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Compressed sensing allows perfect recovery of sparse signals (or signals sparse in some basis) using only a small number of random measurements. Existing results in compressed sensing literature have focused on characterizing the achievable…

We consider reconstruction of an ambient signal in a compressed sensing (CS) setup where the ambient signal has a neural network based generative model. The generative model has a sparse-latent input and we refer to the generated ambient…

We explore the methodology and theory of reward-directed generation via conditional diffusion models. Directed generation aims to generate samples with desired properties as measured by a reward function, which has broad applications in…

This paper investigates the problem of recovering the support of structured signals via adaptive compressive sensing. We examine several classes of structured support sets, and characterize the fundamental limits of accurately recovering…

Advances in compressive sensing provided reconstruction algorithms of sparse signals from linear measurements with optimal sample complexity, but natural extensions of this methodology to nonlinear inverse problems have been met with…

Sampling-based motion planning under task constraints is challenging because the null-measure constraint manifold in the configuration space makes rejection sampling extremely inefficient, if not impossible. This paper presents a…

Compressed sensing (CS) MRI relies on adequate undersampling of the k-space to accelerate the acquisition without compromising image quality. Consequently, the design of optimal sampling patterns for these k-space coefficients has received…

In the recent years, there has been a significant improvement in the quality of samples produced by (deep) generative models such as variational auto-encoders and generative adversarial networks. However, the representation capabilities of…

It has recently been shown that for compressive sensing, significantly fewer measurements may be required if the sparsity assumption is replaced by the assumption the unknown vector lies near the range of a suitably-chosen generative model.…

While learned image compression (LIC) focuses on efficient data transmission, generative image compression (GIC) extends this framework by integrating generative modeling to produce photo-realistic reconstructed images. In this paper, we…

Compressive phase retrieval is a popular variant of the standard compressive sensing problem in which the measurements only contain magnitude information. In this paper, motivated by recent advances in deep generative models, we provide…

We study domain-adaptive image synthesis, the problem of teaching pretrained image generative models a new style or concept from as few as one image to synthesize novel images, to better understand the compositional image synthesis. We…

We consider the problem of compressed sensing and of (real-valued) phase retrieval with random measurement matrix. We derive sharp asymptotics for the information-theoretically optimal performance and for the best known polynomial algorithm…

We propose a deep generative approach to sampling from a conditional distribution based on a unified formulation of conditional distribution and generalized nonparametric regression function using the noise-outsourcing lemma. The proposed…

In this paper, we propose a new and unified approach for nonparametric regression and conditional distribution learning. Our approach simultaneously estimates a regression function and a conditional generator using a generative learning…

In compressed sensing, the goal is to reconstruct the signal from an underdetermined system of linear measurements. Thus, prior knowledge about the signal of interest and its structure is required. Additionally, in many scenarios, the…

We address the problem of compressed sensing using a deep generative prior model and consider both linear and learned nonlinear sensing mechanisms, where the nonlinear one involves either a fully connected neural network or a convolutional…

The goal of compressed sensing is to estimate a high dimensional vector from an underdetermined system of noisy linear equations. In analogy to classical compressed sensing, here we assume a generative model as a prior, that is, we assume…

Random sampling in compressive sensing (CS) enables the compression of large amounts of input signals in an efficient manner, which is useful for many applications. CS reconstructs the compressed signals exactly with overwhelming…

In this paper, we propose the application of conditional generative adversarial networks to solve various phase retrieval problems. We show that including knowledge of the measurement process at training time leads to an optimization at…