On an iteratively reweighted linesearch based algorithm for nonconvex composite optimization

In this paper we propose a new algorithm for solving a class of nonsmooth nonconvex problems, which is obtained by combining the iteratively reweighted scheme with a finite number of forward–backward iterations based on a linesearch procedure. The new method overcomes some limitations of linesearch forward–backward methods, since it can be applied also to minimize functions containing terms that are both nonsmooth and nonconvex. Moreover, the combined scheme can take advantage of acceleration techniques consisting in suitable selection rules for the algorithm parameters. We develop the convergence analysis of the new method within the framework of the Kurdyka– Lojasiewicz property. Finally, we present the results of a numerical experience on microscopy image super resolution, showing that the performances of our method are comparable or superior to those of other algorithms designed for this specific application

Optical trapping with structured light : a review

Funding: This work was supported by the National Natural Science Foundation of China (11874102 and 61975047), the Sichuan Province Science and Technology Support Program (2020JDRC0006), and the Fundamental Research Funds for the Central Universities (ZYGX2019J102). M.C. and Y.A. thank the UK Engineering and Physical Sciences Research Council for funding.Optical trapping describes the interaction between light and matter to manipulate micro-objects through momentum transfer. In the case of 3D trapping with a single beam, this is termed optical tweezers. Optical tweezers are a powerful and noninvasive tool for manipulating small objects, and have become indispensable in many fields, including physics, biology, soft condensed matter, among others. In the early days, optical trapping was typically accomplished with a single Gaussian beam. In recent years, we have witnessed rapid progress in the use of structured light beams with customized phase, amplitude, and polarization in optical trapping. Unusual beam properties, such as phase singularities on-axis and propagation invariant nature, have opened up novel capabilities to the study of micromanipulation in liquid, air, and vacuum. We summarize the recent advances in the field of optical trapping using structured light beams.Publisher PDFPeer reviewe

Linear Spectral Unmixing Algorithms for Abundance Fraction Estimation in Spectroscopy

Fluorescence spectroscopy is commonly used in modern biological and chemical studies, especially for cellular and molecular analysis. Since the measured fluorescence spectrum is the sum of the spectrum of each fluorophore in a sample, a reliable separation of fluorescent labels is the key to the successful analysis of the sample. A technique known as linear spectral unmixing is often used to linearly decompose the measured fluorescence spectrum into a set of constituent fluorescence spectra with abundance fractions. Various algorithms have been developed for linear spectral unmixing. In this work, we implement the existing linear unmixing algorithms and compare their results to discuss their strengths and drawbacks. Furthermore, we apply optimization methods to the linear unmixing problem and evaluate their performance to demonstrate their capabilities of solving the linear unmixing problem. Finally, we denoise noisy fluorescence emission spectra and examine how noise may affect the performance of the algorithms