A Segmentation-aware Deep Fusion Network for Compressed Sensing MRI

Compressed sensing MRI is a classic inverse problem in the field of computational imaging, accelerating the MR imaging by measuring less k-space data. The deep neural network models provide the stronger representation ability and faster reconstruction compared with "shallow" optimization-based methods. However, in the existing deep-based CS-MRI models, the high-level semantic supervision information from massive segmentation-labels in MRI dataset is overlooked. In this paper, we proposed a segmentation-aware deep fusion network called SADFN for compressed sensing MRI. The multilayer feature aggregation (MLFA) method is introduced here to fuse all the features from different layers in the segmentation network. Then, the aggregated feature maps containing semantic information are provided to each layer in the reconstruction network with a feature fusion strategy. This guarantees the reconstruction network is aware of the different regions in the image it reconstructs, simplifying the function mapping. We prove the utility of the cross-layer and cross-task information fusion strategy by comparative study. Extensive experiments on brain segmentation benchmark MRBrainS validated that the proposed SADFN model achieves state-of-the-art accuracy in compressed sensing MRI. This paper provides a novel approach to guide the low-level visual task using the information from mid- or high-level task.

A Divide-and-Conquer Approach to Compressed Sensing MRI

Compressed sensing (CS) theory assures us that we can accurately reconstruct magnetic resonance images using fewer k-space measurements than the Nyquist sampling rate requires. In traditional CS-MRI inversion methods, the fact that the energy within the Fourier measurement domain is distributed non-uniformly is often neglected during reconstruction. As a result, more densely sampled low-frequency information tends to dominate penalization schemes for reconstructing MRI at the expense of high-frequency details. In this paper, we propose a new framework for CS-MRI inversion in which we decompose the observed k-space data into "subspaces" via sets of filters in a lossless way, and reconstruct the images in these various spaces individually using off-the-shelf algorithms. We then fuse the results to obtain the final reconstruction. In this way we are able to focus reconstruction on frequency information within the entire k-space more equally, preserving both high and low frequency details. We demonstrate that the proposed framework is competitive with state-of-the-art methods in CS-MRI in terms of quantitative performance, and often improves an algorithm's results qualitatively compared with it's direct application to k-space.

A Deep Error Correction Network for Compressed Sensing MRI

Compressed sensing for magnetic resonance imaging (CS-MRI) exploits image sparsity properties to reconstruct MRI from very few Fourier k-space measurements. The goal is to minimize any structural errors in the reconstruction that could have a negative impact on its diagnostic quality. To this end, we propose a deep error correction network (DECN) for CS-MRI. The DECN model consists of three parts, which we refer to as modules: a guide, or template, module, an error correction module, and a data fidelity module. Existing CS-MRI algorithms can serve as the template module for guiding the reconstruction. Using this template as a guide, the error correction module learns a convolutional neural network (CNN) to map the k-space data in a way that adjusts for the reconstruction error of the template image. Our experimental results show the proposed DECN CS-MRI reconstruction framework can considerably improve upon existing inversion algorithms by supplementing with an error-correcting CNN.

Online Forecasting Matrix Factorization

In this paper the problem of forecasting high dimensional time series is considered. Such time series can be modeled as matrices where each column denotes a measurement. In addition, when missing values are present, low rank matrix factorization approaches are suitable for predicting future values. This paper formally defines and analyzes the forecasting problem in the online setting, i.e. where the data arrives as a stream and only a single pass is allowed. We present and analyze novel matrix factorization techniques which can learn low-dimensional embeddings effectively in an online manner. Based on these embeddings a recursive minimum mean square error estimator is derived, which learns an autoregressive model on them. Experiments with two real datasets with tens of millions of measurements show the benefits of the proposed approach.

Variational Inference via $χ$-Upper Bound Minimization

Variational inference (VI) is widely used as an efficient alternative to Markov chain Monte Carlo. It posits a family of approximating distributions $q$ and finds the closest member to the exact posterior $p$. Closeness is usually measured via a divergence $D(q || p)$ from $q$ to $p$. While successful, this approach also has problems. Notably, it typically leads to underestimation of the posterior variance. In this paper we propose CHIVI, a black-box variational inference algorithm that minimizes $D_{\chi}(p || q)$, the $\chi$-divergence from $p$ to $q$. CHIVI minimizes an upper bound of the model evidence, which we term the $\chi$ upper bound (CUBO). Minimizing the CUBO leads to improved posterior uncertainty, and it can also be used with the classical VI lower bound (ELBO) to provide a sandwich estimate of the model evidence. We study CHIVI on three models: probit regression, Gaussian process classification, and a Cox process model of basketball plays. When compared to expectation propagation and classical VI, CHIVI produces better error rates and more accurate estimates of posterior variance.

