On the Convergence and Consistency of the Blurring Mean-Shift Process

The mean-shift algorithm is a popular algorithm in computer vision and image processing. It can also be cast as a minimum gamma-divergence estimation. In this paper we focus on the "blurring" mean shift algorithm, which is one version of the mean-shift process that successively blurs the dataset. The analysis of the blurring mean-shift is relatively more complicated compared to the nonblurring version, yet the algorithm convergence and the estimation consistency have not been well studied in the literature. In this paper we prove both the convergence and the consistency of the blurring mean-shift. We also perform simulation studies to compare the efficiency of the blurring and the nonblurring versions of the mean-shift algorithms. Our results show that the blurring mean-shift has more efficiency.Comment: arXiv admin note: text overlap with arXiv:1201.197

Convergence Analysis of Blurring Mean Shift

Blurring mean shift (BMS) algorithm, a variant of the mean shift algorithm, is a kernel-based iterative method for data clustering, where data points are clustered according to their convergent points via iterative blurring. In this paper, we analyze convergence properties of the BMS algorithm by leveraging its interpretation as an optimization procedure, which is known but has been underutilized in existing convergence studies. Whereas existing results on convergence properties applicable to multi-dimensional data only cover the case where all the blurred data point sequences converge to a single point, this study provides a convergence guarantee even when those sequences can converge to multiple points, yielding multiple clusters. This study also shows that the convergence of the BMS algorithm is fast by further leveraging geometrical characterization of the convergent points.Comment: Blurring mean shift, mean shift, clustering, convergence, kernel. arXiv admin note: text overlap with arXiv:2305.0846

Phase Aberration Correction: A Deep Learning-Based Aberration to Aberration Approach

One of the primary sources of suboptimal image quality in ultrasound imaging is phase aberration. It is caused by spatial changes in sound speed over a heterogeneous medium, which disturbs the transmitted waves and prevents coherent summation of echo signals. Obtaining non-aberrated ground truths in real-world scenarios can be extremely challenging, if not impossible. This challenge hinders training of deep learning-based techniques' performance due to the presence of domain shift between simulated and experimental data. Here, for the first time, we propose a deep learning-based method that does not require ground truth to correct the phase aberration problem, and as such, can be directly trained on real data. We train a network wherein both the input and target output are randomly aberrated radio frequency (RF) data. Moreover, we demonstrate that a conventional loss function such as mean square error is inadequate for training such a network to achieve optimal performance. Instead, we propose an adaptive mixed loss function that employs both B-mode and RF data, resulting in more efficient convergence and enhanced performance. Finally, we publicly release our dataset, including 161,701 single plane-wave images (RF data). This dataset serves to mitigate the data scarcity problem in the development of deep learning-based techniques for phase aberration correction.Comment: arXiv admin note: text overlap with arXiv:2303.0574

On APF Test for Poisson Process with Shift and Scale Parameters

We propose the goodness of fit test for inhomogeneous Poisson processes with unknown scale and shift parameters. A test statistic of Cramer-von Mises type is proposed and its asymptotic behavior is studied. We show that under null hypothesis the limit distribution of this statistic does not depend on unknown parameters.Comment: 15 page

Fixing Nonconvergence of Algebraic Iterative Reconstruction with an Unmatched Backprojector

We consider algebraic iterative reconstruction methods with applications in image reconstruction. In particular, we are concerned with methods based on an unmatched projector/backprojector pair; i.e., the backprojector is not the exact adjoint or transpose of the forward projector. Such situations are common in large-scale computed tomography, and we consider the common situation where the method does not converge due to the nonsymmetry of the iteration matrix. We propose a modified algorithm that incorporates a small shift parameter, and we give the conditions that guarantee convergence of this method to a fixed point of a slightly perturbed problem. We also give perturbation bounds for this fixed point. Moreover, we discuss how to use Krylov subspace methods to efficiently estimate the leftmost eigenvalue of a certain matrix to select a proper shift parameter. The modified algorithm is illustrated with test problems from computed tomography

Weak Lensing by Intergalactic Mini-Structures in Quadruple Lens Systems: Simulation and Detection

We investigate the weak lensing effects of line-of-sight structures on quadruple images in quasar-galaxy strong lens systems based on N-body and ray-tracing simulations that can resolve halos with a mass of 10^5 solar mass. The intervening halos and voids disturb the magnification ratios of lensed images as well as their relative positions due to lensing. The magnification ratios typically change by O(10%) when the shifts of relative angular positions of lensed images are constrained to <0.004 arcsec. The constrained amplitudes of projected density perturbations due to line-of-sight structures are O(10^8) solar mass per arcsec^2. These results are consistent with our new analytical estimate based on the two-point correlation of density fluctuations. The observed mid-infrared (MIR) flux ratios for 6 quasar-galaxy lens systems with quadruple images agree well with the numerically estimated values without taking into account of subhalos residing in the lensing galaxies. We find that the constrained mean amplitudes of projected density perturbations in the line-of-sight are negative, which suggests that the fluxes of lensed images are perturbed mainly by minivoids and minihalos in underdense regions. We derive a new fitting formula for estimating the probability distribution function of magnification perturbation. We also find that the mean amplitude of magnification perturbation roughly equals the standard deviation regardless of the model parameters.Comment: 22 pages, 15 figures, accepted for publication in MNRA