arXiv subjects

Hieu Thao Nguyen

Publications and source records attributed to Hieu Thao Nguyen.

3 recordsLinked to original sources

arXiv2021

Subpixel image reconstruction using nonuniform defocused images

This paper considers the problem of reconstructing an object with high-resolution using several low-resolution images, which are degraded due to nonuniform defocus effects caused by angular misalignment of the subpixel motions. The new algorithm, indicated by the Superresolution And Nonuniform Defocus Removal (SANDR) algorithm, simultaneously performs the nonuniform defocus removal as well as the superresolution reconstruction. The SANDR algorithm combines non-sequentially the nonuniform defocus removal method recently developed by Thao et al. and the least squares approach for subpixel image reconstruction. Hence, it inherits global convergence from its two component techniques and avoids the typical error amplification of multi-step optimization contributing to its robustness. Further, existing acceleration techniques for optimization have been proposed that assure fast convergence of the SANDR algorithm going from rate O(1/k) to O(1/k^2) compared to most existing superresolution (SR) techniques using the gradient descent method. An extensive simulation study evaluating the new SANDR algorithm has been conducted. As no algorithms are available to address the combined problem, in this simulation study we restrict the comparison of SANDR with other SR algorithms neglecting the defocus aberrations. Even for this case the advantages of the SANDR algorithm have been demonstrated.

math.OC↗

arXiv2020

Shack-Hartmann sensor as an imaging system with a phase diversity

Conventional methods of wavefront reconstruction from the raw data of the Shack-Hartmann sensor use the focal spot shifts and discard the high-frequency information about the wavefront. Phase-retrieval-based methods treat the Hartmann pattern as the diffraction image and use the Rayleigh-Sommerfeld propagation to estimate the wavefront with greater accuracy and resolution. In this Letter, we propose a novel approach to the phase-retrieval-based reconstruction by considering the Hartmann pattern as a point-spread function of a general imaging system with an introduced phase diversity of a special type. This model allows one not only to use any phase retrieval algorithm to reconstruct the wavefront but also to analyse the limitations of the phase-retrieval-based methods. We demonstrate the validity of this approach both on the simulated and experimental data.

physics.optics↗

arXiv2019

Phase retrieval with sparse phase constraint

For the first time, this paper investigates the phase retrieval problem with the assumption that the phase (of the complex signal) is sparse in contrast to the sparsity assumption on the signal itself as considered in the literature of sparse signal processing. The intended application of this new problem model, which will be conducted in a follow-up paper, is to practical phase retrieval problems where the aberration phase is sparse with respect to the orthogonal basis of Zernike polynomials. Such a problem is called sparse phase retrieval (SPR) problem in this paper. When the amplitude modulation at the exit pupil is uniform, a new scheme of sparsity regularization on phase is proposed to capture the sparsity property of the SPR problem. Based on this regularization scheme, we design and analyze an efficient solution method, named SROP algorithm, for solving SPR given only a single intensity point-spread-function image. The algorithm is a combination of the Gerchberg-Saxton algorithm with the newly proposed sparsity regularization on the phase. The latter regularization step is mathematically a rotation but with direction varying in iterations. Surprisingly, this rotation is shown to be a metric projection on an auxiliary set which is independent of iterations. As a consequence, SROP algorithm is proved to be the cyclic projections algorithm for solving a feasibility problem involving three auxiliary sets. Analyzing regularity properties of the latter auxiliary sets, we obtain convergence results for SROP algorithm based on recent convergence theory for the cyclic projections algorithm. Numerical results show clear effectiveness of the new regularization scheme for solving the SPR problem.

math.OC↗