Blind identification of an unknown interleaved convolutional code

We give here an efficient method to reconstruct the block interleaver and recover the convolutional code when several noisy interleaved codewords are given. We reconstruct the block interleaver without assumption on its structure. By running some experimental tests we show the efficiency of this method even with moderate noise

Optimal Haplotype Assembly from High-Throughput Mate-Pair Reads

Humans have $23$ pairs of homologous chromosomes. The homologous pairs are almost identical pairs of chromosomes. For the most part, differences in homologous chromosome occur at certain documented positions called single nucleotide polymorphisms (SNPs). A haplotype of an individual is the pair of sequences of SNPs on the two homologous chromosomes. In this paper, we study the problem of inferring haplotypes of individuals from mate-pair reads of their genome. We give a simple formula for the coverage needed for haplotype assembly, under a generative model. The analysis here leverages connections of this problem with decoding convolutional codes.Comment: 10 pages, 4 figures, Submitted to ISIT 201

Sparse-View X-Ray CT Reconstruction Using ℓ1\ell_1 Prior with Learned Transform

A major challenge in X-ray computed tomography (CT) is reducing radiation dose while maintaining high quality of reconstructed images. To reduce the radiation dose, one can reduce the number of projection views (sparse-view CT); however, it becomes difficult to achieve high-quality image reconstruction as the number of projection views decreases. Researchers have applied the concept of learning sparse representations from (high-quality) CT image dataset to the sparse-view CT reconstruction. We propose a new statistical CT reconstruction model that combines penalized weighted-least squares (PWLS) and $\ell_1$ prior with learned sparsifying transform (PWLS-ST-$\ell_1$), and a corresponding efficient algorithm based on Alternating Direction Method of Multipliers (ADMM). To moderate the difficulty of tuning ADMM parameters, we propose a new ADMM parameter selection scheme based on approximated condition numbers. We interpret the proposed model by analyzing the minimum mean square error of its ($\ell_2$-norm relaxed) image update estimator. Our results with the extended cardiac-torso (XCAT) phantom data and clinical chest data show that, for sparse-view 2D fan-beam CT and 3D axial cone-beam CT, PWLS-ST-$\ell_1$ improves the quality of reconstructed images compared to the CT reconstruction methods using edge-preserving regularizer and $\ell_2$ prior with learned ST. These results also show that, for sparse-view 2D fan-beam CT, PWLS-ST-$\ell_1$ achieves comparable or better image quality and requires much shorter runtime than PWLS-DL using a learned overcomplete dictionary. Our results with clinical chest data show that, methods using the unsupervised learned prior generalize better than a state-of-the-art deep "denoising" neural network that does not use a physical imaging model.Comment: The first two authors contributed equally to this wor

Deep Residual Auto-Encoders for Expectation Maximization-inspired Dictionary Learning

We introduce a neural-network architecture, termed the constrained recurrent sparse auto-encoder (CRsAE), that solves convolutional dictionary learning problems, thus establishing a link between dictionary learning and neural networks. Specifically, we leverage the interpretation of the alternating-minimization algorithm for dictionary learning as an approximate Expectation-Maximization algorithm to develop auto-encoders that enable the simultaneous training of the dictionary and regularization parameter (ReLU bias). The forward pass of the encoder approximates the sufficient statistics of the E-step as the solution to a sparse coding problem, using an iterative proximal gradient algorithm called FISTA. The encoder can be interpreted either as a recurrent neural network or as a deep residual network, with two-sided ReLU non-linearities in both cases. The M-step is implemented via a two-stage back-propagation. The first stage relies on a linear decoder applied to the encoder and a norm-squared loss. It parallels the dictionary update step in dictionary learning. The second stage updates the regularization parameter by applying a loss function to the encoder that includes a prior on the parameter motivated by Bayesian statistics. We demonstrate in an image-denoising task that CRsAE learns Gabor-like filters, and that the EM-inspired approach for learning biases is superior to the conventional approach. In an application to recordings of electrical activity from the brain, we demonstrate that CRsAE learns realistic spike templates and speeds up the process of identifying spike times by 900x compared to algorithms based on convex optimization

