A Novel Truncated Norm Regularization Method for Multi-channel Color Image Denoising

Due to the high flexibility and remarkable performance, low-rank approximation methods has been widely studied for color image denoising. However, those methods mostly ignore either the cross-channel difference or the spatial variation of noise, which limits their capacity in real world color image denoising. To overcome those drawbacks, this paper is proposed to denoise color images with a double-weighted truncated nuclear norm minus truncated Frobenius norm minimization (DtNFM) method. Through exploiting the nonlocal self-similarity of the noisy image, the similar structures are gathered and a series of similar patch matrices are constructed. For each group, the DtNFM model is conducted for estimating its denoised version. The denoised image would be obtained by concatenating all the denoised patch matrices. The proposed DtNFM model has two merits. First, it models and utilizes both the cross-channel difference and the spatial variation of noise. This provides sufficient flexibility for handling the complex distribution of noise in real world images. Second, the proposed DtNFM model provides a close approximation to the underlying clean matrix since it can treat different rank components flexibly. To solve the problem resulted from DtNFM model, an accurate and effective algorithm is proposed by exploiting the framework of the alternating direction method of multipliers (ADMM). The generated subproblems are discussed in detail. And their global optima can be easily obtained in closed-form. Rigorous mathematical derivation proves that the solution sequences generated by the algorithm converge to a single critical point. Extensive experiments on synthetic and real noise datasets demonstrate that the proposed method outperforms many state-of-the-art color image denoising methods

ULTRA-LOW-LOSS SILICON NITRIDE WAVEGUIDE GRATINGS AND THEIR APPLICATIONS IN ASTROPHOTONICS

Recent progresses in silicon photonics have enabled many exciting applications in data communications, sensing, quantum information, and astrophotonics. Astrophotonics is an emerging research field which aims to apply the fast-evolving photonics technology to astronomy. Compared with the silicon-on-insulator (SOI) based silicon photonics, silicon nitride (SiN) based silicon photonics inherits many prominent characteristics such as CMOS compatibility and fabrication flexibility. Furthermore, SiN-based photonics excels in applications strongly associated with low loss level and wide transparent window. All these features are all very attractive for astronomical instrumentation. Typical applications of astrophotonic components are photonic lanterns, frequency combs, highly selective optical filters, and on-chip spectroscopy. Specifically, the scope of this dissertation covers the astrophotonic filters and spectroscopy, from the design, fabrication to characterization. The photonic components which they are based on are ultra-low-loss SiN waveguide and waveguide gratings. The fabrication techniques of ultra-low-loss SiN photonic devices will be first discussed. I will demonstrate several methods to reduce the waveguide and grating losses, including the optimization of SiN deposition, e-beam lithography, etching, cladding oxide deposition, and thermal annealing. In the third chapter, an efficient waveguide characterization approach is developed for measuring losses in on-chip waveguides. This approach is based on measuring the transmission of a Fabry-Perot Bragg grating cavity formed by two highly reflective and low loss Bragg grating mirrors. In the fourth chapter, I will discuss on the design and characterization of a high performance integrated arbitrary filter from 1450 nm to 1640 nm. The filter’s target spectrum is chosen to suppress the night-sky OH emission lines, which is critical for ground-based astronomical telescopes. To reduce the device footprint, the designed 50-mm-long 55-notch filter is mapped to a compact spiral waveguide. The last topic of this dissertation is on-chip spectroscopy with arrayed waveguide grating (AWG). Different with conventional AWG used in WDM telecommunication applications, this astrophotonic spectroscopic AWG particularly needs a large free spectral range (FSR) and a flat focal-plane for the following up free-space cross disperser. The basic principle and preliminary experimental results of AWG will be first presented, followed by discussions of two AWG designs with flat output-plane

Development of high resolution arrayed waveguide grating spectrometers for astronomical applications: first results

Astrophotonics is the next-generation approach that provides the means to miniaturize near-infrared (NIR) spectrometers for upcoming large telescopes and make them more robust and inexpensive. The target requirements for our spectrograph are: a resolving power of about 3000, wide spectral range (J and H bands), free spectral range of about 30 nm, high on-chip throughput of about 80% (-1dB) and low crosstalk (high contrast ratio) between adjacent on-chip wavelength channels of less than 1% (-20dB). A promising photonic technology to achieve these requirements is Arrayed Waveguide Gratings (AWGs). We have developed our first generation of AWG devices using a silica-on-silicon substrate with a very thin layer of silicon-nitride in the core of our waveguides. The waveguide bending losses are minimized by optimizing the geometry of the waveguides. Our first generation of AWG devices are designed for H band and have a resolving power of around 1500 and free spectral range of about 10 nm around a central wavelength of 1600 nm. The devices have a footprint of only 12 mm x 6 mm. They are broadband (1450-1650 nm), have a peak on-chip throughput of about 80% (-1 dB) and contrast ratio of about 1.5% (-18 dB). These results confirm the robustness of our design, fabrication and simulation methods. Currently, the devices are designed for Transverse Electric (TE) polarization and all the results are for TE mode. We are developing separate J- and H-band AWGs with higher resolving power, higher throughput and lower crosstalk over a wider free spectral range to make them better suited for astronomical applications.Comment: 12 pages, 13 figures, 3 tables. SPIE Astronomical Telescopes and Instrumentation, Edinburgh (26 June - 1 July, 2016

Multi-channel Nuclear Norm Minus Frobenius Norm Minimization for Color Image Denoising

Color image denoising is frequently encountered in various image processing and computer vision tasks. One traditional strategy is to convert the RGB image to a less correlated color space and denoise each channel of the new space separately. However, such a strategy can not fully exploit the correlated information between channels and is inadequate to obtain satisfactory results. To address this issue, this paper proposes a new multi-channel optimization model for color image denoising under the nuclear norm minus Frobenius norm minimization framework. Specifically, based on the block-matching, the color image is decomposed into overlapping RGB patches. For each patch, we stack its similar neighbors to form the corresponding patch matrix. The proposed model is performed on the patch matrix to recover its noise-free version. During the recovery process, a) a weight matrix is introduced to fully utilize the noise difference between channels; b) the singular values are shrunk adaptively without additionally assigning weights. With them, the proposed model can achieve promising results while keeping simplicity. To solve the proposed model, an accurate and effective algorithm is built based on the alternating direction method of multipliers framework. The solution of each updating step can be analytically expressed in closed-from. Rigorous theoretical analysis proves the solution sequences generated by the proposed algorithm converge to their respective stationary points. Experimental results on both synthetic and real noise datasets demonstrate the proposed model outperforms state-of-the-art models

Progress in the Application of Gait Analysis in Orthopedics and Physical Rehabilitation

Human walking function is the biggest characteristic that distinguishes other animals, and it needs the coordination of multiple parts of the body to complete the movement.Gait analysis is a new method to study walking function and state, and it is also a hot topic of medical researchers and medical workers in orthopedics, physical rehabilitation and other fields in recent years.After hundreds of years of development, the medical field has realized the accurate and objective measurement of gait, and developed a variety of gait analysis systems suitable for different needs, such as plantar pressure measurement system, unmarked gait analysis system, wearable sensor system, etc.In the context of the continuous progress of related hardware and software technology, the scope of application of gait analysis is also gradually expanding. This paper mainly combined with the research situation of gait analysis in orthopedics and physical rehabilitation in recent years, to review the new progress of related research