Optimization Methods for Inverse Problems

Optimization plays an important role in solving many inverse problems. Indeed, the task of inversion often either involves or is fully cast as a solution of an optimization problem. In this light, the mere non-linear, non-convex, and large-scale nature of many of these inversions gives rise to some very challenging optimization problems. The inverse problem community has long been developing various techniques for solving such optimization tasks. However, other, seemingly disjoint communities, such as that of machine learning, have developed, almost in parallel, interesting alternative methods which might have stayed under the radar of the inverse problem community. In this survey, we aim to change that. In doing so, we first discuss current state-of-the-art optimization methods widely used in inverse problems. We then survey recent related advances in addressing similar challenges in problems faced by the machine learning community, and discuss their potential advantages for solving inverse problems. By highlighting the similarities among the optimization challenges faced by the inverse problem and the machine learning communities, we hope that this survey can serve as a bridge in bringing together these two communities and encourage cross fertilization of ideas.Comment: 13 page

Bio-Inspired Multi-Spectral Image Sensor and Augmented Reality Display for Near-Infrared Fluorescence Image-Guided Surgery

Background: Cancer remains a major public health problem worldwide and poses a huge economic burden. Near-infrared (NIR) fluorescence image-guided surgery (IGS) utilizes molecular markers and imaging instruments to identify and locate tumors during surgical resection. Unfortunately, current state-of-the-art NIR fluorescence imaging systems are bulky, costly, and lack both fluorescence sensitivity under surgical illumination and co-registration accuracy between multimodal images. Additionally, the monitor-based display units are disruptive to the surgical workflow and are suboptimal at indicating the 3-dimensional position of labeled tumors. These major obstacles have prevented the wide acceptance of NIR fluorescence imaging as the standard of care for cancer surgery. The goal of this dissertation is to enhance cancer treatment by developing novel image sensors and presenting the information using holographic augmented reality (AR) display to the physician in intraoperative settings. Method: By mimicking the visual system of the Morpho butterfly, several single-chip, color-NIR fluorescence image sensors and systems were developed with CMOS technologies and pixelated interference filters. Using a holographic AR goggle platform, an NIR fluorescence IGS display system was developed. Optoelectronic evaluation was performed on the prototypes to evaluate the performance of each component, and small animal models and large animal models were used to verify the overall effectiveness of the integrated systems at cancer detection. Result: The single-chip bio-inspired multispectral logarithmic image sensor I developed has better main performance indicators than the state-of-the-art NIR fluorescence imaging instruments. The image sensors achieve up to 140 dB dynamic range. The sensitivity under surgical illumination achieves 6108 V/(mW/cm2), which is up to 25 times higher. The signal-to-noise ratio is up to 56 dB, which is 11 dB greater. These enable high sensitivity fluorescence imaging under surgical illumination. The pixelated interference filters enable temperature-independent co-registration accuracy between multimodal images. Pre-clinical trials with small animal model demonstrate that the sensor can achieve up to 95% sensitivity and 94% specificity with tumor-targeted NIR molecular probes. The holographic AR goggle provides the physician with a non-disruptive 3-dimensional display in the clinical setup. This is the first display system that co-registers a virtual image with human eyes and allows video rate image transmission. The imaging system is tested in the veterinary science operating room on canine patients with naturally occurring cancers. In addition, a time domain pulse-width-modulation address-event-representation multispectral image sensor and a handheld multispectral camera prototype are developed. Conclusion: The major problems of current state-of-the-art NIR fluorescence imaging systems are successfully solved. Due to enhanced performance and user experience, the bio-inspired sensors and augmented reality display system will give medical care providers much needed technology to enable more accurate value-based healthcare

Phase Lag and Coherence Function of X-ray emission from Black Hole Candidate XTE J1550-564

We report the results from measuring the phase lag and coherence function of X-ray emission from black hole candidate (BHC) XTE J1550-564. These X-ray temporal properties have been recognized to be increasingly important in providing important diagnostics of the dynamics of accretion flows around black holes. For XTE J1550-564, we found significant hard lag --- the X-ray variability in high energy bands {\em lags} behind that in low energy bands --- associated both with broad-band variability and quasi-periodic oscillation (QPO). However, the situation is more complicated for the QPO: while hard lag was measured for the first harmonic of the signal, the fundamental component showed significant {\em soft} lag. Such behavior is remarkably similar to what was observed of microquasar GRS 1915+105. The phase lag evolved during the initial rising phase of the 1998 outburst. The magnitude of both the soft and hard lags of the QPO increases with X-ray flux, while the Fourier spectrum of the broad-band lag varies significantly in shape. The coherence function is relatively high and roughly constant at low frequencies, and begins to drop almost right after the first harmonic of the QPO. It is near unity at the beginning and decreases rapidly during the rising phase. Also observed is that the more widely separated the two energy bands are the less the coherence function between the two. It is interesting that the coherence function increases significantly at the frequencies of the QPO and its harmonics. We discuss the implications of the results on the models proposed for BHCs.Comment: To appear in ApJ Letter

OPTIMAL PORTFOLIO CONSTRUCTION BY MIXING HEDGE FUND

The returns of the hedge fund are declining in recent years, accompanying with the impact of the financial crisis in 2008. There will be a question that whether the hedge fund can still be used to blend in a conventional portfolio to improve the performance. Our paper focuses on the comparison analysis and does the basic asset allocation for the hedge fund and traditional portfolio. We analyze the risk-adjusted returns for conventional assets of US Equities, EAFE Equities, US Bonds and International Bonds as well as the hedge fund. Finally we find that, under current market condition, hedge fund is still an ideal alternative asset for the choice of the portfolio to increase the risk-adjusted return level

Coil combination using linear deconvolution in k-space for phase imaging

Background: The combination of multi-channel data is a critical step for the imaging of phase and susceptibility contrast in magnetic resonance imaging (MRI). Magnitude-weighted phase combination methods often produce noise and aliasing artifacts in the magnitude images at accelerated imaging sceneries. To address this issue, an optimal coil combination method through deconvolution in k-space is proposed in this paper. Methods: The proposed method firstly employs the sum-of-squares and phase aligning method to yield a complex reference coil image which is then used to calculate the coil sensitivity and its Fourier transform. Then, the coil k-space combining weights is computed, taking into account the truncated frequency data of coil sensitivity and the acquired k-space data. Finally, combining the coil k-space data with the acquired weights generates the k-space data of proton distribution, with which both phase and magnitude information can be obtained straightforwardly. Both phantom and in vivo imaging experiments were conducted to evaluate the performance of the proposed method. Results: Compared with magnitude-weighted method and MCPC-C, the proposed method can alleviate the phase cancellation in coil combination, resulting in a less wrapped phase. Conclusions: The proposed method provides an effective and efficient approach to combine multiple coil image in parallel MRI reconstruction, and has potential to benefit routine clinical practice in the future