Kevin Bui

Kevin Bui, Yifei Lou, Fredrick Park et al.

Poisson noise commonly occurs in images captured by photon-limited imaging systems such as in astronomy and medicine. As the distribution of Poisson noise depends on the pixel intensity value, noise levels vary from pixels to pixels. Hence, denoising a Poisson-corrupted image while preserving important details can be challenging. In this paper, we propose a Poisson denoising model by incorporating the weighted anisotropic-isotropic total variation (AITV) as a regularization. We then develop an alternating direction method of multipliers with a combination of a proximal operator for an efficient implementation. Lastly, numerical experiments demonstrate that our algorithm outperforms other Poisson denoising methods in terms of image quality and computational efficiency.

Kevin Bui, Fanghui Xue, Fredrick Park et al.

As a popular channel pruning method for convolutional neural networks (CNNs), network slimming (NS) has a three-stage process: (1) it trains a CNN with $\ell_1$ regularization applied to the scaling factors of the batch normalization layers; (2) it removes channels whose scaling factors are below a chosen threshold; and (3) it retrains the pruned model to recover the original accuracy. This time-consuming, three-step process is a result of using subgradient descent to train CNNs. Because subgradient descent does not exactly train CNNs towards sparse, accurate structures, the latter two steps are necessary. Moreover, subgradient descent does not have any convergence guarantee. Therefore, we develop an alternative algorithm called proximal NS. Our proposed algorithm trains CNNs towards sparse, accurate structures, so identifying a scaling factor threshold is unnecessary and fine tuning the pruned CNNs is optional. Using Kurdyka-Łojasiewicz assumptions, we establish global convergence of proximal NS. Lastly, we validate the efficacy of the proposed algorithm on VGGNet, DenseNet and ResNet on CIFAR 10/100. Our experiments demonstrate that after one round of training, proximal NS yields a CNN with competitive accuracy and compression.

Kevin Bui, Yifei Lou, Fredrick Park et al.

In this paper, we aim to segment an image degraded by blur and Poisson noise. We adopt a smoothing-and-thresholding (SaT) segmentation framework that finds a piecewise-smooth solution, followed by $k$-means clustering to segment the image. Specifically for the image smoothing step, we replace the least-squares fidelity for Gaussian noise in the Mumford-Shah model with a maximum posterior (MAP) term to deal with Poisson noise and we incorporate the weighted difference of anisotropic and isotropic total variation (AITV) as a regularization to promote the sparsity of image gradients. For such a nonconvex model, we develop a specific splitting scheme and utilize a proximal operator to apply the alternating direction method of multipliers (ADMM). Convergence analysis is provided to validate the efficacy of the ADMM scheme. Numerical experiments on various segmentation scenarios (grayscale/color and multiphase) showcase that our proposed method outperforms a number of segmentation methods, including the original SaT.

Yu Lu, Kevin Bui, Roummel F. Marcia

Matrix completion focuses on recovering missing or incomplete information in matrices. This problem arises in various applications, including image processing and network analysis. Previous research proposed Poisson matrix completion for count data with noise that follows a Poisson distribution, which assumes that the mean and variance are equal. Since overdispersed count data, whose variance is greater than the mean, is more likely to occur in realistic settings, we assume that the noise follows the negative binomial (NB) distribution, which can be more general than the Poisson distribution. In this paper, we introduce NB matrix completion by proposing a nuclear-norm regularized model that can be solved by proximal gradient descent. In our experiments, we demonstrate that the NB model outperforms Poisson matrix completion in various noise and missing data settings on real data.

Yu Lu, Kevin Bui, Roummel F. Marcia

In many applications such as medical imaging, the measurement data represent counts of photons hitting a detector. Such counts in low-photon settings are often modeled using a Poisson distribution. However, this model assumes that the mean and variance of the signal's noise distribution are equal. For overdispersed data where the variance is greater than the mean, the negative binomial distribution is a more appropriate statistical model. In this paper, we propose an optimization approach for recovering images corrupted by overdispersed Poisson noise. In particular, we incorporate a weighted anisotropic-isotropic total variation regularizer, which avoids staircasing artifacts that are introduced by a regular total variation penalty. We use an alternating direction method of multipliers, where each subproblem has a closed-form solution. Numerical experiments demonstrate the effectiveness of our proposed approach, especially in very photon-limited settings.

Jiahao Pang, Kevin Bui, Dong Tian

The universality of the point cloud format enables many 3D applications, making the compression of point clouds a critical phase in practice. Sampled as discrete 3D points, a point cloud approximates 2D surface(s) embedded in 3D with a finite bit-depth. However, the point distribution of a practical point cloud changes drastically as its bit-depth increases, requiring different methodologies for effective consumption/analysis. In this regard, a heterogeneous point cloud compression (PCC) framework is proposed. We unify typical point cloud representations -- point-based, voxel-based, and tree-based representations -- and their associated backbones under a learning-based framework to compress an input point cloud at different bit-depth levels. Having recognized the importance of voxel-domain processing, we augment the framework with a proposed context-aware upsampling for decoding and an enhanced voxel transformer for feature aggregation. Extensive experimentation demonstrates the state-of-the-art performance of our proposal on a wide range of point clouds.

