Related papers: Signal retrieval with measurement system knowledge…

The traditional approach of hand-crafting priors (such as sparsity) for solving inverse problems is slowly being replaced by the use of richer learned priors (such as those modeled by deep generative networks). In this work, we study the…

We present a statistical framework to benchmark the performance of reconstruction algorithms for linear inverse problems, in particular, neural-network-based methods that require large quantities of training data. We generate synthetic…

Inverse problems in imaging are typically ill-posed and are usually solved by employing regularized optimization techniques. The usage of appropriate constraints can restrict the solution space, thus making it feasible for a reconstruction…

Suppose that we observe noisy linear measurements of an unknown signal that can be modeled as the sum of two component signals, each of which arises from a nonlinear sub-manifold of a high dimensional ambient space. We introduce SPIN, a…

Image recovery from compressive measurements requires a signal prior for the images being reconstructed. Recent work has explored the use of deep generative models with low latent dimension as signal priors for such problems. However, their…

Time-frequency analysis is an important and challenging task in many applications. Fourier and wavelet analysis are two classic methods that have achieved remarkable success in many fields. However, they also exhibit limitations when…

Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric…

Inverse problems consist in reconstructing signals from incomplete sets of measurements and their performance is highly dependent on the quality of the prior knowledge encoded via regularization. While traditional approaches focus on…

Finite time-vertex graph signals (FTVGS) provide an efficient representation for capturing spatio-temporal correlations across multiple data sources on irregular structures. Although sampling and reconstruction of FTVGS with known spectral…

Direct prediction of material properties from microstructures through statistical models has shown to be a potential approach to accelerating computational material design with large design spaces. However, statistical modeling of highly…

In many areas of imaging science, it is difficult to measure the phase of linear measurements. As such, one often wishes to reconstruct a signal from intensity measurements, that is, perform phase retrieval. In several applications the…

This paper shows how data-driven deep generative models can be utilized to solve challenging phase retrieval problems, in which one wants to reconstruct a signal from only few intensity measurements. Classical iterative algorithms are known…

When building a geometric scene understanding system for autonomous vehicles, it is crucial to know when the system might fail. Most contemporary approaches cast the problem as depth regression, whose output is a depth value for each pixel.…

Biological structure and function depend on complex regulatory interactions between many genes. A wealth of gene expression data is available from high-throughput genome-wide measurement technologies, but effective gene regulatory network…

Reconstruction of signals from compressively sensed measurements is an ill-posed problem. In this paper, we leverage the recurrent generative model, RIDE, as an image prior for compressive image reconstruction. Recurrent networks can model…

We study high-dimensional signal recovery from non-linear measurements with design vectors having elliptically symmetric distribution. Special attention is devoted to the situation when the unknown signal belongs to a set of low statistical…

The standard approach to compressive sampling considers recovering an unknown deterministic signal with certain known structure, and designing the sub-sampling pattern and recovery algorithm based on the known structure. This approach…

Recovery of arbitrarily positioned samples that are missing in sparse signals recently attracted significant research interest. Sparse signals with heavily corrupted arbitrary positioned samples could be analyzed in the same way as…

Accurate learning of system dynamics is becoming increasingly crucial for advanced control and decision-making in engineering. However, real-world systems often exhibit multiple channels and highly nonlinear transition dynamics, challenging…

Recovering a source signal from indirect measurements often requires estimating latent parameters, such as wireless channel states or MRI coil sensitivities, that cannot be directly observed. Here, we introduce Physics-Embedded Inverse…