance and robustness of the proposed GAN-MRF model. Moreover, the MRF dictionary generation time is reduced from hours to sub-second for the testing dictionary. Conclusion: The GAN-MRF model enables a fast and accurate generation of the MRF fingerprints. It significantly reduces the MRF dictionary generation process and opens the door for real-time applications and sequence optimization problems.

preprint2015arXiv

Real-valued valuations on Sobolev spaces

Continuous, SL($n$) and translation invariant real-valued valuations on Sobolev spaces are classified.

preprint2014arXiv

Asymmetric anisotropic fractional Sobolev norms

Bourgain, Brezis & Mironescu showed that (with suitable scaling) the fractional Sobolev $s$-seminorm of a function $f\in W^{1,p}(\mathbb{R}^n)$ converges to the Sobolev seminorm of $f$ as $s\rightarrow1^-$. Ludwig introduced the anisotropic fractional Sobolev $s$-seminorms of $f$ defined by a norm on $\mathbb{R}^n$ with unit ball $K$, and showed that they converge to the anisotropic Sobolev seminorm of $f$ defined by the norm whose unit ball is the polar $L_p$ moment body of $K$, as $s\rightarrow1^-$. The asymmetric anisotropic $s$-seminorms are shown to converge to the anisotropic Sobolev seminorm of $f$ defined by the Minkowski functional of the polar asymmetric $L_p$ moment body of $K$.

preprint2013arXiv

Twins:Device-free Object Tracking using Passive Tags

Without requiring objects to carry any transceiver, device-free based object tracking provides a promising solution for many localization and tracking systems to monitor non-cooperative objects such as intruders. However, existing device-free solutions mainly use sensors and active RFID tags, which are much more expensive compared to passive tags. In this paper, we propose a novel motion detection and tracking method using passive RFID tags, named Twins. The method leverages a newly observed phenomenon called critical state caused by interference among passive tags. We contribute to both theory and practice of such phenomenon by presenting a new interference model that perfectly explains this phenomenon and using extensive experiments to validate it. We design a practical Twins based intrusion detection scheme and implement a real prototype with commercial off-the-shelf reader and tags. The results show that Twins is effective in detecting the moving object, with low location error of 0.75m in average.

preprint2011arXiv

Stability and slicing inequalities for intersection bodies

We prove a generalization of the hyperplane inequality for intersection bodies, where volume is replaced by an arbitrary measure $μ$ with even continuous density and sections are of arbitrary dimension $n-k,\ 1\le k <n.$ If $K$ is a generalized $k$-intersection body, then $$μ(K)\,\leq\,\frac{n}{n-k}c_{n,k}\max_{H} μ(K\cap H) \vol_n(K)^{k/n}.$$ Here $c_{n,k} = |B_2^n|^{(n-k)/n}/|B_2^{n-k}|<1,$ $|B_2^n|$ is the volume of the unit Euclidean ball, and maximum is taken over all $(n-k)$-dimensional subspaces of $\R^n.$ The constant is optimal, and for each intersection body the inequality holds for every $k.$ We also prove a stronger "difference" inequality. The proof is based on stability in the lower dimensional Busemann-Petty problem for arbitrary measures in the following sense. Let $\e>0,\ 1\le k <n.$ Suppose that $K$ and $L$ are origin-symmetric star bodies in $\R^n,$ and $K$ is a generalized $k$-intersection body. If for every $(n-k)$-dimensional subspace $H$ of $\R^n$ $$μ(K\cap H)\leq μ(L\cap H)+\e,$$ then $$μ(K)\leq μ(L) +\frac{n}{n-k}c_{n,k} \vol_n(K)^{k/n}\e.$$