Single-pixel imaging of a randomly moving object.

Single-pixel imaging enjoys advantages of low budget, broad spectrum, and high imaging speed. However, existing methods cannot clearly reconstruct the object that is fast rotating or randomly moving. In this work, we put forward an effective method to image a randomly moving object based on geometric moment analysis. To the best of our knowledge, this is the first work that reconstructs the shape and motion state of the target without prior knowledge of the speed or position. By using the cake-cutting order Hadamard illumination patterns and low-order geometric moment patterns, we obtain a high-quality video stream of the target which moves at high and varying translational and rotational speeds. The efficient method as verified by simulation and experimental results has great potential for practical applications such as Brownian motion microscopy and remote sensing.

Fast non-line-of-sight imaging based on first photon event stamping.

Non-line-of-sight (NLOS) imaging enables people to see a hidden scene based on multiple interaction information between the object and the carrier. There have been numerous studies focusing on the physical modeling of photon scattering, but few have explored the detection process, which also plays a vital role. In this paper, we put forward a novel, to the best of our knowledge, detection methodology for NLOS imaging based on time-sequential first photon (TSFP) data. We verify the method with both synthetic and experimental data, showing a dramatic reduction in acquisition time cost compared with traditional methods for the same reconstruction quality. This work may contribute to real-time and photon-starved NLOS imaging for practical applications.

Sparse time-frequency decomposition based on dictionary adaptation.

In this paper, we propose a time-frequency analysis method to obtain instantaneous frequencies and the corresponding decomposition by solving an optimization problem. In this optimization problem, the basis that is used to decompose the signal is not known a priori. Instead, it is adapted to the signal and is determined as part of the optimization problem. In this sense, this optimization problem can be seen as a dictionary adaptation problem, in which the dictionary is adaptive to one signal rather than a training set in dictionary learning. This dictionary adaptation problem is solved by using the augmented Lagrangian multiplier (ALM) method iteratively. We further accelerate the ALM method in each iteration by using the fast wavelet transform. We apply our method to decompose several signals, including signals with poor scale separation, signals with outliers and polluted by noise and a real signal. The results show that this method can give accurate recovery of both the instantaneous frequencies and the intrinsic mode functions.

Extracting a shape function for a signal with intra-wave frequency modulation.

In this paper, we develop an effective and robust adaptive time-frequency analysis method for signals with intra-wave frequency modulation. To handle this kind of signals effectively, we generalize our data-driven time-frequency analysis by using a shape function to describe the intra-wave frequency modulation. The idea of using a shape function in time-frequency analysis was first proposed by Wu (Wu 2013 Appl. Comput. Harmon. Anal. 35, 181-199. (doi:10.1016/j.acha.2012.08.008)). A shape function could be any smooth 2π-periodic function. Based on this model, we propose to solve an optimization problem to extract the shape function. By exploring the fact that the shape function is a periodic function with respect to its phase function, we can identify certain low-rank structure of the signal. This low-rank structure enables us to extract the shape function from the signal. Once the shape function is obtained, the instantaneous frequency with intra-wave modulation can be recovered from the shape function. We demonstrate the robustness and efficiency of our method by applying it to several synthetic and real signals. One important observation is that this approach is very stable to noise perturbation. By using the shape function approach, we can capture the intra-wave frequency modulation very well even for noise-polluted signals. In comparison, existing methods such as empirical mode decomposition/ensemble empirical mode decomposition seem to have difficulty in capturing the intra-wave modulation when the signal is polluted by noise.

Diffusion Mechanism in Residual Neural Network: Theory and Applications.

