Light Field Compressive Sensing in Camera Arrays

This paper presents a novel approach to capture light field in cam- era arrays based on the compressive sensing framework

Imaging With Nature: Compressive Imaging Using a Multiply Scattering Medium

The recent theory of compressive sensing leverages upon the structure of signals to acquire them with much fewer measurements than was previously thought necessary, and certainly well below the traditional Nyquist-Shannon sampling rate. However, most implementations developed to take advantage of this framework revolve around controlling the measurements with carefully engineered material or acquisition sequences. Instead, we use the natural randomness of wave propagation through multiply scattering media as an optimal and instantaneous compressive imaging mechanism. Waves reflected from an object are detected after propagation through a well-characterized complex medium. Each local measurement thus contains global information about the object, yielding a purely analog compressive sensing method. We experimentally demonstrate the effectiveness of the proposed approach for optical imaging by using a 300-micrometer thick layer of white paint as the compressive imaging device. Scattering media are thus promising candidates for designing efficient and compact compressive imagers.Comment: 17 pages, 8 figure

Structured random measurements in signal processing

Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse signal reconstruction guarantees for efficient and stable algorithms with a minimal number of samples. While this was first shown for (unstructured) Gaussian random measurement matrices, applications require certain structure of the measurements leading to structured random measurement matrices. Near optimal recovery guarantees for such structured measurements have been developed over the past years in a variety of contexts. This article surveys the theory in three scenarios: compressed sensing (sparse recovery), low rank matrix recovery, and phaseless estimation. The random measurement matrices to be considered include random partial Fourier matrices, partial random circulant matrices (subsampled convolutions), matrix completion, and phase estimation from magnitudes of Fourier type measurements. The article concludes with a brief discussion of the mathematical techniques for the analysis of such structured random measurements.Comment: 22 pages, 2 figure

Light Field Compressive Sensing in Camera Arrays

This paper presents a novel approach to capture light field in camera arrays based on the compressive sensing framework. Light fields are captured by a linear array of cameras with overlapping field of view. In this work, we design a redundant dictionary to exploit cross-cameras correlated structures to sparsely represent cameras image. Our main contributions are threefold. First, we exploit the correlations between the set of views by making use of a specially designed redundant dictionary. We show experimentally that the projection of complex scenes onto this dictionary yields very sparse coefficients. Second, we propose an efficient compressive encoding scheme based on the random convolution framework. Finally, we develop a joint sparse recovery algorithm for decoding the compressed measurements and show a marked improvement over independent decoding of CS measurements

Joint Low-rank and Sparse Light Field Modeling for Dense Multiview Data Compression

The effective representation of the structures in the multiview images is an important problem that arises in visual sensor networks. This paper presents a novel recovery scheme from compressive samples which exploit local and non-local correlated structures in dense multiview images. The recovery model casts into convex minimization framework which penalizes the sparse and low-rank constraints on the data. The sparsity constraint models the correlations among pixels in a single image whereas the global correlations across images are modelled with the low-rank prior. Simulation results demonstrate that our approach achieves better reconstruct quality in comparison with the state-of-the-art reconstruction schemes

Design of Scalable Hardware-Efficient Compressive Sensing Image Sensors

This work presents a new compressive sensing (CS) measurement method for image sensors, which limits pixel summation within neighbor pixels and follows regular summation patterns. Simulations with a large set of benchmark images show that the proposed method leads to improved image quality. Circuit implementation for the proposed CS measurement method is presented with the use of current mode pixel cells; and the resultant CS image sensor circuit is significantly simpler than existing designs. With compression rates of 4 and 8, the developed CS image sensors can achieve 34.2 dB and 29.6 dB PSNR values with energy consumption of 1.4 mJ and 0.73 mJ per frame, respectively

Structured Compressed Sensing: From Theory to Applications

Compressed sensing (CS) is an emerging field that has attracted considerable research interest over the past few years. Previous review articles in CS limit their scope to standard discrete-to-discrete measurement architectures using matrices of randomized nature and signal models based on standard sparsity. In recent years, CS has worked its way into several new application areas. This, in turn, necessitates a fresh look on many of the basics of CS. The random matrix measurement operator must be replaced by more structured sensing architectures that correspond to the characteristics of feasible acquisition hardware. The standard sparsity prior has to be extended to include a much richer class of signals and to encode broader data models, including continuous-time signals. In our overview, the theme is exploiting signal and measurement structure in compressive sensing. The prime focus is bridging theory and practice; that is, to pinpoint the potential of structured CS strategies to emerge from the math to the hardware. Our summary highlights new directions as well as relations to more traditional CS, with the hope of serving both as a review to practitioners wanting to join this emerging field, and as a reference for researchers that attempts to put some of the existing ideas in perspective of practical applications.Comment: To appear as an overview paper in IEEE Transactions on Signal Processin

