Title: Applications of high-speed optical signal processing in high-dimensional data acquisition
Abstract: Thanks to large bandwidth, and the ability to capture large amount of information in parallel, optical technologies have transformed the way we capture, process, and communicate information. During this talk I will discuss how optical signal processing can be used in conjunction with novel data compression strategies in order to break the decades long bottleneck faced by electronic systems. I will particularly discuss utility of optical signal processing on big data applications ranging from high speed material characterization, to capturing neural signals over large volume at unprecedented depth and speed.
During the first half of this talk I will discuss how we are taking advantage of parallel image acquisition techniques in order to gain a deeper understanding of rapidly evolving combustion events over a broad spectral range. Despite the rich body of scientific research, the volatile nature of the combustion process has presented an obstacle to our understanding of the chemical kinetics involved in flame propagation and evolution. Many combustive reactions occur in the sub mili-second time scale and involve high velocity motion and interaction of fuel reagents. Hyperspectral imaging technologies are an attractive solution which combine high spatial resolution with fine spectral resolution. However, most conventional hyperspectral cameras rely on slow scanning mechanisms and therefore are ill-suited for capturing fast evolving events. The emergence of Compressive Sensing (CS) over the past decade, has opened the doors to acquiring high dimensional signals at high speed. In the first part of this talk I will discuss how novel optical techniques can be combined with CS algorithms to realize Mega Frame hyperspectral imaging platforms for material diagnostics.
The second portion of my talk will focus on high spatio-temporal neural recording applications. Multi-photon microscopy has been a major breakthrough in overcoming optical scattering when imaging individual neurons deep inside the brain of live animals. Despite the impressive image quality and robustness to scattering, point scanning multi-photon microscopes face a fundamental trade-off between the field of view (FOV) and imaging speed. Higher speed, volumetric multi-photon imaging and stimulation technologies have the potential to revolutionize monitoring of neural network activity in vivo. In this part I will discuss our efforts to develop a scalable, volumetric, two-photon neural recording technology that combines rapid, volumetric scanning of a wide illumination field with synchronized high-resolution dynamic spatial patterning within the illumination field. This approach will allow us to both rapidly address large volumes and also achieve high-resolution random access within the sub-regions of the scan. We will leverage the random access capabilities of this hardware to implement compressive and adaptive imaging strategies that maximize the image information acquired for a given time and laser energy.
Title: Control of pattern formation in excitable systems
Abstract: Pattern formation embodies the beauty and complexity of nature. Some patterns like traveling and rotating waves are dynamic, while others such as dots and stripes are static. Both dynamic and static patterns have been observed in a variety of physiological and biological processes such as rotating action potential waves in the brain during sleep, traveling calcium waves in the cardiac muscle, static patterns on the skins of animals, and self-regulated patterns in the animal embryo. Excitable systems represent a class of ultrasensitive systems that are capable of generating different kinds of patterns depending on the interplay between activator and inhibitor dynamics. Through manipulation of different excitable parameters, a diverse array of traveling wave and standing wave patterns can be obtained. In this thesis, I use pattern formation theory to control the excitable systems involved in cell migration and neuroscience to alter the observed phenotype, in an attempt to affect the underlying biological process.
Cell migration is critical in many processes such as cancer metastasis and wound healing. Cells move by extending periodic protrusions of their cortex, and recent years have shown that the cellular cortex is an excitable medium where waves of biochemical species organize the cellular protrusion. Altering the protrusive phenotype can drastically alter cell migration — that can potentially affect critical physiological processes. In the first part of this thesis, I use excitable wave theory to model and predict wave pattern changes in amoeboid cells.
Excitable systems originated in neuroscience, where different patterns of activity reflect different brain states. Sleep is associated with slow waves, while repeated high-frequency waves are associated with epileptic seizures. These patterns arise from the interplay between the cerebral cortex and the thalamus, which form a closed-loop architecture. In the second part of this thesis, I use a three-layer two-dimensional thalamocortical model, to explore the different parameters that may influence different spatio-temporal dynamics on the cortex.
Title: Collaborative Regression and Classification via Bootstrapping
Abstract: In modern machine learning problems and applications, the data that we are dealing with have large dimensions as well as amount, making data analysis time-consuming and computationally inefficient. Sparse recovery algorithms are developed to extract the underlining low dimensional structure from the data. Classical signal recovery based on l1 minimization solves the least squares problem with all available measurements via sparsity-promoting regularization. It has shown promising performances in regression and classification. Previous work on Compressed Sensing (CS) theory reveals that when the true solution is sparse and if the number of measurements is large enough, then solutions to l1 converge to the ground truths. In practice, when the number of measurements is low or when the noise level is high or when measurements arrive sequentially in streaming fashion, conventional l1 minimization algorithms tend to struggle in signal recovery.
This research work aims at using multiple local measurements generated from resampling using bootstrap or sub-sampling to efficiently make global predictions to deal with aforementioned challenging scenarios in practice. We develop two main approaches – one extends the conventional bagging scheme in sparse regression from a fixed bootstrapping ratio whereas the other called JOBS applies a support consistency among bootstrapped estimators in a collaborative fashion. We first derive rigorous theoretical guarantees for both proposed approaches and then carefully evaluate them with extensive simulations to quantify their performances. Our algorithms are quite robust compared to the conventional l1 minimization, especially in the scenarios with high measurements noise and low number of measurements. Our theoretical analysis also provides key guidance on how to choose optimal parameters, including bootstrapping ratios and number of collaborative estimates. Finally, we demonstrate that our proposed approaches yield significant performance gains in both sparse regression and classification, which are two crucial problems in the field of signal processing and machine learning.