Multi-Scale Deep Compressive Sensing Network

With joint learning of sampling and recovery, the deep learning-based compressive sensing (DCS) has shown significant improvement in performance and running time reduction. Its reconstructed image, however, losses high-frequency content especially at low subrates. This happens similarly in the multi-scale sampling scheme which also samples more low-frequency components. In this paper, we propose a multi-scale DCS convolutional neural network (MS-DCSNet) in which we convert image signal using multiple scale-based wavelet transform, then capture it through convolution block by block across scales. The initial reconstructed image is directly recovered from multi-scale measurements. Multi-scale wavelet convolution is utilized to enhance the final reconstruction quality. The network is able to learn both multi-scale sampling and multi-scale reconstruction, thus results in better reconstruction quality.Comment: 4 pages, 4 figures, 2 tables, IEEE International Conference on Visual Communication and Image Processing (VCIP

Deep Sparse Coding Using Optimized Linear Expansion of Thresholds

We address the problem of reconstructing sparse signals from noisy and compressive measurements using a feed-forward deep neural network (DNN) with an architecture motivated by the iterative shrinkage-thresholding algorithm (ISTA). We maintain the weights and biases of the network links as prescribed by ISTA and model the nonlinear activation function using a linear expansion of thresholds (LET), which has been very successful in image denoising and deconvolution. The optimal set of coefficients of the parametrized activation is learned over a training dataset containing measurement-sparse signal pairs, corresponding to a fixed sensing matrix. For training, we develop an efficient second-order algorithm, which requires only matrix-vector product computations in every training epoch (Hessian-free optimization) and offers superior convergence performance than gradient-descent optimization. Subsequently, we derive an improved network architecture inspired by FISTA, a faster version of ISTA, to achieve similar signal estimation performance with about 50% of the number of layers. The resulting architecture turns out to be a deep residual network, which has recently been shown to exhibit superior performance in several visual recognition tasks. Numerical experiments demonstrate that the proposed DNN architectures lead to 3 to 4 dB improvement in the reconstruction signal-to-noise ratio (SNR), compared with the state-of-the-art sparse coding algorithms.Comment: Submission date: November 11, 2016. 19 pages; 9 figure

Hardware Implementation of Compressed Sensing based Low Complex Video Encoder

This paper presents a memory efficient VLSI architecture of low complex video encoder using three dimensional (3-D) wavelet and Compressed Sensing (CS) is proposed for space and low power video applications. Majority of the conventional video coding schemes are based on hybrid model, which requires complex operations like transform coding (DCT), motion estimation and deblocking filter at the encoder. Complexity of the proposed encoder is reduced by replacing those complex operations by 3-D DWT and CS at the encoder. The proposed architecture uses 3-D DWT to enable the scalability with levels of wavelet decomposition and also to exploit the spatial and the temporal redundancies. CS provides the good error resilience and coding efficiency. At the first stage of the proposed architecture for encoder, 3-D DWT has been applied (Lifting based 2-D DWT in spatial domain and Haar wavelet in temporal domain) on each frame of the group of frames (GOF), and in the second stage CS module exploits the sparsity of the wavelet coefficients. Small set of linear measurements are extracted by projecting the sparse 3-D wavelet coefficients onto random Bernoulli matrix at the encoder. Compared with the best existing 3-D DWT architectures, the proposed architecture for 3-D DWT requires less memory and provide high throughput. For an N?N image, the proposed 3-D DWT architecture consumes a total of only 2?(3N +40P) words of on-chip memory for the one level of decomposition. The proposed architecture for an encoder is first of its kind and to the best of my knowledge, no architecture is noted for comparison. The proposed VLSI architecture of the encoder has been synthesized on 90-nm CMOS process technology and results show that it consumes 90.08 mW power and occupies an area equivalent to 416.799 K equivalent gate at frequency of 158 MHz.Comment: Submitted in IEEE transactions on VLS

Applications of Compressed Sensing in Communications Networks

This paper presents a tutorial for CS applications in communications networks. The Shannon's sampling theorem states that to recover a signal, the sampling rate must be as least the Nyquist rate. Compressed sensing (CS) is based on the surprising fact that to recover a signal that is sparse in certain representations, one can sample at the rate far below the Nyquist rate. Since its inception in 2006, CS attracted much interest in the research community and found wide-ranging applications from astronomy, biology, communications, image and video processing, medicine, to radar. CS also found successful applications in communications networks. CS was applied in the detection and estimation of wireless signals, source coding, multi-access channels, data collection in sensor networks, and network monitoring, etc. In many cases, CS was shown to bring performance gains on the order of 10X. We believe this is just the beginning of CS applications in communications networks, and the future will see even more fruitful applications of CS in our field.Comment: 18 page

Deep Compressive Autoencoder for Action Potential Compression in Large-Scale Neural Recording

Understanding the coordinated activity underlying brain computations requires large-scale, simultaneous recordings from distributed neuronal structures at a cellular-level resolution. One major hurdle to design high-bandwidth, high-precision, large-scale neural interfaces lies in the formidable data streams that are generated by the recorder chip and need to be online transferred to a remote computer. The data rates can require hundreds to thousands of I/O pads on the recorder chip and power consumption on the order of Watts for data streaming alone. We developed a deep learning-based compression model to reduce the data rate of multichannel action potentials. The proposed model is built upon a deep compressive autoencoder (CAE) with discrete latent embeddings. The encoder is equipped with residual transformations to extract representative features from spikes, which are mapped into the latent embedding space and updated via vector quantization (VQ). The decoder network reconstructs spike waveforms from the quantized latent embeddings. Experimental results show that the proposed model consistently outperforms conventional methods by achieving much higher compression ratios (20-500x) and better or comparable reconstruction accuracies. Testing results also indicate that CAE is robust against a diverse range of imperfections, such as waveform variation and spike misalignment, and has minor influence on spike sorting accuracy. Furthermore, we have estimated the hardware cost and real-time performance of CAE and shown that it could support thousands of recording channels simultaneously without excessive power/heat dissipation. The proposed model can reduce the required data transmission bandwidth in large-scale recording experiments and maintain good signal qualities. The code of this work has been made available at https://github.com/tong-wu-umn/spike-compression-autoencoderComment: 19 pages, 13 figure

