Image Compression Based on Compressive Sensing: End-to-End Comparison with JPEG

We present an end-to-end image compression system based on compressive sensing. The presented system integrates the conventional scheme of compressive sampling and reconstruction with quantization and entropy coding. The compression performance, in terms of decoded image quality versus data rate, is shown to be comparable with JPEG and significantly better at the low rate range. We study the parameters that influence the system performance, including (i) the choice of sensing matrix, (ii) the trade-off between quantization and compression ratio, and (iii) the reconstruction algorithms. We propose an effective method to jointly control the quantization step and compression ratio in order to achieve near optimal quality at any given bit rate. Furthermore, our proposed image compression system can be directly used in the compressive sensing camera, e.g. the single pixel camera, to construct a hardware compressive sampling system.Comment: 17 pages, 13 figure

Spatio-temporal Compressed Sensing with Coded Apertures and Keyed Exposures

Optical systems which measure independent random projections of a scene according to compressed sensing (CS) theory face a myriad of practical challenges related to the size of the physical platform, photon efficiency, the need for high temporal resolution, and fast reconstruction in video settings. This paper describes a coded aperture and keyed exposure approach to compressive measurement in optical systems. The proposed projections satisfy the Restricted Isometry Property for sufficiently sparse scenes, and hence are compatible with theoretical guarantees on the video reconstruction quality. These concepts can be implemented in both space and time via either amplitude modulation or phase shifting, and this paper describes the relative merits of the two approaches in terms of theoretical performance, noise and hardware considerations, and experimental results. Fast numerical algorithms which account for the nonnegativity of the projections and temporal correlations in a video sequence are developed and applied to microscopy and short-wave infrared data.Comment: 15 pages, 4 figures, 2 tables, submitted to IEEE Transactions on Image Processin

Robust Coding of Encrypted Images via Structural Matrix

The robust coding of natural images and the effective compression of encrypted images have been studied individually in recent years. However, little work has been done in the robust coding of encrypted images. The existing results in these two individual research areas cannot be combined directly for the robust coding of encrypted images. This is because the robust coding of natural images relies on the elimination of spatial correlations using sparse transforms such as discrete wavelet transform (DWT), which is ineffective to encrypted images due to the weak correlation between encrypted pixels. Moreover, the compression of encrypted images always generates code streams with different significance. If one or more such streams are lost, the quality of the reconstructed images may drop substantially or decoding error may exist, which violates the goal of robust coding of encrypted images. In this work, we intend to design a robust coder, based on compressive sensing with structurally random matrix, for encrypted images over packet transmission networks. The proposed coder can be applied in the scenario that Alice needs a semi-trusted channel provider Charlie to encode and transmit the encrypted image to Bob. In particular, Alice first encrypts an image using globally random permutation and then sends the encrypted image to Charlie who samples the encrypted image using a structural matrix. Through an imperfect channel with packet loss, Bob receives the compressive measurements and reconstructs the original image by joint decryption and decoding. Experimental results show that the proposed coder can be considered as an efficient multiple description coder with a number of descriptions against packet loss.Comment: 10 pages, 11 figure

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

Measurement-Adaptive Sparse Image Sampling and Recovery

This paper presents an adaptive and intelligent sparse model for digital image sampling and recovery. In the proposed sampler, we adaptively determine the number of required samples for retrieving image based on space-frequency-gradient information content of image patches. By leveraging texture in space, sparsity locations in DCT domain, and directional decomposition of gradients, the sampler structure consists of a combination of uniform, random, and nonuniform sampling strategies. For reconstruction, we model the recovery problem as a two-state cellular automaton to iteratively restore image with scalable windows from generation to generation. We demonstrate the recovery algorithm quickly converges after a few generations for an image with arbitrary degree of texture. For a given number of measurements, extensive experiments on standard image-sets, infra-red, and mega-pixel range imaging devices show that the proposed measurement matrix considerably increases the overall recovery performance, or equivalently decreases the number of sampled pixels for a specific recovery quality compared to random sampling matrix and Gaussian linear combinations employed by the state-of-the-art compressive sensing methods. In practice, the proposed measurement-adaptive sampling/recovery framework includes various applications from intelligent compressive imaging-based acquisition devices to computer vision and graphics, and image processing technology. Simulation codes are available online for reproduction purposes

State of the Art and Prospects of Structured Sensing Matrices in Compressed Sensing

Compressed sensing (CS) enables people to acquire the compressed measurements directly and recover sparse or compressible signals faithfully even when the sampling rate is much lower than the Nyquist rate. However, the pure random sensing matrices usually require huge memory for storage and high computational cost for signal reconstruction. Many structured sensing matrices have been proposed recently to simplify the sensing scheme and the hardware implementation in practice. Based on the restricted isometry property and coherence, couples of existing structured sensing matrices are reviewed in this paper, which have special structures, high recovery performance, and many advantages such as the simple construction, fast calculation and easy hardware implementation. The number of measurements and the universality of different structure matrices are compared

Coded aperture compressive temporal imaging

We use mechanical translation of a coded aperture for code division multiple access compression of video. We present experimental results for reconstruction at 148 frames per coded snapshot.Comment: 19 pages (when compiled with Optics Express' TEX template), 15 figure

Data-Driven Learning of a Union of Sparsifying Transforms Model for Blind Compressed Sensing

Compressed sensing is a powerful tool in applications such as magnetic resonance imaging (MRI). It enables accurate recovery of images from highly undersampled measurements by exploiting the sparsity of the images or image patches in a transform domain or dictionary. In this work, we focus on blind compressed sensing (BCS), where the underlying sparse signal model is a priori unknown, and propose a framework to simultaneously reconstruct the underlying image as well as the unknown model from highly undersampled measurements. Specifically, our model is that the patches of the underlying image(s) are approximately sparse in a transform domain. We also extend this model to a union of transforms model that better captures the diversity of features in natural images. The proposed block coordinate descent type algorithms for blind compressed sensing are highly efficient, and are guaranteed to converge to at least the partial global and partial local minimizers of the highly non-convex BCS problems. Our numerical experiments show that the proposed framework usually leads to better quality of image reconstructions in MRI compared to several recent image reconstruction methods. Importantly, the learning of a union of sparsifying transforms leads to better image reconstructions than a single adaptive transform.Comment: Appears in IEEE Transactions on Computational Imaging, 201

Compressive sensing based privacy for fall detection

Fall detection holds immense importance in the field of healthcare, where timely detection allows for instant medical assistance. In this context, we propose a 3D ConvNet architecture which consists of 3D Inception modules for fall detection. The proposed architecture is a custom version of Inflated 3D (I3D) architecture, that takes compressed measurements of video sequence as spatio-temporal input, obtained from compressive sensing framework, rather than video sequence as input, as in the case of I3D convolutional neural network. This is adopted since privacy raises a huge concern for patients being monitored through these RGB cameras. The proposed framework for fall detection is flexible enough with respect to a wide variety of measurement matrices. Ten action classes randomly selected from Kinetics-400 with no fall examples, are employed to train our 3D ConvNet post compressive sensing with different types of sensing matrices on the original video clips. Our results show that 3D ConvNet performance remains unchanged with different sensing matrices. Also, the performance obtained with Kinetics pre-trained 3D ConvNet on compressively sensed fall videos from benchmark datasets is better than the state-of-the-art techniques.Comment: accepted in NCVPRIPG 201

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