Diffusion, a fundamental internal mechanism emerging in many physical processes, describes the interaction among different objects. In many learning tasks with limited training samples, the diffusion connects the labeled and unlabeled data points and is a critical component for achieving high classification accuracy. Many existing deep learning approaches directly impose the fusion loss when training neural networks. In this work, inspired by the convection-diffusion ordinary differential equations (ODEs), we propose a novel diffusion residual network (Diff-ResNet), internally introduces diffusion into the architectures of neural networks. Under the structured data assumption, it is proved that the proposed diffusion block can increase the distance-diameter ratio that improves the separability of inter-class points and reduces the distance among local intra-class points. Moreover, this property can be easily adopted by the residual networks for constructing the separable hyperplanes. Extensive experiments of synthetic binary classification, semi-supervised graph node classification and few-shot image classification in various datasets validate the effectiveness of the proposed method.

Enhancing Density Maps by Removing the Majority of Particles in Single Particle Cryogenic Electron Microscopy Final Stacks.

Over the past decade, advancements in technology and methodology within the field of cryogenic electron microscopy (cryo-EM) single-particle analysis (SPA) have substantially improved our capacity for high-resolution structural examination of biological macromolecules. This advancement has ushered in a new era of molecular insights, replacing X-ray crystallography as the dominant method and providing answers to longstanding questions in biology. Since cryo-EM does not depend on crystallization, which is a significant limitation of X-ray crystallography, it captures particles of varying quality. Consequently, the selection of particles is crucial, as the quality of the selected particles directly influences the resolution of the reconstructed density map. An innovative iterative approach for particle selection, termed CryoSieve, significantly improves the quality of reconstructed density maps by effectively reducing the number of particles in the final stack. Experimental evidence shows that this method can eliminate the majority of particles in final stacks, resulting in a notable enhancement in the quality of density maps. This article outlines the detailed workflow of this approach and showcases its application on a real-world dataset.

Non-line-of-sight imaging with arbitrary illumination and detection pattern.

Non-line-of-sight (NLOS) imaging aims at reconstructing targets obscured from the direct line of sight. Existing NLOS imaging algorithms require dense measurements at regular grid points in a large area of the relay surface, which severely hinders their availability to variable relay scenarios in practical applications such as robotic vision, autonomous driving, rescue operations and remote sensing. In this work, we propose a Bayesian framework for NLOS imaging without specific requirements on the spatial pattern of illumination and detection points. By introducing virtual confocal signals, we design a confocal complemented signal-object collaborative regularization (CC-SOCR) algorithm for high-quality reconstructions. Our approach is capable of reconstructing both the albedo and surface normal of the hidden objects with fine details under general relay settings. Moreover, with a regular relay surface, coarse rather than dense measurements are enough for our approach such that the acquisition time can be reduced significantly. As demonstrated in multiple experiments, the proposed framework substantially extends the application range of NLOS imaging.

A minority of final stacks yields superior amplitude in single-particle cryo-EM.

Cryogenic electron microscopy (cryo-EM) is widely used to determine near-atomic resolution structures of biological macromolecules. Due to the low signal-to-noise ratio, cryo-EM relies on averaging many images. However, a crucial question in the field of cryo-EM remains unanswered: how close can we get to the minimum number of particles required to reach a specific resolution in practice? The absence of an answer to this question has impeded progress in understanding sample behavior and the performance of sample preparation methods. To address this issue, we develop an iterative particle sorting and/or sieving method called CryoSieve. Extensive experiments demonstrate that CryoSieve outperforms other cryo-EM particle sorting algorithms, revealing that most particles are unnecessary in final stacks. The minority of particles remaining in the final stacks yield superior high-resolution amplitude in reconstructed density maps. For some datasets, the size of the finest subset approaches the theoretical limit.

Non-line-of-sight reconstruction with signal-object collaborative regularization.

Non-line-of-sight imaging aims at recovering obscured objects from multiple scattered lights. It has recently received widespread attention due to its potential applications, such as autonomous driving, rescue operations, and remote sensing. However, in cases with high measurement noise, obtaining high-quality reconstructions remains a challenging task. In this work, we establish a unified regularization framework, which can be tailored for different scenarios, including indoor and outdoor scenes with substantial background noise under both confocal and non-confocal settings. The proposed regularization framework incorporates sparseness and non-local self-similarity of the hidden objects as well as the smoothness of the signals. We show that the estimated signals, albedo, and surface normal of the hidden objects can be reconstructed robustly even with high measurement noise under the proposed framework. Reconstruction results on synthetic and experimental data show that our approach recovers the hidden objects faithfully and outperforms state-of-the-art reconstruction algorithms in terms of both quantitative criteria and visual quality.

