On Convergence of Approximate Message Passing

Approximate message passing is an iterative algorithm for compressed sensing and related applications. A solid theory about the performance and convergence of the algorithm exists for measurement matrices having iid entries of zero mean. However, it was observed by several authors that for more general matrices the algorithm often encounters convergence problems. In this paper we identify the reason of the non-convergence for measurement matrices with iid entries and non-zero mean in the context of Bayes optimal inference. Finally we demonstrate numerically that when the iterative update is changed from parallel to sequential the convergence is restored.Comment: 5 pages, 3 figure

Accelerated High-Resolution Photoacoustic Tomography via Compressed Sensing

Current 3D photoacoustic tomography (PAT) systems offer either high image quality or high frame rates but are not able to deliver high spatial and temporal resolution simultaneously, which limits their ability to image dynamic processes in living tissue. A particular example is the planar Fabry-Perot (FP) scanner, which yields high-resolution images but takes several minutes to sequentially map the photoacoustic field on the sensor plane, point-by-point. However, as the spatio-temporal complexity of many absorbing tissue structures is rather low, the data recorded in such a conventional, regularly sampled fashion is often highly redundant. We demonstrate that combining variational image reconstruction methods using spatial sparsity constraints with the development of novel PAT acquisition systems capable of sub-sampling the acoustic wave field can dramatically increase the acquisition speed while maintaining a good spatial resolution: First, we describe and model two general spatial sub-sampling schemes. Then, we discuss how to implement them using the FP scanner and demonstrate the potential of these novel compressed sensing PAT devices through simulated data from a realistic numerical phantom and through measured data from a dynamic experimental phantom as well as from in-vivo experiments. Our results show that images with good spatial resolution and contrast can be obtained from highly sub-sampled PAT data if variational image reconstruction methods that describe the tissues structures with suitable sparsity-constraints are used. In particular, we examine the use of total variation regularization enhanced by Bregman iterations. These novel reconstruction strategies offer new opportunities to dramatically increase the acquisition speed of PAT scanners that employ point-by-point sequential scanning as well as reducing the channel count of parallelized schemes that use detector arrays.Comment: submitted to "Physics in Medicine and Biology

Wireless Interference Identification with Convolutional Neural Networks

The steadily growing use of license-free frequency bands requires reliable coexistence management for deterministic medium utilization. For interference mitigation, proper wireless interference identification (WII) is essential. In this work we propose the first WII approach based upon deep convolutional neural networks (CNNs). The CNN naively learns its features through self-optimization during an extensive data-driven GPU-based training process. We propose a CNN example which is based upon sensing snapshots with a limited duration of 12.8 {\mu}s and an acquisition bandwidth of 10 MHz. The CNN differs between 15 classes. They represent packet transmissions of IEEE 802.11 b/g, IEEE 802.15.4 and IEEE 802.15.1 with overlapping frequency channels within the 2.4 GHz ISM band. We show that the CNN outperforms state-of-the-art WII approaches and has a classification accuracy greater than 95% for signal-to-noise ratio of at least -5 dB

Sparsity-Based Super Resolution for SEM Images

The scanning electron microscope (SEM) produces an image of a sample by scanning it with a focused beam of electrons. The electrons interact with the atoms in the sample, which emit secondary electrons that contain information about the surface topography and composition. The sample is scanned by the electron beam point by point, until an image of the surface is formed. Since its invention in 1942, SEMs have become paramount in the discovery and understanding of the nanometer world, and today it is extensively used for both research and in industry. In principle, SEMs can achieve resolution better than one nanometer. However, for many applications, working at sub-nanometer resolution implies an exceedingly large number of scanning points. For exactly this reason, the SEM diagnostics of microelectronic chips is performed either at high resolution (HR) over a small area or at low resolution (LR) while capturing a larger portion of the chip. Here, we employ sparse coding and dictionary learning to algorithmically enhance LR SEM images of microelectronic chips up to the level of the HR images acquired by slow SEM scans, while considerably reducing the noise. Our methodology consists of two steps: an offline stage of learning a joint dictionary from a sequence of LR and HR images of the same region in the chip, followed by a fast-online super-resolution step where the resolution of a new LR image is enhanced. We provide several examples with typical chips used in the microelectronics industry, as well as a statistical study on arbitrary images with characteristic structural features. Conceptually, our method works well when the images have similar characteristics. This work demonstrates that employing sparsity concepts can greatly improve the performance of SEM, thereby considerably increasing the scanning throughput without compromising on analysis quality and resolution.Comment: Final publication available at ACS Nano Letter