Regime Change: Sampling Rate vs. Bit-Depth in Compressive Sensing

The compressive sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by exploiting inherent structure in natural and man-made signals. It has been demonstrated that structured signals can be acquired with just a small number of linear measurements, on the order of the signal complexity. In practice, this enables lower sampling rates that can be more easily achieved by current hardware designs. The primary bottleneck that limits ADC sampling rates is quantization, i.e., higher bit-depths impose lower sampling rates. Thus, the decreased sampling rates of CS ADCs accommodate the otherwise limiting quantizer of conventional ADCs. In this thesis, we consider a different approach to CS ADC by shifting towards lower quantizer bit-depths rather than lower sampling rates. We explore the extreme case where each measurement is quantized to just one bit, representing its sign. We develop a new theoretical framework to analyze this extreme case and develop new algorithms for signal reconstruction from such coarsely quantized measurements. The 1-bit CS framework leads us to scenarios where it may be more appropriate to reduce bit-depth instead of sampling rate. We find that there exist two distinct regimes of operation that correspond to high/low signal-to-noise ratio (SNR). In the measurement compression (MC) regime, a high SNR favors acquiring fewer measurements with more bits per measurement (as in conventional CS); in the quantization compression (QC) regime, a low SNR favors acquiring more measurements with fewer bits per measurement (as in this thesis). A surprise from our analysis and experiments is that in many practical applications it is better to operate in the QC regime, even acquiring as few as 1 bit per measurement. The above philosophy extends further to practical CS ADC system designs. We propose two new CS architectures, one of which takes advantage of the fact that the sampling and quantization operations are performed by two different hardware components. The former can be employed at high rates with minimal costs while the latter cannot. Thus, we develop a system that discretizes in time, performs CS preconditioning techniques, and then quantizes at a low rate

Exploring information retrieval using image sparse representations:from circuit designs and acquisition processes to specific reconstruction algorithms

New advances in the field of image sensors (especially in CMOS technology) tend to question the conventional methods used to acquire the image. Compressive Sensing (CS) plays a major role in this, especially to unclog the Analog to Digital Converters which are generally representing the bottleneck of this type of sensors. In addition, CS eliminates traditional compression processing stages that are performed by embedded digital signal processors dedicated to this purpose. The interest is twofold because it allows both to consistently reduce the amount of data to be converted but also to suppress digital processing performed out of the sensor chip. For the moment, regarding the use of CS in image sensors, the main route of exploration as well as the intended applications aims at reducing power consumption related to these components (i.e. ADC & DSP represent 99% of the total power consumption). More broadly, the paradigm of CS allows to question or at least to extend the Nyquist-Shannon sampling theory. This thesis shows developments in the field of image sensors demonstrating that is possible to consider alternative applications linked to CS. Indeed, advances are presented in the fields of hyperspectral imaging, super-resolution, high dynamic range, high speed and non-uniform sampling. In particular, three research axes have been deepened, aiming to design proper architectures and acquisition processes with their associated reconstruction techniques taking advantage of image sparse representations. How the on-chip implementation of Compressed Sensing can relax sensor constraints, improving the acquisition characteristics (speed, dynamic range, power consumption) ? How CS can be combined with simple analysis to provide useful image features for high level applications (adding semantic information) and improve the reconstructed image quality at a certain compression ratio ? Finally, how CS can improve physical limitations (i.e. spectral sensitivity and pixel pitch) of imaging systems without a major impact neither on the sensing strategy nor on the optical elements involved ? A CMOS image sensor has been developed and manufactured during this Ph.D. to validate concepts such as the High Dynamic Range - CS. A new design approach was employed resulting in innovative solutions for pixels addressing and conversion to perform specific acquisition in a compressed mode. On the other hand, the principle of adaptive CS combined with the non-uniform sampling has been developed. Possible implementations of this type of acquisition are proposed. Finally, preliminary works are exhibited on the use of Liquid Crystal Devices to allow hyperspectral imaging combined with spatial super-resolution. The conclusion of this study can be summarized as follows: CS must now be considered as a toolbox for defining more easily compromises between the different characteristics of the sensors: integration time, converters speed, dynamic range, resolution and digital processing resources. However, if CS relaxes some material constraints at the sensor level, it is possible that the collected data are difficult to interpret and process at the decoder side, involving massive computational resources compared to so-called conventional techniques. The application field is wide, implying that for a targeted application, an accurate characterization of the constraints concerning both the sensor (encoder), but also the decoder need to be defined