Compressed sensing with approximate message passing: measurement matrix and algorithm design

Compressed sensing (CS) is an emerging technique that exploits the properties of a sparse or compressible signal to efficiently and faithfully capture it with a sampling rate far below the Nyquist rate. The primary goal of compressed sensing is to achieve the best signal recovery with the least number of samples. To this end, two research directions have been receiving increasing attention: customizing the measurement matrix to the signal of interest and optimizing the reconstruction algorithm. In this thesis, contributions in both directions are made in the Bayesian setting for compressed sensing. The work presented in this thesis focuses on the approximate message passing (AMP) schemes, a new class of recovery algorithm that takes advantage of the statistical properties of the CS problem. First of all, a complete sample distortion (SD) framework is presented to fundamentally quantify the reconstruction performance for a certain pair of measurement matrix and recovery scheme. In the SD setting, the non-optimality region of the homogeneous Gaussian matrix is identified and the novel zeroing matrix is proposed with an improved performance. With the SD framework, the optimal sample allocation strategy for the block diagonal measurement matrix are derived for the wavelet representation of natural images. Extensive simulations validate the optimality of the proposed measurement matrix design. Motivated by the zeroing matrix, we extend the seeded matrix design in the CS literature to the novel modulated matrix structure. The major advantage of the modulated matrix over the seeded matrix lies in the simplicity of its state evolution dynamics. Together with the AMP based algorithm, the modulated matrix possesses a 1-D performance prediction system, with which we can optimize the matrix configuration. We then focus on a special modulated matrix form, designated as the two block matrix, which can also be seen as a generalization of the zeroing matrix. The effectiveness of the two block matrix is demonstrated through both sparse and compressible signals. The underlining reason for the improved performance is presented through the analysis of the state evolution dynamics. The final contribution of the thesis explores improving the reconstruction algorithm. By taking the signal prior into account, the Bayesian optimal AMP (BAMP) algorithm is demonstrated to dramatically improve the reconstruction quality. The key insight for its success is that it utilizes the minimum mean square error (MMSE) estimator for the CS denoising. However, the prerequisite of the prior information makes it often impractical. A novel SURE-AMP algorithm is proposed to address the dilemma. The critical feature of SURE-AMP is that the Stein’s unbiased risk estimate (SURE) based parametric least square estimator is used to replace the MMSE estimator. Given the optimization of the SURE estimator only involves the noisy data, it eliminates the need for the signal prior, thus can accommodate more general sparse models

Near Optimal Compressed Sensing Without Priors:Parametric SURE Approximate Message Passing

Both theoretical analysis and empirical evidence confirm that the approximate message passing (AMP) algorithm can be interpreted as recursively solving a signal denoising problem: at each AMP iteration, one observes a Gaussian noise perturbed original signal. Retrieving the signal amounts to a successive noise cancellation until the noise variance decreases to a satisfactory level. In this paper we incorporate the Stein's unbiased risk estimate (SURE) based parametric denoiser with the AMP framework and propose the novel parametric SURE-AMP algorithm. At each parametric SURE-AMP iteration, the denoiser is adaptively optimized within the parametric class by minimizing SURE, which depends purely on the noisy observation. In this manner, the parametric SURE-AMP is guaranteed with the best-in-class recovery and convergence rate. If the parameter family includes the families of the mimimum mean squared error (MMSE) estimators, we are able to achieve the Bayesian optimal AMP performance without knowing the signal prior. In the paper, we resort to the linear parameterization of the SURE based denoiser and propose three different kernel families as the base functions. Numerical simulations with the Bernoulli-Gaussian, $k$-dense and Student's-t signals demonstrate that the parametric SURE-AMP does not only achieve the state-of-the-art recovery but also runs more than 20 times faster than the EM-GM-GAMP algorithm.Comment: Part of the work will be presented at the European Signal Processing Conference, Lisbon, Portugal, September 201

Influence of viewing conditions on cross-media color matching

We investigated observer metamerism under a variety of viewing conditions, in a set of color-matching experiments using displays and printed color samples under specific light sources. A selection was made of light sources with different illuminances, spectral power distributions, and correlated color temperatures, as well as displays with different sets of primaries. A panel of 157 observers with normal color vision and ages between 20 and 59 years old performed 5465 visual color matches around 9 different color centers. The results from the simulated and real experiments were quite different. Specifically, the mean color difference from the mean changed with experimental viewing conditions, ranging from 0.73 to 1.64 CIELAB units (average 0.99 CIELAB units) in simulated experiments, and from 3.12 to 4.03 CIELAB units (average 3.55 CIELAB units) in real experiments. In real experiments, observers’ variability reduced for light sources with high illuminance and high correlated color temperature. Spectral power distributions affected observer metamerism, but the role played by the primaries of the two displays employed was unclear.National Natural Science Foundation of China (NNSFC), 61675029. Ministry of Economy and Competitiveness of the Government of Spain, co-financed by the European Regional Development Fund (ERDF) of the European Union, research project FIS2016-80983-P