Recurrent Generative Adversarial Networks for Proximal Learning and Automated Compressive Image Recovery

Recovering images from undersampled linear measurements typically leads to an ill-posed linear inverse problem, that asks for proper statistical priors. Building effective priors is however challenged by the low train and test overhead dictated by real-time tasks; and the need for retrieving visually "plausible" and physically "feasible" images with minimal hallucination. To cope with these challenges, we design a cascaded network architecture that unrolls the proximal gradient iterations by permeating benefits from generative residual networks (ResNet) to modeling the proximal operator. A mixture of pixel-wise and perceptual costs is then deployed to train proximals. The overall architecture resembles back-and-forth projection onto the intersection of feasible and plausible images. Extensive computational experiments are examined for a global task of reconstructing MR images of pediatric patients, and a more local task of superresolving CelebA faces, that are insightful to design efficient architectures. Our observations indicate that for MRI reconstruction, a recurrent ResNet with a single residual block effectively learns the proximal. This simple architecture appears to significantly outperform the alternative deep ResNet architecture by 2dB SNR, and the conventional compressed-sensing MRI by 4dB SNR with 100x faster inference. For image superresolution, our preliminary results indicate that modeling the denoising proximal demands deep ResNets.Comment: 11 pages, 11 figure

Learning Multi-Layer Transform Models

Learned data models based on sparsity are widely used in signal processing and imaging applications. A variety of methods for learning synthesis dictionaries, sparsifying transforms, etc., have been proposed in recent years, often imposing useful structures or properties on the models. In this work, we focus on sparsifying transform learning, which enjoys a number of advantages. We consider multi-layer or nested extensions of the transform model, and propose efficient learning algorithms. Numerical experiments with image data illustrate the behavior of the multi-layer transform learning algorithm and its usefulness for image denoising. Multi-layer models provide better denoising quality than single layer schemes.Comment: In Proceedings of the Annual Allerton Conference on Communication, Control, and Computing, 201

Multiscale Shrinkage and L\'evy Processes

A new shrinkage-based construction is developed for a compressible vector $\boldsymbol{x}\in\mathbb{R}^n$, for cases in which the components of \xv are naturally associated with a tree structure. Important examples are when \xv corresponds to the coefficients of a wavelet or block-DCT representation of data. The method we consider in detail, and for which numerical results are presented, is based on increments of a gamma process. However, we demonstrate that the general framework is appropriate for many other types of shrinkage priors, all within the L\'{e}vy process family, with the gamma process a special case. Bayesian inference is carried out by approximating the posterior with samples from an MCMC algorithm, as well as by constructing a heuristic variational approximation to the posterior. We also consider expectation-maximization (EM) for a MAP (point) solution. State-of-the-art results are manifested for compressive sensing and denoising applications, the latter with spiky (non-Gaussian) noise.Comment: 11 pages, 5 figure

Efficient B-mode Ultrasound Image Reconstruction from Sub-sampled RF Data using Deep Learning

In portable, three dimensional, and ultra-fast ultrasound imaging systems, there is an increasing demand for the reconstruction of high quality images from a limited number of radio-frequency (RF) measurements due to receiver (Rx) or transmit (Xmit) event sub-sampling. However, due to the presence of side lobe artifacts from RF sub-sampling, the standard beamformer often produces blurry images with less contrast, which are unsuitable for diagnostic purposes. Existing compressed sensing approaches often require either hardware changes or computationally expensive algorithms, but their quality improvements are limited. To address this problem, here we propose a novel deep learning approach that directly interpolates the missing RF data by utilizing redundancy in the Rx-Xmit plane. Our extensive experimental results using sub-sampled RF data from a multi-line acquisition B-mode system confirm that the proposed method can effectively reduce the data rate without sacrificing image quality.Comment: The title has been changed. This version will appear in IEEE Trans. on Medical Imagin

Robust flow field reconstruction from limited measurements via sparse representation

In many applications it is important to estimate a fluid flow field from limited and possibly corrupt measurements. Current methods in flow estimation often use least squares regression to reconstruct the flow field, finding the minimum-energy solution that is consistent with the measured data. However, this approach may be prone to overfitting and sensitive to noise. To address these challenges we instead seek a sparse representation of the data in a library of examples. Sparse representation has been widely used for image recognition and reconstruction, and it is well-suited to structured data with limited, corrupt measurements. We explore sparse representation for flow reconstruction on a variety of fluid data sets with a wide range of complexity, including vortex shedding past a cylinder at low Reynolds number, a mixing layer, and two geophysical flows. In addition, we compare several measurement strategies and consider various types of noise and corruption over a range of intensities. We find that sparse representation has considerably improved estimation accuracy and robustness to noise and corruption compared with least squares methods. We also introduce a sparse estimation procedure on local spatial patches for complex multiscale flows that preclude a global sparse representation. Based on these results, sparse representation is a promising framework for extracting useful information from complex flow fields with realistic measurements