New results on multidimensional Chinese remainder theorem

The Chinese remainder theorem (CRT) [McClellan and Rader 1979] has been well known for applications in fast DFT computations and computer arithmetic. Guessoum and Mersereau [1986] first made headway in extending the CRT to multidimensional (MD) nonseparable systems and showing its usefulness. The present letter generalize the result and present a more general form. This more general MDCRT is an exact counterpart of 1DCRT

Discrete multitone modulation with principal component filter banks

Discrete multitone (DMT) modulation is an attractive method for communication over a nonflat channel with possibly colored noise. The uniform discrete Fourier transform (DFT) filter bank and cosine modulated filter bank have in the past been used in this system because of low complexity. We show in this paper that principal component filter banks (PCFB) which are known to be optimal for data compression and denoising applications, are also optimal for a number of criteria in DMT modulation communication. For example, the PCFB of the effective channel noise power spectrum (noise psd weighted by the inverse of the channel gain) is optimal for DMT modulation in the sense of maximizing bit rate for fixed power and error probabilities. We also establish an optimality property of the PCFB when scalar prefilters and postfilters are used around the channel. The difference between the PCFB and a traditional filter bank such as the brickwall filter bank or DFT filter bank is significant for effective power spectra which depart considerably from monotonicity. The twisted pair channel with its bridged taps, next and fext noises, and AM interference, therefore appears to be a good candidate for the application of a PCFB. This is demonstrated with the help of numerical results for the case of the ADSL channel

Enriched Long-term Recurrent Convolutional Network for Facial Micro-Expression Recognition

Facial micro-expression (ME) recognition has posed a huge challenge to researchers for its subtlety in motion and limited databases. Recently, handcrafted techniques have achieved superior performance in micro-expression recognition but at the cost of domain specificity and cumbersome parametric tunings. In this paper, we propose an Enriched Long-term Recurrent Convolutional Network (ELRCN) that first encodes each micro-expression frame into a feature vector through CNN module(s), then predicts the micro-expression by passing the feature vector through a Long Short-term Memory (LSTM) module. The framework contains two different network variants: (1) Channel-wise stacking of input data for spatial enrichment, (2) Feature-wise stacking of features for temporal enrichment. We demonstrate that the proposed approach is able to achieve reasonably good performance, without data augmentation. In addition, we also present ablation studies conducted on the framework and visualizations of what CNN "sees" when predicting the micro-expression classes.Comment: Published in Micro-Expression Grand Challenge 2018, Workshop of 13th IEEE Facial & Gesture 201

Towards Accurate One-Stage Object Detection with AP-Loss

One-stage object detectors are trained by optimizing classification-loss and localization-loss simultaneously, with the former suffering much from extreme foreground-background class imbalance issue due to the large number of anchors. This paper alleviates this issue by proposing a novel framework to replace the classification task in one-stage detectors with a ranking task, and adopting the Average-Precision loss (AP-loss) for the ranking problem. Due to its non-differentiability and non-convexity, the AP-loss cannot be optimized directly. For this purpose, we develop a novel optimization algorithm, which seamlessly combines the error-driven update scheme in perceptron learning and backpropagation algorithm in deep networks. We verify good convergence property of the proposed algorithm theoretically and empirically. Experimental results demonstrate notable performance improvement in state-of-the-art one-stage detectors based on AP-loss over different kinds of classification-losses on various benchmarks, without changing the network architectures. Code is available at https://github.com/cccorn/AP-loss.Comment: 13 pages, 7 figures, 4 tables, main paper + supplementary material, accepted to CVPR 201

Stochastic Downsampling for Cost-Adjustable Inference and Improved Regularization in Convolutional Networks

It is desirable to train convolutional networks (CNNs) to run more efficiently during inference. In many cases however, the computational budget that the system has for inference cannot be known beforehand during training, or the inference budget is dependent on the changing real-time resource availability. Thus, it is inadequate to train just inference-efficient CNNs, whose inference costs are not adjustable and cannot adapt to varied inference budgets. We propose a novel approach for cost-adjustable inference in CNNs - Stochastic Downsampling Point (SDPoint). During training, SDPoint applies feature map downsampling to a random point in the layer hierarchy, with a random downsampling ratio. The different stochastic downsampling configurations known as SDPoint instances (of the same model) have computational costs different from each other, while being trained to minimize the same prediction loss. Sharing network parameters across different instances provides significant regularization boost. During inference, one may handpick a SDPoint instance that best fits the inference budget. The effectiveness of SDPoint, as both a cost-adjustable inference approach and a regularizer, is validated through extensive experiments on image classification

Optimizing the capacity of orthogonal and biorthogonal DMT channels

The uniform DFT filter bank has been used routinely in discrete multitone modulation (DMT) systems because of implementation efficiency. It has recently been shown that principal component filter banks (PCFB) which are known to be optimal for data compression and denoising applications, are also optimal for a number of criteria in DMT communication. In this paper we show that such filter banks are optimal even when scalar prefilters and postfilters are used around the channel. We show that the theoretically optimum scalar prefilter is the half-whitening solution, well known in data compression theory. We conclude with the observation that the PCFB continues to be optimal for the maximization of theoretical capacity as well

Transient Three-Dimensional Side Load Analysis of Out-of-Round Film Cooled Nozzles

The objective of this study is to investigate the effect of nozzle out-of-roundness on the transient startup side loads. The out-of-roundness could be the result of asymmetric loads induced by hardware attached to the nozzle, asymmetric internal stresses induced by previous tests and/or deformation, such as creep, from previous tests. The rocket engine studied encompasses a regeneratively cooled thrust chamber and a film cooled nozzle extension with film coolant distributed from a turbine exhaust manifold. The computational methodology is based on an unstructured-grid, pressure-based computational fluid dynamics formulation, and a transient inlet history based on an engine system simulation. Transient startup computations were performed with the out-of-roundness achieved by four degrees of ovalization of the nozzle: one perfectly round, one slightly out-of-round, one more out-of-round, and one significantly out-of-round. The computed side load physics caused by the nozzle out-of-roundness and its effect on nozzle side load are reported and discussed