For example, in medical imaging, it is not always possible to obtain fully sampled images of patients as they require long acquisition times.

We study compressive sensing with a deep generative network prior. Initial theoretical guarantees for efficient recovery from compressed linear measurements have been developed for signals in the range of a ReLU network with Gaussian weights and logarithmic expansivity: that is when each layer is larger than the previous one by a logarithmic factor. It was later shown that constant expansivity is sufficient for recovery. It has remained open whether the expansivity can be relaxed, allowing for networks with contractive layers (as often the case of real generators). In this work we answer this question, proving that a signal in the range of a Gaussian generative network can be recovered from few linear measurements provided that the width of the layers is proportional to the input layer size (up to log factors).

Our algorithm is simple and can be obtained via a natural combination of the classical alternating minimization approach for phase retrieval, with the CoSaMP algorithm for sparse recovery.

We put forth a novel procedure, that starts with a weighted maximal correlation initialization obtainable with a few power iterations, followed by successive refinements based on iteratively reweighted gradient-type iterations . The novel techniques distinguish themselves from prior works by the inclusion of a fresh (re)weighting regularization.

's are the rows of a known measurement matrix

Stochastic resonance (SR), a phenomenon originally introduced in climate modeling, enhances signal detection by leveraging optimal noise levels within non-linear systems. Traditional SR techniques, mainly based on single-threshold detectors, are limited to signals whose behavior does not depend on time. Often large amounts of noise are needed to detect weak signals, which can distort complex signal characteristics. To address these limitations, this study explores multi-threshold systems and the application of SR in multiscale applications using wavelet transforms. In the multiscale domain signals can be analyzed at different levels of resolution to better understand the underlying dynamics. We propose a double-threshold detection system that integrates two single-threshold detectors to enhance weak signal detection. We evaluate it both in the original data domain and in the multiscale domain using simulated and real-world signals and compare its performance with existing methods. Experimental results demonstrate that, in the original data domain, the proposed double-threshold detector significantly improves weak signal detection compared to conventional single-threshold approaches. Its performance is further improved in the frequency domain, requiring lower noise levels while outperforming existing detection systems. This study advances SR-based detection methodologies by introducing a robust approach to weak signal identification, with potential applications in various disciplines.

This paper tackles the challenging problem of jointly inferring time-varying network topologies and imputing missing data from partially observed graph signals. We propose a unified non-convex optimization framework to simultaneously recover a sequence of graph Laplacian matrices while reconstructing the unobserved signal entries. Unlike conventional decoupled methods, our integrated approach facilitates a bidirectional flow of information between the graph and signal domains, yielding superior robustness, particularly in high missing-data regimes. To capture realistic network dynamics, we introduce a fused-lasso type regularizer on the sequence of Laplacians. This penalty promotes temporal smoothness by penalizing large successive changes, thereby preventing spurious variations induced by noise while still permitting gradual topological evolution. For solving the joint optimization problem, we develop an efficient Alternating Direction Method of Multipliers (ADMM) algorithm, which leverages the problem's structure to yield closed-form solutions for both the graph and signal subproblems. This design ensures scalability to large-scale networks and long time horizons. On the theoretical front, despite the inherent non-convexity, we establish a convergence guarantee, proving that the proposed ADMM scheme converges to a stationary point. Furthermore, we derive non-asymptotic statistical guarantees, providing high-probability error bounds for the graph estimator as a function of sample size, signal smoothness, and the intrinsic temporal variability of the graph. Extensive numerical experiments validate the approach, demonstrating that it significantly outperforms state-of-the-art baselines in both convergence speed and the joint accuracy of graph learning and signal recovery.

Neural Information Processing Systems http://nips.cc/

We consider the problem of recovering latent information from graphs under $\varepsilon$-edge local differential privacy where the presence of relationships/edges between two users/vertices remains confidential, even from the data curator. For the class of generalized random dot-product graphs, we show that a standard local differential privacy mechanism induces a specific geometric distortion in the latent positions. Leveraging this insight, we show that consistent recovery of the latent positions is achievable by appropriately adjusting the statistical inference procedure for the privatized graph. Furthermore, we prove that our procedure is nearly minimax-optimal under local edge differential privacy constraints. Lastly, we show that this framework allows for consistent recovery of geometric and topological information underlying the latent positions, as encoded in their persistence diagrams. Our results extend previous work from the private community detection literature to a substantially richer class of models and inferential tasks.