MAGIC: Manifold and Graph Integrative Convolutional Network for Low-Dose CT Reconstruction.

Low-dose computed tomography (LDCT) scans, which can effectively alleviate the radiation problem, will degrade the imaging quality. In this paper, we propose a novel LDCT reconstruction network that unrolls the iterative scheme and performs in both image and manifold spaces. Because patch manifolds of medical images have low-dimensional structures, we can build graphs from the manifolds. Then, we simultaneously leverage the spatial convolution to extract the local pixel-level features from the images and incorporate the graph convolution to analyze the nonlocal topological features in manifold space. The experiments show that our proposed method outperforms both the quantitative and qualitative aspects of state-of-the-art methods. In addition, aided by a projection loss component, our proposed method also demonstrates superior performance for semi-supervised learning. The network can remove most noise while maintaining the details of only 10% (40 slices) of the training data labeled.

Group-Sparsity-Based Super-Resolution Dipole Orientation Mapping.

The dipole orientation of fluorophores could be resolved by fluorescence polarization microscopy (FPM), which in turn reveals structural specificity for the labeled organelles. Conventional FPM can detect only the averaged fluorescence anisotropy collected from dipoles within the diffraction-limited volume. Super-resolution dipole orientation mapping (SDOM) method, which applies sparse deconvolution and least square estimation to fluorescence polarization modulation data, achieves the dipole orientation measurement within a sub-diffraction focal area. However, during SDOM analysis, some pixels with fluorescence signal are not resolved with orientation for relatively small adjusted R2. Here we report group-sparsity-based SDOM (GS-SDOM), which utilizes the relevance of modulation sequences to effectively improve the SDOM reconstruction model. More credible resolved dipole orientations with higher adjusted R2 can be mapped and false positive estimation for local dipole orientation is vitally corrected. In addition to achieving the same spatial super-resolution as SDOM does, GS-SDOM accesses more morphological information with more credible orientations and more accurate local dipole distribution estimation. During the GS-SDOM analysis of actin filaments in mammalian kidney cells, the dipole orientation of fluorescence is detected always parallel to the direction of the actin filaments. Also with dipole orientation information extracted by GS-SDOM, the reconstructed visual circle from intensity dimension is discerned as jointed by double close filaments and 3-dimensional co-localization is accomplished in the intersection of actin filaments.

Solitary waves bifurcated from Bloch-band edges in two-dimensional periodic media.

Solitary waves bifurcated from edges of Bloch bands in two-dimensional periodic media are determined both analytically and numerically in the context of a two-dimensional nonlinear Schrödinger equation with a periodic potential. Using multiscale perturbation methods, the envelope equations of solitary waves near Bloch bands are analytically derived. These envelope equations reveal that solitary waves can bifurcate from edges of Bloch bands under either focusing or defocusing nonlinearity, depending on the signs of the second-order dispersion coefficients at the edge points. Interestingly, at edge points with two linearly independent Bloch modes, the envelope equations lead to a host of solitary wave structures, including reduced-symmetry solitons, dipole-array solitons, vortex-cell solitons, and so on-many of which have not been reported before to our knowledge. It is also shown analytically that the centers of envelope solutions can be positioned at only four possible locations at or between potential peaks. Numerically, families of these solitary waves are directly computed both near and far away from the band edges. Near the band edges, the numerical solutions spread over many lattice sites, and they fully agree with the analytical solutions obtained from the envelope equations. Far away from the band edges, solitary waves are strongly localized, with intensity and phase profiles characteristic of individual families.