Liu Zhang

Liu Zhang, Amit Singer

Moment-based estimation is a theoretically attractive approach to parametric inference, especially when likelihood-based estimation is unavailable, misspecified, or computationally inconvenient. However, the moment equations involve sample averages, which makes moment-based estimation sensitive to outliers. We propose the SGR-GMM algorithm, a robust generalized method of moments (GMM) procedure that uses a spectral gradient reweighting (SGR) primitive to soft-reweight the per-observation gradients during the moment-matching optimization. Our analysis has three layers. First, for a fixed center, the SGR primitive is formulated as an entropy-regularized spectral game between a sample-weight player and a density-matrix player, which is analyzed using classical multiplicative-weights and matrix-multiplicative-weights regret bounds. Second, we establish explicit convergence radius and finite termination bound for the fixed-center updates in the SGR primitive. Third, we prove a local finite-sample parameter estimation error bound with explicit dependence on the contamination fraction, inlier gradient stability, local GMM identification strength, and optimization accuracy. We further specialize the SGR-GMM algorithm to obtain a robust diagonally-weighted GMM (DGMM) estimator for estimating heteroscedastic low-rank Gaussian mixtures observed under additive Gaussian noise and strong contamination. In the numerical experiments, the SGR primitive produces nearly-oracle gradient estimation and the robust DGMM specialization substantially improves over non-robust moment baselines. The code and data are available at https://github.com/liu-lzhang/sgr-gmm.

Bing Guan, Cailian Yang, Liu Zhang et al.

The radiation dose in computed tomography (CT) examinations is harmful for patients but can be significantly reduced by intuitively decreasing the number of projection views. Reducing projection views usually leads to severe aliasing artifacts in reconstructed images. Previous deep learning (DL) techniques with sparse-view data require sparse-view/full-view CT image pairs to train the network with supervised manners. When the number of projection view changes, the DL network should be retrained with updated sparse-view/full-view CT image pairs. To relieve this limitation, we present a fully unsupervised score-based generative model in sinogram domain for sparse-view CT reconstruction. Specifically, we first train a score-based generative model on full-view sinogram data and use multi-channel strategy to form highdimensional tensor as the network input to capture their prior distribution. Then, at the inference stage, the stochastic differential equation (SDE) solver and data-consistency step were performed iteratively to achieve fullview projection. Filtered back-projection (FBP) algorithm was used to achieve the final image reconstruction. Qualitative and quantitative studies were implemented to evaluate the presented method with several CT data. Experimental results demonstrated that our method achieved comparable or better performance than the supervised learning counterparts.

Bin Huang, Liu Zhang, Shiyu Lu et al.

Low-dose computed tomography (CT) plays a significant role in reducing the radiation risk in clinical applications. However, lowering the radiation dose will significantly degrade the image quality. With the rapid development and wide application of deep learning, it has brought new directions for the development of low-dose CT imaging algorithms. Therefore, we propose a fully unsupervised one sample diffusion model (OSDM)in projection domain for low-dose CT reconstruction. To extract sufficient prior information from single sample, the Hankel matrix formulation is employed. Besides, the penalized weighted least-squares and total variation are introduced to achieve superior image quality. Specifically, we first train a score-based generative model on one sinogram by extracting a great number of tensors from the structural-Hankel matrix as the network input to capture prior distribution. Then, at the inference stage, the stochastic differential equation solver and data consistency step are performed iteratively to obtain the sinogram data. Finally, the final image is obtained through the filtered back-projection algorithm. The reconstructed results are approaching to the normal-dose counterparts. The results prove that OSDM is practical and effective model for reducing the artifacts and preserving the image quality.

Liu Zhang, Jinyu Lu, Zilong Wang et al.

In CRYPTO 2019, Gohr presented differential-neural cryptanalysis by building the differential distinguisher with a neural network, achieving practical 11-, and 12-round key recovery attack for Speck32/64. Inspired by this framework, we develop the Inception neural network that is compatible with the round function of Simeck to improve the accuracy of the neural distinguishers, thus improving the accuracy of (9-12)-round neural distinguishers for Simeck32/64. To provide solid baselines for neural distinguishers, we compute the full distribution of differences induced by one specific input difference up to 13-round Simeck32/64. Moreover, the performance of the DDT-based distinguishers in multiple ciphertext pairs is evaluated. Compared with the DDT-based distinguishers, the 9-, and 10-round neural distinguishers achieve better accuracy. Also, an in-depth analysis of the wrong key response profile revealed that the 12-th and 13-th bits of the subkey have little effect on the score of the neural distinguisher, thereby accelerating key recovery attacks. Finally, an enhanced 15-round and the first practical 16-, and 17-round attacks are implemented for Simeck32/64, and the success rate of both the 15-, and 16-round attacks is almost 100%.

Liu Zhang, Oscar Mickelin, Sheng Xu et al.

Since Pearson [Philosophical Transactions of the Royal Society of London. A, 185 (1894), pp. 71-110] first applied the method of moments (MM) for modeling data as a mixture of one-dimensional Gaussians, moment-based estimation methods have proliferated. Among these methods, the generalized method of moments (GMM) improves the statistical efficiency of MM by weighting the moments appropriately. However, the computational complexity and storage complexity of MM and GMM grow exponentially with the dimension, making these methods impractical for high-dimensional data or when higher-order moments are required. Such computational bottlenecks are more severe in GMM since it additionally requires estimating a large weighting matrix. To overcome these bottlenecks, we propose the diagonally-weighted GMM (DGMM), which achieves a balance among statistical efficiency, computational complexity, and numerical stability. We apply DGMM to study the parameter estimation problem for weakly separated heteroscedastic low-rank Gaussian mixtures and design a computationally efficient and numerically stable algorithm that obtains the DGMM estimator without explicitly computing or storing the moment tensors. We implement the proposed algorithm and empirically validate the advantages of DGMM: in numerical studies, DGMM attains smaller estimation errors while requiring substantially shorter runtime than MM and GMM. The code and data will be available upon publication at https://github.com/liu-lzhang/dgmm.