Hyperspectral Image Classification with Markov Random Fields and a Convolutional Neural Network

This paper presents a new supervised classification algorithm for remotely sensed hyperspectral image (HSI) which integrates spectral and spatial information in a unified Bayesian framework. First, we formulate the HSI classification problem from a Bayesian perspective. Then, we adopt a convolutional neural network (CNN) to learn the posterior class distributions using a patch-wise training strategy to better use the spatial information. Next, spatial information is further considered by placing a spatial smoothness prior on the labels. Finally, we iteratively update the CNN parameters using stochastic gradient decent (SGD) and update the class labels of all pixel vectors using an alpha-expansion min-cut-based algorithm. Compared with other state-of-the-art methods, the proposed classification method achieves better performance on one synthetic dataset and two benchmark HSI datasets in a number of experimental settings.

Location Dependent Dirichlet Processes

Dirichlet processes (DP) are widely applied in Bayesian nonparametric modeling. However, in their basic form they do not directly integrate dependency information among data arising from space and time. In this paper, we propose location dependent Dirichlet processes (LDDP) which incorporate nonparametric Gaussian processes in the DP modeling framework to model such dependencies. We develop the LDDP in the context of mixture modeling, and develop a mean field variational inference algorithm for this mixture model. The effectiveness of the proposed modeling framework is shown on an image segmentation task.

Nonlinear Kalman Filtering with Divergence Minimization

We consider the nonlinear Kalman filtering problem using Kullback-Leibler (KL) and $\alpha$-divergence measures as optimization criteria. Unlike linear Kalman filters, nonlinear Kalman filters do not have closed form Gaussian posteriors because of a lack of conjugacy due to the nonlinearity in the likelihood. In this paper we propose novel algorithms to optimize the forward and reverse forms of the KL divergence, as well as the alpha-divergence which contains these two as limiting cases. Unlike previous approaches, our algorithms do not make approximations to the divergences being optimized, but use Monte Carlo integration techniques to derive unbiased algorithms for direct optimization. We assess performance on radar and sensor tracking, and options pricing problems, showing general improvement over the UKF and EKF, as well as competitive performance with particle filtering.

TopicRNN: A Recurrent Neural Network with Long-Range Semantic Dependency

In this paper, we propose TopicRNN, a recurrent neural network (RNN)-based language model designed to directly capture the global semantic meaning relating words in a document via latent topics. Because of their sequential nature, RNNs are good at capturing the local structure of a word sequence - both semantic and syntactic - but might face difficulty remembering long-range dependencies. Intuitively, these long-range dependencies are of semantic nature. In contrast, latent topic models are able to capture the global underlying semantic structure of a document but do not account for word ordering. The proposed TopicRNN model integrates the merits of RNNs and latent topic models: it captures local (syntactic) dependencies using an RNN and global (semantic) dependencies using latent topics. Unlike previous work on contextual RNN language modeling, our model is learned end-to-end. Empirical results on word prediction show that TopicRNN outperforms existing contextual RNN baselines. In addition, TopicRNN can be used as an unsupervised feature extractor for documents. We do this for sentiment analysis on the IMDB movie review dataset and report an error rate of $6.28\%$. This is comparable to the state-of-the-art $5.91\%$ resulting from a semi-supervised approach. Finally, TopicRNN also yields sensible topics, making it a useful alternative to document models such as latent Dirichlet allocation.

Clearing the Skies: A deep network architecture for single-image rain removal

We introduce a deep network architecture called DerainNet for removing rain streaks from an image. Based on the deep convolutional neural network (CNN), we directly learn the mapping relationship between rainy and clean image detail layers from data. Because we do not possess the ground truth corresponding to real-world rainy images, we synthesize images with rain for training. In contrast to other common strategies that increase depth or breadth of the network, we use image processing domain knowledge to modify the objective function and improve deraining with a modestly-sized CNN. Specifically, we train our DerainNet on the detail (high-pass) layer rather than in the image domain. Though DerainNet is trained on synthetic data, we find that the learned network translates very effectively to real-world images for testing. Moreover, we augment the CNN framework with image enhancement to improve the visual results. Compared with state-of-the-art single image de-raining methods, our method has improved rain removal and much faster computation time after network training.