ReconNet: Non-Iterative Reconstruction of Images from Compressively Sensed Random Measurements

The goal of this paper is to present a non-iterative and more importantly an extremely fast algorithm to reconstruct images from compressively sensed (CS) random measurements. To this end, we propose a novel convolutional neural network (CNN) architecture which takes in CS measurements of an image as input and outputs an intermediate reconstruction. We call this network, ReconNet. The intermediate reconstruction is fed into an off-the-shelf denoiser to obtain the final reconstructed image. On a standard dataset of images we show significant improvements in reconstruction results (both in terms of PSNR and time complexity) over state-of-the-art iterative CS reconstruction algorithms at various measurement rates. Further, through qualitative experiments on real data collected using our block single pixel camera (SPC), we show that our network is highly robust to sensor noise and can recover visually better quality images than competitive algorithms at extremely low sensing rates of 0.1 and 0.04. To demonstrate that our algorithm can recover semantically informative images even at a low measurement rate of 0.01, we present a very robust proof of concept real-time visual tracking application.Comment: Accepted at IEEE International Conference on Computer Vision and Pattern Recognition (CVPR), 201

Video Compressive Sensing for Dynamic MRI

We present a video compressive sensing framework, termed kt-CSLDS, to accelerate the image acquisition process of dynamic magnetic resonance imaging (MRI). We are inspired by a state-of-the-art model for video compressive sensing that utilizes a linear dynamical system (LDS) to model the motion manifold. Given compressive measurements, the state sequence of an LDS can be first estimated using system identification techniques. We then reconstruct the observation matrix using a joint structured sparsity assumption. In particular, we minimize an objective function with a mixture of wavelet sparsity and joint sparsity within the observation matrix. We derive an efficient convex optimization algorithm through alternating direction method of multipliers (ADMM), and provide a theoretical guarantee for global convergence. We demonstrate the performance of our approach for video compressive sensing, in terms of reconstruction accuracy. We also investigate the impact of various sampling strategies. We apply this framework to accelerate the acquisition process of dynamic MRI and show it achieves the best reconstruction accuracy with the least computational time compared with existing algorithms in the literature.Comment: 30 pages, 9 figure

Compressive Coded Aperture Keyed Exposure Imaging with Optical Flow Reconstruction

This paper describes a coded aperture and keyed exposure approach to compressive video measurement which admits a small physical platform, high photon efficiency, high temporal resolution, and fast reconstruction algorithms. The proposed projections satisfy the Restricted Isometry Property (RIP), and hence compressed sensing theory provides theoretical guarantees on the video reconstruction quality. Moreover, the projections can be easily implemented using existing optical elements such as spatial light modulators (SLMs). We extend these coded mask designs to novel dual-scale masks (DSMs) which enable the recovery of a coarse-resolution estimate of the scene with negligible computational cost. We develop fast numerical algorithms which utilize both temporal correlations and optical flow in the video sequence as well as the innovative structure of the projections. Our numerical experiments demonstrate the efficacy of the proposed approach on short-wave infrared data.Comment: 13 pages, 4 figures, Submitted to IEEE Transactions on Image Processing. arXiv admin note: substantial text overlap with arXiv:1111.724

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

Compressive Time-of-Flight 3D Imaging Using Block-Structured Sensing Matrices

Spatially and temporally highly resolved depth information enables numerous applications including human-machine interaction in gaming or safety functions in the automotive industry. In this paper, we address this issue using Time-of-flight (ToF) 3D cameras which are compact devices providing highly resolved depth information. Practical restrictions often require to reduce the amount of data to be read-out and transmitted. Using standard ToF cameras, this can only be achieved by lowering the spatial or temporal resolution. To overcome such a limitation, we propose a compressive ToF camera design using block-structured sensing matrices that allows to reduce the amount of data while keeping high spatial and temporal resolution. We propose the use of efficient reconstruction algorithms based on l^1-minimization and TV-regularization. The reconstruction methods are applied to data captured by a real ToF camera system and evaluated in terms of reconstruction quality and computational effort. For both, l^1-minimization and TV-regularization, we use a local as well as a global reconstruction strategy. For all considered instances, global TV-regularization turns out to clearly perform best in terms of evaluation metrics including the PSNR.Comment: According to a suggestion, we changed the old title "A Framework for Compressive Time-of-Flight 3D Sensing" to "Compressive Time-of-Flight 3D Imaging Using Block-Structured Sensing Matrices

On some common compressive sensing recovery algorithms and applications - Review paper

