A Cognitive Radio Compressive Sensing Framework

With the proliferation of wireless devices and services, allied with further significant predicted growth, there is an ever increasing demand for higher transmission rates. This is especially challenging given the limited availability of radio spectrum, and is further exacerbated by a rigid licensing regulatory regime. Spectrum however, is largely underutilized and this has prompted regulators to promote the concept of opportunistic spectrum access. This allows unlicensed secondary users to use bands which are licensed to primary users, but are currently unoccupied, so leading to more efficient spectrum utilization. A potentially attractive solution to this spectrum underutilisation problem is cognitive radio (CR) technology, which enables the identification and usage of vacant bands by continuously sensing the radio environment, though CR enforces stringent timing requirements and high sampling rates. Compressive sensing (CS) has emerged as a novel sampling paradigm, which provides the theoretical basis to resolve some of these issues, especially for signals exhibiting sparsity in some domain. For CR-related signals however, existing CS architectures such as the random demodulator and compressive multiplexer have limitations in regard to the signal types used, spectrum estimation methods applied, spectral band classification and a dependence on Fourier domain based sparsity. This thesis presents a new generic CS framework which addresses these issues by specifically embracing three original scientific contributions: i) seamless embedding of the concept of precolouring into existing CS architectures to enhance signal sparsity for CR-related digital modulation schemes; ii) integration of the multitaper spectral estimator to improve sparsity in CR narrowband modulation schemes; and iii) exploiting sparsity in an alternative, non-Fourier (Walsh-Hadamard) domain to expand the applicable CR-related modulation schemes. Critical analysis reveals the new CS framework provides a consistently superior and robust solution for the recovery of an extensive set of currently employed CR-type signals encountered in wireless communication standards. Significantly, the generic and portable nature of the framework affords the opportunity for further extensions into other CS architectures and sparsity domains

Source Modulated Multiplexed Hyperspectral Imaging: Theory, Hardware and Application

The design, analysis and application of a multiplexing hyperspectral imager is presented. The hyperspectral imager consists of a broadband digital light projector that uses a digital micromirror array as the optical engine to project light patterns onto a sample object. A single point spectrometer measures light that is reflected from the sample. Multiplexing patterns encode the spectral response from the sample, where each spectrum taken is the sum of a set of spectral responses from a number of pixels. Decoding in software recovers the spectral response of each pixel. A technique, which we call complement encoding, is introduced for the removal of background light effects. Complement encoding requires the use of multiplexing matrices with positive and negative entries. The theory of multiplexing using the Hadamard matrices is developed. Results from prior art are incorporated into a singular notational system under which the different Hadamard matrices are compared with each other and with acquisition of data without multiplexing (pointwise acquisition). The link between Hadamard matrices with strongly regular graphs is extended to incorporate all three types of Hadamard matrices. The effect of the number of measurements used in compressed sensing on measurement precision is derived by inference using results concerning the eigenvalues of large random matrices. The literature shows that more measurements increases accuracy of reconstruction. In contrast we find that more measurement reduces precision, so there is a tradeoff between precision and accuracy. The effect of error in the reference on the Wilcoxon statistic is derived. Reference error reduces the estimate of the Wilcoxon, however given an estimate of theWilcoxon and the proportion of error in the reference, we show thatWilcoxon without error can be estimated. Imaging of simple objects and signal to noise ratio (SNR) experiments are used to test the hyperspectral imager. The simple objects allow us to see that the imager produces sensible spectra. The experiments involve looking at the SNR itself and the SNR boost, that is ratio of the SNR from multiplexing to the SNR from pointwise acquisition. The SNR boost varies dramatically across the spectral domain from 3 to the theoretical maximum of 16. The range of boost values is due to the relative Poisson to additive noise variance changing over the spectral domain, an effect that is due to the light bulb output and detector sensitivity not being flat over the spectral domain. It is shown that the SNR boost is least where the SNR is high and is greatest where the SNR is least, so the boost is provided where it is needed most. The varying SNR boost is interpreted as a preferential boost, that is useful when the dominant noise source is indeterminate or varying. Compressed sensing precision is compared with the accuracy in reconstruction and with the precision in Hadamard multiplexing. A tradeoff is observed between accuracy and precision as the number of measurements increases. Generally Hadamard multiplexing is found to be superior to compressed sensing, but compressed sensing is considered suitable when shortened data acquisition time is important and poorer data quality is acceptable. To further show the use of the hyperspectral imager, volumetric mapping and analysis of beef m. longissimus dorsi are performed. Hyperspectral images are taken of successive slices down the length of the muscle. Classification of the spectra according to visible content as lean or nonlean is trialled, resulting in a Wilcoxon value greater than 0.95, indicating very strong classification power. Analysis of the variation in the spectra down the length of the muscles is performed using variography. The variation in spectra of a muscle is small but increases with distance, and there is a periodic effect possibly due to water seepage from where connective tissue is removed from the meat while cutting from the carcass. The spectra are compared to parameters concerning the rate and value of meat bloom (change of colour post slicing), pH and tenderometry reading (shear force). Mixed results for prediction of blooming parameters are obtained, pH shows strong correlation (R² = 0.797) with the spectral band 598-949 nm despite the narrow range of pH readings obtained. A likewise narrow range of tenderometry readings resulted in no useful correlation with the spectra. Overall the spatial multiplexed imaging with a DMA based light modulation is successful. The theoretical analysis of multiplexing gives a general description of the system performance, particularly for multiplexing with the Hadamard matrices. Experiments show that the Hadamard multiplexing technique improves the SNR of spectra taken over pointwise imaging. Aspects of the theoretical analysis are demonstrated. Hyperspectral images are acquired and analysed that demonstrate that the spectra acquired are sensible and useful

