Disparity-Compensated Compressed-Sensing Reconstruction for Multiview Images

In a multiview-imaging setting, image-acquisition costs could be substantially diminished if some of the cameras operate at a reduced quality. Compressed sensing is proposed to effectuate such a reduction in image quality wherein certain images are acquired with random measurements at a reduced sampling rate via projection onto a random basis of lower dimension. To recover such projected images, compressed-sensing recovery incorporating disparity compensation is employed. Based on a recent compressed-sensing recovery algorithm for images that couples an iterative projection-based reconstruction with a smoothing step, the proposed algorithm drives image recovery using the projection-domain residual between the random measurements of the image in question and a disparity-based prediction created from adjacent, high-quality images. Experimental results reveal that the disparity-based reconstruction significantly outperforms direct reconstruction using simply the random measurements of the image alone

Compressive Imaging Using RIP-Compliant CMOS Imager Architecture and Landweber Reconstruction

In this paper, we present a new image sensor architecture for fast and accurate compressive sensing (CS) of natural images. Measurement matrices usually employed in CS CMOS image sensors are recursive pseudo-random binary matrices. We have proved that the restricted isometry property of these matrices is limited by a low sparsity constant. The quality of these matrices is also affected by the non-idealities of pseudo-random number generators (PRNG). To overcome these limitations, we propose a hardware-friendly pseudo-random ternary measurement matrix generated on-chip by means of class III elementary cellular automata (ECA). These ECA present a chaotic behavior that emulates random CS measurement matrices better than other PRNG. We have combined this new architecture with a block-based CS smoothed-projected Landweber reconstruction algorithm. By means of single value decomposition, we have adapted this algorithm to perform fast and precise reconstruction while operating with binary and ternary matrices. Simulations are provided to qualify the approach.Ministerio de Economía y Competitividad TEC2015-66878-C3-1-RJunta de Andalucía TIC 2338-2013Office of Naval Research (USA) N000141410355European Union H2020 76586

Distributed Representation of Geometrically Correlated Images with Compressed Linear Measurements

This paper addresses the problem of distributed coding of images whose correlation is driven by the motion of objects or positioning of the vision sensors. It concentrates on the problem where images are encoded with compressed linear measurements. We propose a geometry-based correlation model in order to describe the common information in pairs of images. We assume that the constitutive components of natural images can be captured by visual features that undergo local transformations (e.g., translation) in different images. We first identify prominent visual features by computing a sparse approximation of a reference image with a dictionary of geometric basis functions. We then pose a regularized optimization problem to estimate the corresponding features in correlated images given by quantized linear measurements. The estimated features have to comply with the compressed information and to represent consistent transformation between images. The correlation model is given by the relative geometric transformations between corresponding features. We then propose an efficient joint decoding algorithm that estimates the compressed images such that they stay consistent with both the quantized measurements and the correlation model. Experimental results show that the proposed algorithm effectively estimates the correlation between images in multi-view datasets. In addition, the proposed algorithm provides effective decoding performance that compares advantageously to independent coding solutions as well as state-of-the-art distributed coding schemes based on disparity learning

Heterogeneous Networked Data Recovery from Compressive Measurements Using a Copula Prior

Large-scale data collection by means of wireless sensor network and internet-of-things technology poses various challenges in view of the limitations in transmission, computation, and energy resources of the associated wireless devices. Compressive data gathering based on compressed sensing has been proven a well-suited solution to the problem. Existing designs exploit the spatiotemporal correlations among data collected by a specific sensing modality. However, many applications, such as environmental monitoring, involve collecting heterogeneous data that are intrinsically correlated. In this study, we propose to leverage the correlation from multiple heterogeneous signals when recovering the data from compressive measurements. To this end, we propose a novel recovery algorithm---built upon belief-propagation principles---that leverages correlated information from multiple heterogeneous signals. To efficiently capture the statistical dependencies among diverse sensor data, the proposed algorithm uses the statistical model of copula functions. Experiments with heterogeneous air-pollution sensor measurements show that the proposed design provides significant performance improvements against state-of-the-art compressive data gathering and recovery schemes that use classical compressed sensing, compressed sensing with side information, and distributed compressed sensing.Comment: accepted to IEEE Transactions on Communication

Correlation Estimation from Compressed Images

This paper addresses the problem of correlation estimation in sets of compressed images. We consider a framework where images are represented under the form of linear measurements due to low complexity sensing or security requirements. We assume that the images are correlated through the displacement of visual objects due to motion or viewpoint change and the correlation is effectively represented by optical flow or motion field models. The correlation is estimated in the compressed domain by jointly processing the linear measurements. We first show that the correlated images can be efficiently related using a linear operator. Using this linear relationship we then describe the dependencies between images in the compressed domain. We further cast a regularized optimization problem where the correlation is estimated in order to satisfy both data consistency and motion smoothness objectives with a modified Graph Cut algorithm. We analyze in detail the correlation estimation performance and quantify the penalty due to image compression. Extensive experiments in stereo and video imaging applications show that our novel solution stays competitive with methods that implement complex image reconstruction steps prior to correlation estimation. We finally use the estimated correlation in a novel joint image reconstruction scheme that is based on an optimization problem with sparsity priors on the reconstructed images. Additional experiments show that our correlation estimation algorithm leads to an effective reconstruction of pairs of images in distributed image coding schemes that outperform independent reconstruction algorithms by 2 to 4 dB

Compressed Sensing With Prior Information: Strategies, Geometry, and Bounds

We address the problem of compressed sensing (CS) with prior information: reconstruct a target CS signal with the aid of a similar signal that is known beforehand, our prior information. We integrate the additional knowledge of the similar signal into CS via 1-1 and 1-2 minimization. We then establish bounds on the number of measurements required by these problems to successfully reconstruct the original signal. Our bounds and geometrical interpretations reveal that if the prior information has good enough quality, 1-1 minimization improves the performance of CS dramatically. In contrast, 1-2 minimization has a performance very similar to classical CS, and brings no significant benefits. In addition, we use the insight provided by our bounds to design practical schemes to improve prior information. All our findings are illustrated with experimental results