Recognition of sign language subwords based on boosted hidden Markov models

Sign language recognition (SLR) plays an important role in human-computer interaction (HCI), especially for the convenient communication between deaf and hearing society. How to enhance the traditional hidden Markov models (HMM) based SLR is an important issue in the SLR community. And how to refine the boundaries of the classifiers to effectively characterize the property of spread-out of the training samples is another significant issue. In this paper, a new classification framework applying adaptive boosting (AdaBoost) strategy to continuous HMM (CHMM) training procedure at the subwords classification level for SLR is presented. The ensemble of multiple composite CHMMs for each subword trained in boosting iterations tends to concentrate more on the hard-to-classify samples so as to generate more complex decision boundary than that of the single HMM classifier. Experimental results on the vocabulary of frequently used Chinese sign language (CSL) subwords show that the proposed boosted CHMM outperforms the conventional CHMM for SLR

Early Cretaceous high-Ti and low-Ti mafic magmatism in Southeastern Tibet: Insights into magmatic evolution of the Comei Large Igneous Province

The Dala diabase intrusion, at the southeastern margin of the Yardoi gneiss dome, is located within the outcrop area of the ~ 132 Ma Comei Large Igneous Province (LIP), the result of initial activity of the Kerguelen plume. We present new zircon U-Pb geochronology results to show that the Dala diabase was emplaced at ~ 132 Ma and geochemical data (whole-rock element and Sr-Nd isotope ratios, zircon Hf isotopes and Fe-Ti oxide mineral chemistry) to confirm that the Dala diabase intrusion is part of the Comei LIP. The Dala diabase can be divided into a high-Mg/low-Ti series and a low-Mg/high-Ti series. The high-Mg/low-Ti series represents more primitive mafic magma compositions that we demonstrate are parental to the low-Mg/high-Ti series. Fractionation of olivine and clinopyroxene, followed by plagioclase within the low-Mg series, lead to systematic changes in concentrations of mantle compatible elements (Cr, Co, Ni, and V), REEs, HFSEs, and major elements such as Ti and P. Some Dala samples from the low-Mg/high-Ti series contain large ilmenite clusters and show extreme enrichment of Ti with elevated Ti/Y ratios, likely due to settling and accumulation of ilmenite during the magma chamber evolution. However, most samples from throughout the Comei LIP follow the Ti-evolution trend of the typical liquid line of descent (LLD) of primary OIB compositions, showing strong evidence of control of Ti contents by differentiation processes. In many other localities, however, primitive magmas are absent and observed Ti contents of evolved magmas cannot be quantitatively related to source processes. Careful examination of the petrogenetic relationship between co-existing low-Ti and high-Ti mafic rocks is essential to using observed rock chemistry to infer source composition, location, and degree of melting

The Effect of Vinpocetine on Human Cytochrome P450 Isoenzymes by Using a Cocktail Method

Vinpocetine is a derivative of the alkaloid vincamine, which had been prescribed for chronic cerebral vascular ischemia and acute ischemic stroke or used as a dietary supplement for its several different mechanisms of biological activities. However, information on the cytochrome P450 (CYP) enzyme-mediated drug metabolism has not been previously studied. The present study was performed to investigate the effects of vinpocetine on CYPs activity, and cocktail method was used, respectively. To evaluate the effects of vinpocetine on the activity of human CYP3A4, CYP2C9, CYP2C19, CYP2D6, and CYP2E1, human liver microsomes were utilized to incubate with the mixed CYPs probe substrates and the target components. The results indicate that vinpocetine exhibited weak inhibitory effect on the CYP2C9, where the IC50 value is 68.96 μM, whereas the IC50 values for CYP3A4, CYP2C19, CYP2D6, and CYP2E1 were all over range of 100 μM, which showed that vinpocetine had no apparent inhibitory effects on these CYPs. In conclusion, the results indicated that drugs metabolized by CYP2C9 coadministrated with vinpocetine may require attention or dose adjustment

The high contact principle with reward functions involving initial points

This paper examines a class of general optimal stopping problems in which reward functions depend on initial points. Two points of view on the initial point are introduced: one is to view it as a constant, and the other is to view it as a constant process starting from the point. Based on the two different views, two versions of the generalized high contact principle are derived. Finally, we apply the generalized high contact principle to one example

Chromosome-Level Genome Assembly for Acer pseudosieboldianum and Highlights to Mechanisms for Leaf Color and Shape Change

Acer pseudosieboldianum (Pax) Komarov is an ornamental plant with prominent potential and is naturally distributed in Northeast China. Here, we obtained a chromosome-scale genome assembly of A. pseudosieboldianum combining HiFi and Hi-C data, and the final assembled genome size was 690.24 Mb and consisted of 287 contigs, with a contig N50 value of 5.7 Mb and a BUSCO complete gene percentage of 98.4%. Genome evolution analysis showed that an ancient duplication occurred in A. pseudosieboldianum. Phylogenetic analyses revealed that Aceraceae family could be incorporated into Sapindaceae, consistent with the present Angiosperm Phylogeny Group system. We further construct a gene-to-metabolite correlation network and identified key genes and metabolites that might be involved in anthocyanin biosynthesis pathways during leaf color change. Additionally, we identified crucial teosinte branched1, cycloidea, and proliferating cell factors (TCP) transcription factors that might be involved in leaf morphology regulation of A. pseudosieboldianum, Acer yangbiense and Acer truncatum. Overall, this reference genome is a valuable resource for evolutionary history studies of A. pseudosieboldianum and lays a fundamental foundation for its molecular breeding