Discrete-Time Chaotic-Map Truly Random Number Generators: Design, Implementation, and Variability Analysis of the Zigzag Map

In this paper, we introduce a novel discrete chaotic map named zigzag map that demonstrates excellent chaotic behaviors and can be utilized in Truly Random Number Generators (TRNGs). We comprehensively investigate the map and explore its critical chaotic characteristics and parameters. We further present two circuit implementations for the zigzag map based on the switched current technique as well as the current-mode affine interpolation of the breakpoints. In practice, implementation variations can deteriorate the quality of the output sequence as a result of variation of the chaotic map parameters. In order to quantify the impact of variations on the map performance, we model the variations using a combination of theoretical analysis and Monte-Carlo simulations on the circuits. We demonstrate that even in the presence of the map variations, a TRNG based on the zigzag map passes all of the NIST 800-22 statistical randomness tests using simple post processing of the output data.Comment: To appear in Analog Integrated Circuits and Signal Processing (ALOG

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

Data-guided statistical sparse measurements modeling for compressive sensing

Digital image acquisition can be a time consuming process for situations where high spatial resolution is required. As such, optimizing the acquisition mechanism is of high importance for many measurement applications. Acquiring such data through a dynamically small subset of measurement locations can address this problem. In such a case, the measured information can be regarded as incomplete, which necessitates the application of special reconstruction tools to recover the original data set. The reconstruction can be performed based on the concept of sparse signal representation. Recovering signals and images from their sub-Nyquist measurements forms the core idea of compressive sensing (CS). In this work, a CS-based data-guided statistical sparse measurements method is presented, implemented and evaluated. This method significantly improves image reconstruction from sparse measurements. In the data-guided statistical sparse measurements approach, signal sampling distribution is optimized for improving image reconstruction performance. The sampling distribution is based on underlying data rather than the commonly used uniform random distribution. The optimal sampling pattern probability is accomplished by learning process through two methods - direct and indirect. The direct method is implemented for learning a nonparametric probability density function directly from the dataset. The indirect learning method is implemented for cases where a mapping between extracted features and the probability density function is required. The unified model is implemented for different representation domains, including frequency domain and spatial domain. Experiments were performed for multiple applications such as optical coherence tomography, bridge structure vibration, robotic vision, 3D laser range measurements and fluorescence microscopy. Results show that the data-guided statistical sparse measurements method significantly outperforms the conventional CS reconstruction performance. Data-guided statistical sparse measurements method achieves much higher reconstruction signal-to-noise ratio for the same compression rate as the conventional CS. Alternatively, Data-guided statistical sparse measurements method achieves similar reconstruction signal-to-noise ratio as the conventional CS with significantly fewer samples

Passive Remote Sensing of Lake Ice and Snow using Wideband Autocorrelation Radiometer (WiBAR).

Snow cover plays a vital role in providing the water supplies for domestic, industrial, and agricultural purposes. Conventionally, differential scatter darkening technique is used to detect the snow thickness. This technique is region specific and depends on the statistics of snow grain sizes. Ice formation process and ice thickness monitoring are important parameters in analyzing the overall pressure exerted to the off-shore structures such as wind farms. The traditional method for measuring the lake ice thickness is by a cumbersome drilling process through the ice. For future in-situ or remote planetary applications, the detection and analysis of ice sheets on or near the surface is one of the primary objectives of many planetary exploration missions. These applications demonstrate the requirement for an accurate remote sensing instrument, which can estimate the ice thickness without disturbing or breaking the ice. In this work, a novel microwave remote sensing technique to accurately estimate the thickness of any layered low-absorbing media including snow pack and fresh water ice using wideband autocorrelation radiometer (WiBAR) is presented. This technique relies on finding the autocorrelation response of the upwelling brightness temperature. The autocorrelation response provides enough information to estimate the microwave travel time delay of the doubly reflected thermal emission between the top and bottom interfaces an consequently the thickness of the snow or ice layer can be obtained. Several post processing techniques are developed to capture the periodicity of the ripples in the power spectral density domain. These techniques are capable of detecting very weak ripples deeply buried under noise. A compressive sensing based algorithm is also developed for detecting the thickness of ice/snow layers using 1/10 of the Nyquist rate samples. We have successfully designed, implemented, and tested a handheld ground base ice/snow thickness sensor in the frequency range of 1-3GHz or 7-10GHz under several scenarios including snow on top of undulated and vegetation covered terrain, ice over the lake water, air gap above a water surface and below a dielectric sheet, and snow cover under the forest canopy in the presence of radio frequency interference (RFI) with accuracy of within 1.5cm.PhDElectrical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/110419/1/hnejati_1.pd