Sparsity-Free Compressed Sensing With Applications to Generative Priors

Naderi, Alireza; Plan, Yaniv

doi:10.1109/jsait.2022.3219807

Cited by 1 publication

(2 citation statements)

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“…Observe that the number of measurements matches the O(kd log w) upper bound to within a constant factor (first case) or an O(log n) factor (second and third cases). We note that certain cases are known where the logarithmic factor in the upper bound can be slightly reduced [99].…”

Section: Information-theoretic Lower Boundsmentioning

confidence: 95%

“…Non-Gaussian i.i.d. designs have also been considered [68], as well as certain classes of dependent measurements [99]. However, theory is still largely lacking for several kinds of measurements that are used in practice; for instance, in applications such as medical imaging, one is confined to using subsampled Fourier measurements due to the inherent design of the hardware.…”

Section: F Ongoing Challengesmentioning

confidence: 99%

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Theoretical Perspectives on Deep Learning Methods in Inverse Problems

Scarlett

Heckel

Rodrigues

et al. 2022

IEEE J. Sel. Areas Inf. Theory

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In recent years, there have been significant advances in the use of deep learning methods in inverse problems such as denoising, compressive sensing, inpainting, and super-resolution. While this line of works has predominantly been driven by practical algorithms and experiments, it has also given rise to a variety of intriguing theoretical problems. In this paper, we survey some of the prominent theoretical developments in this line of works, focusing in particular on generative priors, untrained neural network priors, and unfolding algorithms. In addition to summarizing existing results in these topics, we highlight several ongoing challenges and open problems.

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Section: Information-theoretic Lower Boundsmentioning

confidence: 95%

Section: F Ongoing Challengesmentioning

confidence: 99%