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Phase retrieval refers to the problem of recovering real- or complex-valued vectors from magnitude measurements. The best-known algorithms for this problem are iterative in nature and rely on so-called spectral initializers that provide…
The problem of recovering a signal from its phaseless Fourier transform measurements, called Fourier phase retrieval, arises in many applications in engineering and science. Fourier phase retrieval poses fundamental theoretical and…
Primary health care frequently relies on low-cost imaging devices, which are commonly used for screening purposes. To ensure accurate diagnosis, these systems depend on advanced reconstruction algorithms designed to approximate the…
In the phase retrieval problem, an unknown vector is to be recovered given quadratic measurements. This problem has received considerable attention in recent times. In this paper, we present an algorithm to solve a nonconvex formulation of…
A foveated image can be entirely reconstructed from a sparse set of samples distributed according to the retinal sensitivity of the human visual system, which rapidly decreases with increasing eccentricity. The use of Generative Adversarial…
A general mathematical framework and recovery algorithm is presented for the holographic phase retrieval problem. In this problem, which arises in holographic coherent diffraction imaging, a "reference" portion of the signal to be recovered…
Metrics for evaluating generative models aim to measure the discrepancy between real and generated images. The often-used Frechet Inception Distance (FID) metric, for example, extracts "high-level" features using a deep network from the two…
Per-scene optimization methods such as 3D Gaussian Splatting provide state-of-the-art novel view synthesis quality but extrapolate poorly to under-observed areas. Methods that leverage generative priors to correct artifacts in these areas…
End-to-end generative methods are considered a more promising solution for image restoration in physics-based vision compared with the traditional deconstructive methods based on handcrafted composition models. However, existing generative…
We study algorithms for solving quadratic systems of equations based on optimization methods over polytopes. Our work is inspired by a recently proposed convex formulation of the phase retrieval problem, which estimates the unknown signal…
A Generative Adversarial Network (GAN) with generator $G$ trained to model the prior of images has been shown to perform better than sparsity-based regularizers in ill-posed inverse problems. Here, we propose a new method of deploying a…
Recent advances in diffusion-based Large Restoration Models (LRMs) have significantly improved photo-realistic image restoration by leveraging the internal knowledge embedded within model weights. However, existing LRMs often suffer from…
Image denoising aims to remove noise while preserving structural details and perceptual realism, yet distortion-driven methods often produce over-smoothed reconstructions, especially under strong noise and distribution shift. This paper…
Signal inpainting is the task of restoring degraded or missing samples in a signal. In this paper we address signal inpainting when Fourier magnitudes are observed. We propose a mathematical formulation of the problem that highlights its…
We study the problem of recovering the phase from magnitude measurements; specifically, we wish to reconstruct a complex-valued signal x of C^n about which we have phaseless samples of the form y_r = |< a_r,x >|^2, r = 1,2,...,m (knowledge…
The problem of phase retrieval is revisited and studied from a fresh perspective. In particular, we establish a connection between the phase retrieval problem and the sensor network localization problem, which allows us to utilize the vast…
Phase retrieval is in general a non-convex and non-linear task and the corresponding algorithms struggle with the issue of local minima. We consider the case where the measurement samples within typically very small and disconnected subsets…
It is well-known that in inverse problems, end-to-end trained networks overfit the degradation model seen in the training set, i.e., they do not generalize to other types of degradations well. Recently, an approach to first map images…
Proximal algorithms have gained popularity in recent years in large-scale and distributed optimization problems. One such problem is the phase retrieval problem, for which proximal operators have been proposed recently. The phase retrieval…
Generative models for image generation are now commonly used for a wide variety of applications, ranging from guided image generation for entertainment to solving inverse problems. Nonetheless, training a generator is a non-trivial feat…