Compressively characterizing high-dimensional entangled states with complementary, random filtering

The resources needed to conventionally characterize a quantum system are overwhelmingly large for high- dimensional systems. This obstacle may be overcome by abandoning traditional cornerstones of quantum measurement, such as general quantum states, strong projective measurement, and assumption-free characterization. Following this reasoning, we demonstrate an efficient technique for characterizing high-dimensional, spatial entanglement with one set of measurements. We recover sharp distributions with local, random filtering of the same ensemble in momentum followed by position---something the uncertainty principle forbids for projective measurements. Exploiting the expectation that entangled signals are highly correlated, we use fewer than 5,000 measurements to characterize a 65, 536-dimensional state. Finally, we use entropic inequalities to witness entanglement without a density matrix. Our method represents the sea change unfolding in quantum measurement where methods influenced by the information theory and signal-processing communities replace unscalable, brute-force techniques---a progression previously followed by classical sensing.Comment: 13 pages, 7 figure

Real-time Assessment of Right and Left Ventricular Volumes and Function in Children Using High Spatiotemporal Resolution Spiral bSSFP with Compressed Sensing

Background: Real-time (RT) assessment of ventricular volumes and function enables data acquisition during free-breathing. However, in children the requirement for high spatiotemporal resolution requires accelerated imaging techniques. In this study, we implemented a novel RT bSSFP spiral sequence reconstructed using Compressed Sensing (CS) and validated it against the breath-hold (BH) reference standard for assessment of ventricular volumes in children with heart disease. Methods: Data was acquired in 60 children. Qualitative image scoring and evaluation of ventricular volumes was performed by 3 clinical cardiac MR specialists. 30 cases were reassessed for intra-observer variability, and the other 30 cases for inter-observer variability. Results: Spiral RT images were of good quality, however qualitative scores reflected more residual artefact than standard BH images and slightly lower edge definition. Quantification of Left Ventricular (LV) and Right Ventricular (RV) metrics showed excellent correlation between the techniques with narrow limits of agreement. However, we observed small but statistically significant overestimation of LV end-diastolic volume, underestimation of LV end-systolic volume, as well as a small overestimation of RV stroke volume and ejection fraction using the RT imaging technique. No difference in inter-observer or intra-observer variability were observed between the BH and RT sequences. Conclusions: Real-time bSSFP imaging using spiral trajectories combined with a compressed sensing reconstruction is feasible. The main benefit is that it can be acquired during free breathing. However, another important secondary benefit is that a whole ventricular stack can be acquired in ~20 seconds, as opposed to ~6 minutes for standard BH imaging. Thus, this technique holds the potential to significantly shorten MR scan times in children

On evolution of CMOS image sensors

CMOS Image Sensors have become the principal technology in majority of digital cameras. They started replacing the film and Charge Coupled Devices in the last decade with the promise of lower cost, lower power requirement, higher integration and the potential of focal plane processing. However, the principal factor behind their success has been the ability to utilise the shrinkage in CMOS technology to make smaller pixels, and thereby have more resolution without increasing the cost. With the market of image sensors exploding courtesy their inte- gration with communication and computation devices, technology developers improved the CMOS processes to have better optical performance. Nevertheless, the promises of focal plane processing as well as on-chip integration have not been fulfilled. The market is still being pushed by the desire of having higher number of pixels and better image quality, however, differentiation is being difficult for any image sensor manufacturer. In the paper, we will explore potential disruptive growth directions for CMOS Image sensors and ways to achieve the same