Nonlocal Low-Rank Tensor Factor Analysis for Image Restoration

Low-rank signal modeling has been widely leveraged to capture non-local correlation in image processing applications. We propose a new method that employs low-rank tensor factor analysis for tensors generated by grouped image patches. The low-rank tensors are fed into the alternative direction multiplier method (ADMM) to further improve image reconstruction. The motivating application is compressive sensing (CS), and a deep convolutional architecture is adopted to approximate the expensive matrix inversion in CS applications. An iterative algorithm based on this low-rank tensor factorization strategy, called NLR-TFA, is presented in detail. Experimental results on noiseless and noisy CS measurements demonstrate the superiority of the proposed approach, especially at low CS sampling rates

Approximate message-passing with spatially coupled structured operators, with applications to compressed sensing and sparse superposition codes

We study the behavior of Approximate Message-Passing, a solver for linear sparse estimation problems such as compressed sensing, when the i.i.d matrices -for which it has been specifically designed- are replaced by structured operators, such as Fourier and Hadamard ones. We show empirically that after proper randomization, the structure of the operators does not significantly affect the performances of the solver. Furthermore, for some specially designed spatially coupled operators, this allows a computationally fast and memory efficient reconstruction in compressed sensing up to the information-theoretical limit. We also show how this approach can be applied to sparse superposition codes, allowing the Approximate Message-Passing decoder to perform at large rates for moderate block length.Comment: 20 pages, 10 figure

Imaging through glass diffusers using densely connected convolutional networks

Computational imaging through scatter generally is accomplished by first characterizing the scattering medium so that its forward operator is obtained; and then imposing additional priors in the form of regularizers on the reconstruction functional so as to improve the condition of the originally ill-posed inverse problem. In the functional, the forward operator and regularizer must be entered explicitly or parametrically (e.g. scattering matrices and dictionaries, respectively.) However, the process of determining these representations is often incomplete, prone to errors, or infeasible. Recently, deep learning architectures have been proposed to instead learn both the forward operator and regularizer through examples. Here, we propose for the first time, to our knowledge, a convolutional neural network architecture called "IDiffNet" for the problem of imaging through diffuse media and demonstrate that IDiffNet has superior generalization capability through extensive tests with well-calibrated diffusers. We found that the Negative Pearson Correlation Coefficient loss function for training is more appropriate for spatially sparse objects and strong scattering conditions. Our results show that the convolutional architecture is robust to the choice of prior, as demonstrated by the use of multiple training and testing object databases, and capable of achieving higher space-bandwidth product reconstructions than previously reported

Deep EHR: A Survey of Recent Advances in Deep Learning Techniques for Electronic Health Record (EHR) Analysis

The past decade has seen an explosion in the amount of digital information stored in electronic health records (EHR). While primarily designed for archiving patient clinical information and administrative healthcare tasks, many researchers have found secondary use of these records for various clinical informatics tasks. Over the same period, the machine learning community has seen widespread advances in deep learning techniques, which also have been successfully applied to the vast amount of EHR data. In this paper, we review these deep EHR systems, examining architectures, technical aspects, and clinical applications. We also identify shortcomings of current techniques and discuss avenues of future research for EHR-based deep learning.Comment: Accepted for publication with Journal of Biomedical and Health Informatics: http://ieeexplore.ieee.org/abstract/document/8086133

Deep Shape from Polarization

This paper makes a first attempt to bring the Shape from Polarization (SfP) problem to the realm of deep learning. The previous state-of-the-art methods for SfP have been purely physics-based. We see value in these principled models, and blend these physical models as priors into a neural network architecture. This proposed approach achieves results that exceed the previous state-of-the-art on a challenging dataset we introduce. This dataset consists of polarization images taken over a range of object textures, paints, and lighting conditions. We report that our proposed method achieves the lowest test error on each tested condition in our dataset, showing the value of blending data-driven and physics-driven approaches

Deep Convolutional Compressed Sensing for LiDAR Depth Completion

In this paper we consider the problem of estimating a dense depth map from a set of sparse LiDAR points. We use techniques from compressed sensing and the recently developed Alternating Direction Neural Networks (ADNNs) to create a deep recurrent auto-encoder for this task. Our architecture internally performs an algorithm for extracting multi-level convolutional sparse codes from the input which are then used to make a prediction. Our results demonstrate that with only two layers and 1800 parameters we are able to out perform all previously published results, including deep networks with orders of magnitude more parameters