Solving Inverse Problems with Piecewise Linear Estimators: From Gaussian Mixture Models to Structured Sparsity

A general framework for solving image inverse problems is introduced in this paper. The approach is based on Gaussian mixture models, estimated via a computationally efficient MAP-EM algorithm. A dual mathematical interpretation of the proposed framework with structured sparse estimation is described, which shows that the resulting piecewise linear estimate stabilizes the estimation when compared to traditional sparse inverse problem techniques. This interpretation also suggests an effective dictionary motivated initialization for the MAP-EM algorithm. We demonstrate that in a number of image inverse problems, including inpainting, zooming, and deblurring, the same algorithm produces either equal, often significantly better, or very small margin worse results than the best published ones, at a lower computational cost.Comment: 30 page

Dependent Nonparametric Bayesian Group Dictionary Learning for online reconstruction of Dynamic MR images

In this paper, we introduce a dictionary learning based approach applied to the problem of real-time reconstruction of MR image sequences that are highly undersampled in k-space. Unlike traditional dictionary learning, our method integrates both global and patch-wise (local) sparsity information and incorporates some priori information into the reconstruction process. Moreover, we use a Dependent Hierarchical Beta-process as the prior for the group-based dictionary learning, which adaptively infers the dictionary size and the sparsity of each patch; and also ensures that similar patches are manifested in terms of similar dictionary atoms. An efficient numerical algorithm based on the alternating direction method of multipliers (ADMM) is also presented. Through extensive experimental results we show that our proposed method achieves superior reconstruction quality, compared to the other state-of-the- art DL-based methods

Image Diversification via Deep Learning based Generative Models

Machine learning driven pattern recognition from imagery such as object detection has been prevalenting among society due to the high demand for autonomy and the recent remarkable advances in such technology. The machine learning technologies acquire the abstraction of the existing data and enable inference of the pattern of the future inputs. However, such technologies require a sheer amount of images as a training dataset which well covers the distribution of the future inputs in order to predict the proper patterns whereas it is impracticable to prepare enough variety of images in many cases. To address this problem, this thesis pursues to discover the method to diversify image datasets for fully enabling the capability of machine learning driven applications. Focusing on the plausible image synthesis ability of generative models, we investigate a number of approaches to expand the variety of the output images using image-to-image translation, mixup and diffusion models along with the technique to enable a computation and training dataset efficient diffusion approach. First, we propose the combined use of unpaired image-to-image translation and mixup for data augmentation on limited non-visible imagery. Second, we propose diffusion image-to-image translation that generates greater quality images than other previous adversarial training based translation methods. Third, we propose a patch-wise and discrete conditional training of diffusion method enabling the reduction of the computation and the robustness on small training datasets. Subsequently, we discuss a remaining open challenge about evaluation and the direction of future work. Lastly, we make an overall conclusion after stating social impact of this research field

On Approximations of the Beta Process in Latent Feature Models

The beta process has recently been widely used as a nonparametric prior for different models in machine learning, including latent feature models. In this paper, we prove the asymptotic consistency of the finite dimensional approximation of the beta process due to Paisley \& Carin (2009). In addition, we derive an almost sure approximation of the beta process. This approximation provides a direct method to efficiently simulate the beta process. A simulated example, illustrating the work of the method and comparing its performance to several existing algorithms, is also included.Comment: 25 page

A unifying representation for a class of dependent random measures

We present a general construction for dependent random measures based on thinning Poisson processes on an augmented space. The framework is not restricted to dependent versions of a specific nonparametric model, but can be applied to all models that can be represented using completely random measures. Several existing dependent random measures can be seen as specific cases of this framework. Interesting properties of the resulting measures are derived and the efficacy of the framework is demonstrated by constructing a covariate-dependent latent feature model and topic model that obtain superior predictive performance