A lightweight transformer for faster and robust EBSD data collection.

Three dimensional electron back-scattered diffraction (EBSD) microscopy is a critical tool in many applications in materials science, yet its data quality can fluctuate greatly during the arduous collection process, particularly via serial-sectioning. Fortunately, 3D EBSD data is inherently sequential, opening up the opportunity to use transformers, state-of-the-art deep learning architectures that have made breakthroughs in a plethora of domains, for data processing and recovery. To be more robust to errors and accelerate this 3D EBSD data collection, we introduce a two step method that recovers missing slices in an 3D EBSD volume, using an efficient transformer model and a projection algorithm to process the transformer's outputs.

A large collection of real-world pediatric sleep studies.

Despite being crucial to health and quality of life, sleep-especially pediatric sleep-is not yet well understood. This is exacerbated by lack of access to sufficient pediatric sleep data with clinical annotation. In order to accelerate research on pediatric sleep and its connection to health, we create the Nationwide Children's Hospital (NCH) Sleep DataBank and publish it at Physionet and the National Sleep Research Resource (NSRR), which is a large sleep data common with physiological data, clinical data, and tools for analyses.

NOISY MATRIX COMPLETION: UNDERSTANDING STATISTICAL GUARANTEES FOR CONVEX RELAXATION VIA NONCONVEX OPTIMIZATION.

This paper studies noisy low-rank matrix completion: given partial and noisy entries of a large low-rank matrix, the goal is to estimate the underlying matrix faithfully and efficiently. Arguably one of the most popular paradigms to tackle this problem is convex relaxation, which achieves remarkable efficacy in practice. However, the theoretical support of this approach is still far from optimal in the noisy setting, falling short of explaining its empirical success.

Vector-Valued Graph Trend Filtering with Non-Convex Penalties.

This work studies the denoising of piecewise smooth graph signals that exhibit inhomogeneous levels of smoothness over a graph, where the value at each node can be vector-valued. We extend the graph trend filtering framework to denoising vector-valued graph signals with a family of non-convex regularizers, which exhibit superior recovery performance over existing convex regularizers. Using an oracle inequality, we establish the statistical error rates of first-order stationary points of the proposed non-convex method for generic graphs.

Gradient Descent with Random Initialization: Fast Global Convergence for Nonconvex Phase Retrieval.

This paper considers the problem of solving systems of quadratic equations, namely, recovering an object of interest from quadratic equations/samples . This problem, also dubbed as phase retrieval, spans multiple domains including physical sciences and machine learning. We investigate the efficacy of gradient descent (or Wirtinger flow) designed for the nonconvex least squares problem.

Streaming PCA and Subspace Tracking: The Missing Data Case.

For many modern applications in science and engineering, data are collected in a streaming fashion carrying time-varying information, and practitioners need to process them with a limited amount of memory and computational resources in a timely manner for decision making. This often is coupled with the missing data problem, such that only a small fraction of data attributes are observed. These complications impose significant, and unconventional, constraints on the problem of streaming Principal Component Analysis (PCA) and subspace tracking, which is an essential building block for many inference tasks in signal processing and machine learning.

Classification and Boosting with Multiple Collaborative Representations.

Recent advances have shown a great potential to explore collaborative representations of test samples in a dictionary composed of training samples from all classes in multi-class recognition including sparse representations. In this paper, we present two multi-class classification algorithms that make use of multiple collaborative representations in their formulations, and demonstrate performance gain of exploring this extra degree of freedom. We first present the Collaborative Representation Optimized Classifier (CROC), which strikes a balance between the nearest-subspace classifier, which assigns a test sample to the class that minimizes the distance between the sample and its principal projection in the selected class, and a Collaborative Representation based Classifier (CRC), which assigns a test sample to the class that minimizes the distance between the sample and its collaborative components.

Fast two-dimensional super-resolution image reconstruction algorithm for ultra-high emitter density.

Single-molecule localization microscopy achieves sub-diffraction-limit resolution by localizing a sparse subset of stochastically activated emitters in each frame. Its temporal resolution is limited by the maximal emitter density that can be handled by the image reconstruction algorithms. Multiple algorithms have been developed to accurately locate the emitters even when they have significant overlaps.

3D multifocus astigmatism and compressed sensing (3D MACS) based superresolution reconstruction.

Single molecule based superresolution techniques (STORM/PALM) achieve nanometer spatial resolution by integrating the temporal information of the switching dynamics of fluorophores (emitters). When emitter density is low for each frame, they are located to the nanometer resolution. However, when the emitter density rises, causing significant overlapping, it becomes increasingly difficult to accurately locate individual emitters.

Resolving spatial modes of lasers via matrix completion.

We explain a technique that recovers the structure and the modal weights of spatial modes of lasers from a limited number of spatial coherence measurements. Our approach interpolates the unobserved spatial coherence measurements via the low-rank matrix completion algorithm based on nuclear norm minimization and then extracts the set of modes via singular value decomposition. Numerical examples are provided on a variety of lasers to demonstrate the effectiveness of the method, and it is shown that the proposed method can further reduce the number of measurements by a factor of 2 for a moderate data size.

Diagnostic grade wireless ECG monitoring.

In remote monitoring of Electrocardiogram (ECG), it is very important to ensure that the diagnostic integrity of signals is not compromised by sensing artifacts and channel errors. It is also important for the sensors to be extremely power efficient to enable wearable form factors and long battery life. We present an application of Compressive Sensing (CS) as an error mitigation scheme at the application layer for wearable, wireless sensors in diagnostic grade remote monitoring of ECG.