Nhat Thanh Tran, Kevin Bui, Jack Xin

Image smoothing is a fundamental image processing operation that preserves the underlying structure, such as strong edges and contours, and removes minor details and textures in an image. Many image smoothing algorithms rely on computing local window statistics or solving an optimization problem. Recent state-of-the-art methods leverage deep learning, but they require a carefully curated training dataset. Because constructing a proper training dataset for image smoothing is challenging, we propose DIP-$\ell_0$, a deep image prior framework that incorporates the $\ell_0$ gradient regularizer. This framework can perform high-quality image smoothing without any training data. To properly minimize the associated loss function that has the nonconvex, nonsmooth $\ell_0$ ``norm", we develop an alternating direction method of multipliers algorithm that utilizes an off-the-shelf $\ell_0$ gradient minimization solver. Numerical experiments demonstrate that the proposed DIP-$\ell_0$ outperforms many image smoothing algorithms in edge-preserving image smoothing and JPEG artifact removal.

Elisha Dayag, Kevin Bui, Fredrick Park et al.

Based on transformed $\ell_1$ regularization, transformed total variation (TTV) has robust image recovery that is competitive with other nonconvex total variation (TV) regularizers, such as TV$^p$, $0<p<1$. Inspired by its performance, we propose a TTV-regularized Mumford--Shah model with fuzzy membership function for image segmentation. To solve it, we design an alternating direction method of multipliers (ADMM) algorithm that utilizes the transformed $\ell_1$ proximal operator. Numerical experiments demonstrate that using TTV is more effective than classical TV and other nonconvex TV variants in image segmentation.

Kevin Bui, Yifei Lou, Fredrick Park et al.

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 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 (ADMM) with a closed-form solution of a proximal operator of the $\ell_1 -α\ell_2$ regularizer. 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, efficient 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 TV$^p (0<p<1)$ counterparts, showcasing the qualitative and quantitative advantages of our proposed method.

Kevin Bui, Fredrick Park, Shuai Zhang et al.

Convolutional neural networks (CNNs) have developed to become powerful models for various computer vision tasks ranging from object detection to semantic segmentation. However, most of the state-of-the-art CNNs cannot be deployed directly on edge devices such as smartphones and drones, which need low latency under limited power and memory bandwidth. One popular, straightforward approach to compressing CNNs is network slimming, which imposes $\ell_1$ regularization on the channel-associated scaling factors via the batch normalization layers during training. Network slimming thereby identifies insignificant channels that can be pruned for inference. In this paper, we propose replacing the $\ell_1$ penalty with an alternative nonconvex, sparsity-inducing penalty in order to yield a more compressed and/or accurate CNN architecture. We investigate $\ell_p (0 < p < 1)$, transformed $\ell_1$ (T$\ell_1$), minimax concave penalty (MCP), and smoothly clipped absolute deviation (SCAD) due to their recent successes and popularity in solving sparse optimization problems, such as compressed sensing and variable selection. We demonstrate the effectiveness of network slimming with nonconvex penalties on three neural network architectures -- VGG-19, DenseNet-40, and ResNet-164 -- on standard image classification datasets. Based on the numerical experiments, T$\ell_1$ preserves model accuracy against channel pruning, $\ell_{1/2, 3/4}$ yield better compressed models with similar accuracies after retraining as $\ell_1$, and MCP and SCAD provide more accurate models after retraining with similar compression as $\ell_1$. Network slimming with T$\ell_1$ regularization also outperforms the latest Bayesian modification of network slimming in compressing a CNN architecture in terms of memory storage while preserving its model accuracy after channel pruning.

Kevin Bui, Fredrick Park, Yifei Lou et al.

In a class of piecewise-constant image segmentation models, we propose to incorporate a weighted difference of anisotropic and isotropic total variation (AITV) to regularize the partition boundaries in an image. In particular, we replace the total variation regularization in the Chan-Vese segmentation model and a fuzzy region competition model by the proposed AITV. To deal with the nonconvex nature of AITV, we apply the difference-of-convex algorithm (DCA), in which the subproblems can be minimized by the primal-dual hybrid gradient method with linesearch. The convergence of the DCA scheme is analyzed. In addition, a generalization to color image segmentation is discussed. In the numerical experiments, we compare the proposed models with the classic convex approaches and the two-stage segmentation methods (smoothing and then thresholding) on various images, showing that our models are effective in image segmentation and robust with respect to impulsive noises.

Kevin Bui, Fredrick Park, Shuai Zhang et al.

Deepening and widening convolutional neural networks (CNNs) significantly increases the number of trainable weight parameters by adding more convolutional layers and feature maps per layer, respectively. By imposing inter- and intra-group sparsity onto the weights of the layers during the training process, a compressed network can be obtained with accuracy comparable to a dense one. In this paper, we propose a new variant of sparse group lasso that blends the $\ell_0$ norm onto the individual weight parameters and the $\ell_{2,1}$ norm onto the output channels of a layer. To address the non-differentiability of the $\ell_0$ norm, we apply variable splitting resulting in an algorithm that consists of executing stochastic gradient descent followed by hard thresholding for each iteration. Numerical experiments are demonstrated on LeNet-5 and wide-residual-networks for MNIST and CIFAR 10/100, respectively. They showcase the effectiveness of our proposed method in attaining superior test accuracy with network sparsification on par with the current state of the art.