An Efficient Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-lsotropicTotalVariation

In this paper,we design an efficient,multi-stage image segmentation framework that incorporates a weighted difference of anisotropic and isotropic total variation(AITV).The segmentation framework generally consists of two stages:smoothing and thresholding,thus referred to as smoothing-and-thresholding(SaT).In the first stage,a smoothed image is obtained by an AITV-regularized Mumford-Shah(MS)model,which can be solved efficiently by the alternating direction method of multipliers(ADMMs)with a closed-form solution of a proximal operator of the l_(1)-αl_(2) regularizer.The convergence of the ADMM algorithm is analyzed.In the second stage,we threshold the smoothed image by K-means clustering to obtain the final segmentation result.Numerical experiments demonstrate that the proposed segmentation framework is versatile for both grayscale and color images,effcient in producing high-quality segmentation results within a few seconds,and robust to input images that are corrupted with noise,blur,or both.We compare the AITV method with its original convex TV and nonconvex TVP(O<p<1)counterparts,showcasing the qualitative and quantitative advantages of our proposed method.

Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent

We prove,under mild conditions,the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model,both in batch gradient descent and stochastic gradient descent.We also discuss a Riemannian version of the Adam algorithm.We show numerical simulations of these algorithms on various benchmarks.

QUANTIZATION AND TRAINING OF LOW BIT-WIDTH CONVOLUTIONAL NEURAL NETWORKS FOR OBJECT DETECTION

We presen t LBW-Net,an efficient optimization based method for qua nt ization and training of the low bit-width convolutional neural networks(CNNs).Specifically,we quantize the weights to zero or powers of 2 by minimizing the Euclidean distance between full-precision weights and quantized weights during backpropagation(weight learning).We characterize the combinatorial nature of the low bit-width quantization problem.For 2-bit(ternary)CNNs,the quantization of N weights can be done by an exact formula in O(N log N)complexity.When the bit-width is 3 and above,we further propose a semi-analytical thresholding scheme with a single free parameter for quantization that is computationally inexpensive.The free parameter is further determined by network retraining and object detection tests.The LBW-Net has several desirable advantages over full-precision CNNs,including considerable memory savings,energy efficiency,and faster deployment.Our experiments on PASCAL VOC dataset show that compared with its 32-bit floating-point counterpart,the performance of the 6-bit LBW-Net is nearly lossless in the object detection tasks,and can even do better in real world visual scenes,while empirically enjoying more than 4× faster deployment.

Deep Learning for Real-Time Crime Forecasting and Its Ternarization

Real-time crime forecasting is important.However,accurate prediction of when and where the next crime will happen is difficult.No known physical model provides a reasonable approximation to such a complex system.Historical crime data are sparse in both space and time and the signal of interests is weak.In this work,the authors first present a proper representation of crime data.The authors then adapt the spatial temporal residual network on the well represented data to predict the distribution of crime in Los Angeles at the scale of hours in neighborhood-sized parcels.These experiments as well as comparisons with several existing approaches to prediction demonstrate the superiority of the proposed model in terms of accuracy.Finally,the authors present a ternarization technique to address the resource consumption issue for its deployment in real world.This work is an extension of our short conference proceeding paper[Wang,B.,Zhang,D.,Zhang,D.H.,et al.,Deep learning for real time Crime forecasting,2017,ar Xiv:1707.03340].

ITERATIVE l1 MINIMIZATION FOR NON-CONVEX COMPRESSED SENSING

An algorithmic framework, based on the difference of convex functions algorithm （D- CA）, is proposed for minimizing a class of concave sparse metrics for compressed sensing problems. The resulting algorithm iterates a sequence ofl1 minimization problems. An exact sparse recovery theory is established to show that the proposed framework always improves on the basis pursuit （l1 minimization） and inherits robustness from it. Numerical examples on success rates of sparse solution recovery illustrate further that, unlike most existing non-convex compressed sensing solvers in the literature, our method always out- performs basis pursuit, no matter how ill-conditioned the measurement matrix is. Moreover, the iterative l1 （ILl） algorithm lead by a wide margin the state-of-the-art algorithms on l1/2 and logarithimic minimizations in the strongly coherent （highly ill-conditioned） regime, despite the same objective functions. Last but not least, in the application of magnetic resonance imaging （MRI）, IL1 algorithm easily recovers the phantom image with just 7 line projections.

A TIME DOMAIN BLIND DECORRELATION METHOD OF CONVOLUTIVE MIXTURES BASED ON AN IIR MODEL

We study a time domain decorrelation method of source signal separation from convolutive sound mixtures based on an infinite impulse response （IIR） model. The IIR model uses fewer parameters to capture the physical mixing process and is useful for finding low dimensional separating solutions. We present inversion formulas to decorrelate the mixture signals and derive filter equations involving second order time lagged statistics of mixtures. We then formulate an 11 constrained minimization problem and solve it by an iterative method. Numerical experiments on recorded sound mixtures show that our method is capable of sound separation in low dimensional parameter spaces with good perceptual quality and low correlation coefficient comparable to the known infomax method.