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Signal recovery from nonlinear measurements involves solving an iterative optimization problem. In this paper, we present a framework to optimize the sensing parameters to improve the quality of the signal recovered by the given iterative…
Traditional phase-shifting interferometry technique cannot be used to measure time-varying phase distributions. But single shot techniques could resolve the problem. Many efforts have been made on the phase retrieval methods from a single…
To obtain spatial information about an arbitrary object in x-ray structure analysis, the standard method is to measure the intensity in the far field, i.e., the first-order photon correlation function of the coherently scattered x-ray…
Diffusion models have demonstrated their utility as learned priors for solving various inverse problems. However, most existing approaches are limited to linear inverse problems. This paper exploits the efficient and unsupervised posterior…
In powder diffraction data analysis, phase identification is the process of determining the crystalline phases in a sample using its characteristic Bragg peaks. For multiphasic spectra, we must also determine the relative weight fraction of…
This is a review paper on some of the physics, modeling, and iterative algorithms in proton computed tomography (pCT) image reconstruction. The primary challenge in pCT image reconstruction lies in the degraded spatial resolution resulting…
When x-rays penetrate soft matter, their phase changes more rapidly than their amplitude. In- terference effects visible with high brightness sources creates higher contrast, edge enhanced images. When the object is piecewise smooth (made…
We propose a flexible convex relaxation for the phase retrieval problem that operates in the natural domain of the signal. Therefore, we avoid the prohibitive computational cost associated with "lifting" and semidefinite programming (SDP)…
Turning pass-through network architectures into iterative ones, which use their own output as input, is a well-known approach for boosting performance. In this paper, we argue that such architectures offer an additional benefit: The…
An iterative method is derived for image reconstruction. Among other attributes, this method allows constraints unrelated to the radiation measurements to be incorporated into the reconstructed image. A comparison is made with the widely…
X-ray phase contrast imaging significantly improves the visualization of structures with weak or uniform absorption, broadening its applications across a wide range of scientific disciplines. Propagation-based phase contrast is particularly…
In a variety of fields, in particular those involving imaging and optics, we often measure signals whose phase is missing or has been irremediably distorted. Phase retrieval attempts to recover the phase information of a signal from the…
We propose a new approach to linear ill-posed inverse problems. Our algorithm alternates between enforcing two constraints: the measurements and the statistical correlation structure in some transformed space. We use a non-linear multiscale…
Phase retrieval is a well known ill-posed inverse problem where one tries to recover images given only the magnitude values of their Fourier transform as input. In recent years, new algorithms based on deep learning have been proposed,…
We improve a phase retrieval approach that uses correlation-based measurements with compactly supported measurement masks [27]. The improved algorithm admits deterministic measurement constructions together with a robust, fast recovery…
Phase retrieval in real or complex Hilbert spaces is the task of recovering a vector, up to an overall unimodular multiplicative constant, from magnitudes of linear measurements. In this paper, we assume that the vector is normalized, but…
Machine learning is attracting surging interest across nearly all scientific areas by enabling the analysis of large datasets and the extraction of scientific information from incomplete data. Data-driven science is rapidly growing,…
We consider the problem of computationally-efficient prediction with high dimensional and highly correlated predictors when accurate variable selection is effectively impossible. Direct application of penalization or Bayesian methods…
A simple coherent-imaging method due to Paganin et al. is widely employed for phase-amplitude reconstruction of samples using a single paraxial x-ray propagation-based phase-contrast image. The method assumes that the sample-to-detector…
Phase retrieval (PR), also sometimes referred to as quadratic sensing, is a problem that occurs in numerous signal and image acquisition domains ranging from optics, X-ray crystallography, Fourier ptychography, sub-diffraction imaging, and…