Compressive Sensing, as an emerging technique in signal processing is reviewed in this paper together with its common applications. As an alternative to the traditional signal sampling, Compressive Sensing allows a new acquisition strategy with significantly reduced number of samples needed for accurate signal reconstruction. The basic ideas and motivation behind this approach are provided in the theoretical part of the paper. The commonly used algorithms for missing data reconstruction are presented. The Compressive Sensing applications have gained significant attention leading to an intensive growth of signal processing possibilities. Hence, some of the existing practical applications assuming different types of signals in real-world scenarios are described and analyzed as well.Comment: submitted to Facta Universitatis Scientific Journal, Series: Electronics and Energetics, March 201

Lensless Compressive Imaging

We develop a lensless compressive imaging architecture, which consists of an aperture assembly and a single sensor, without using any lens. An anytime algorithm is proposed to reconstruct images from the compressive measurements; the algorithm produces a sequence of solutions that monotonically converge to the true signal (thus, anytime). The algorithm is developed based on the sparsity of local overlapping patches (in the transformation domain) and state-of-the-art results have been obtained. Experiments on real data demonstrate that encouraging results are obtained by measuring about 10% (of the image pixels) compressive measurements. The reconstruction results of the proposed algorithm are compared with the JPEG compression (based on file sizes) and the reconstructed image quality is close to the JPEG compression, in particular at a high compression rate.Comment: 37 pages, 10 figures. Submitted to SIAM Journal on Imaging Scienc

Scan-based Compressed Terahertz Imaging and Real-Time Reconstruction via the Complex-valued Fast Block Sparse Bayesian Learning Algorithm

Compressed Sensing based Terahertz imaging (CS-THz) is a computational imaging technique. It uses only one THz receiver to accumulate the random modulated image measurements where the original THz image is reconstruct from these measurements using compressed sensing solvers. The advantage of the CS-THz is its reduced acquisition time compared with the raster scan mode. However, when it applied to large-scale two-dimensional (2D) imaging, the increased dimension resulted in both high computational complexity and excessive memory usage. In this paper, we introduced a novel CS-based THz imaging system that progressively compressed the THz image column by column. Therefore, the CS-THz system could be simplified with a much smaller sized modulator and reduced dimension. In order to utilize the block structure and the correlation of adjacent columns of the THz image, a complex-valued block sparse Bayesian learning algorithm was proposed. We conducted systematic evaluation of state-of-the-art CS algorithms under the scan based CS-THz architecture. The compression ratios and the choices of the sensing matrices were analyzed in detail using both synthetic and real-life THz images. Simulation results showed that both the scan based architecture and the proposed recovery algorithm were superior and efficient for large scale CS-THz applications

Video from Stills: Lensless Imaging with Rolling Shutter

Because image sensor chips have a finite bandwidth with which to read out pixels, recording video typically requires a trade-off between frame rate and pixel count. Compressed sensing techniques can circumvent this trade-off by assuming that the image is compressible. Here, we propose using multiplexing optics to spatially compress the scene, enabling information about the whole scene to be sampled from a row of sensor pixels, which can be read off quickly via a rolling shutter CMOS sensor. Conveniently, such multiplexing can be achieved with a simple lensless, diffuser-based imaging system. Using sparse recovery methods, we are able to recover 140 video frames at over 4,500 frames per second, all from a single captured image with a rolling shutter sensor. Our proof-of-concept system uses easily-fabricated diffusers paired with an off-the-shelf sensor. The resulting prototype enables compressive encoding of high frame rate video into a single rolling shutter exposure, and exceeds the sampling-limited performance of an equivalent global shutter system for sufficiently sparse objects.Comment: 8 pages, 7 figures, IEEE International Conference on Computational Photography 2019, Toky

MoDL: Model Based Deep Learning Architecture for Inverse Problems

We introduce a model-based image reconstruction framework with a convolution neural network (CNN) based regularization prior. The proposed formulation provides a systematic approach for deriving deep architectures for inverse problems with the arbitrary structure. Since the forward model is explicitly accounted for, a smaller network with fewer parameters is sufficient to capture the image information compared to black-box deep learning approaches, thus reducing the demand for training data and training time. Since we rely on end-to-end training, the CNN weights are customized to the forward model, thus offering improved performance over approaches that rely on pre-trained denoisers. The main difference of the framework from existing end-to-end training strategies is the sharing of the network weights across iterations and channels. Our experiments show that the decoupling of the number of iterations from the network complexity offered by this approach provides benefits including lower demand for training data, reduced risk of overfitting, and implementations with significantly reduced memory footprint. We propose to enforce data-consistency by using numerical optimization blocks such as conjugate gradients algorithm within the network; this approach offers faster convergence per iteration, compared to methods that rely on proximal gradients steps to enforce data consistency. Our experiments show that the faster convergence translates to improved performance, especially when the available GPU memory restricts the number of iterations.Comment: published in IEEE Transaction on Medical Imagin