Compressive sensing based image processing and energy-efficient hardware implementation with application to MRI and JPG 2000

In the present age of technology, the buzzwords are low-power, energy-efficient and compact systems. This directly leads to the date processing and hardware techniques employed in the core of these devices. One of the most power-hungry and space-consuming schemes is that of image/video processing, due to its high quality requirements. In current design methodologies, a point has nearly been reached in which physical and physiological effects limit the ability to just encode data faster. These limits have led to research into methods to reduce the amount of acquired data without degrading image quality and increasing the energy consumption. Compressive sensing (CS) has emerged as an efficient signal compression and recovery technique, which can be used to efficiently reduce the data acquisition and processing. It exploits the sparsity of a signal in a transform domain to perform sampling and stable recovery. This is an alternative paradigm to conventional data processing and is robust in nature. Unlike the conventional methods, CS provides an information capturing paradigm with both sampling and compression. It permits signals to be sampled below the Nyquist rate, and still allowing optimal reconstruction of the signal. The required measurements are far less than those of conventional methods, and the process is non-adaptive, making the sampling process faster and universal. In this thesis, CS methods are applied to magnetic resonance imaging (MRI) and JPEG 2000, which are popularly used imaging techniques in clinical applications and image compression, respectively. Over the years, MRI has improved dramatically in both imaging quality and speed. This has further revolutionized the field of diagnostic medicine. However, imaging speed, which is essential to many MRI applications still remains a major challenge. The specific challenge addressed in this work is the use of non-Fourier based complex measurement-based data acquisition. This method provides the possibility of reconstructing high quality MRI data with minimal measurements, due to the high incoherence between the two chosen matrices. Similarly, JPEG2000, though providing a high compression, can be further improved upon by using compressive sampling. In addition, the image quality is also improved. Moreover, having a optimized JPEG 2000 architecture reduces the overall processing, and a faster computation when combined with CS. Considering the requirements, this thesis is presented in two parts. In the first part: (1) A complex Hadamard matrix (CHM) based 2D and 3D MRI data acquisition with recovery using a greedy algorithm is proposed. The CHM measurement matrix is shown to satisfy the necessary condition for CS, known as restricted isometry property (RIP). The sparse recovery is done using compressive sampling matching pursuit (CoSaMP); (2) An optimized matrix and modified CoSaMP is presented, which enhances the MRI performance when compared with the conventional sampling; (3) An energy-efficient, cost-efficient hardware design based on field programmable gate array (FPGA) is proposed, to provide a platform for low-cost MRI processing hardware. At every stage, the design is proven to be superior with other commonly used MRI-CS methods and is comparable with the conventional MRI sampling. In the second part, CS techniques are applied to image processing and is combined with JPEG 2000 coder. While CS can reduce the encoding time, the effect on the overall JPEG 2000 encoder is not very significant due to some complex JPEG 2000 algorithms. One problem encountered is the big-level operations in JPEG 2000 arithmetic encoding (AE), which is completely based on bit-level operations. In this work, this problem is tackled by proposing a two-symbol AE with an efficient FPGA based hardware design. Furthermore, this design is energy-efficient, fast and has lower complexity when compared to conventional JPEG 2000 encoding

Compressed sensing in fluorescence microscopy.

Compressed sensing (CS) is a signal processing approach that solves ill-posed inverse problems, from under-sampled data with respect to the Nyquist criterium. CS exploits sparsity constraints based on the knowledge of prior information, relative to the structure of the object in the spatial or other domains. It is commonly used in image and video compression as well as in scientific and medical applications, including computed tomography and magnetic resonance imaging. In the field of fluorescence microscopy, it has been demonstrated to be valuable for fast and high-resolution imaging, from single-molecule localization, super-resolution to light-sheet microscopy. Furthermore, CS has found remarkable applications in the field of mesoscopic imaging, facilitating the study of small animals' organs and entire organisms. This review article illustrates the working principles of CS, its implementations in optical imaging and discusses several relevant uses of CS in the field of fluorescence imaging from super-resolution microscopy to mesoscopy

Flexible resources for quantum metrology

Quantum metrology offers a quadratic advantage over classical approaches to parameter estimation problems by utilizing entanglement and nonclassicality. However, the hurdle of actually implementing the necessary quantum probe states and measurements, which vary drastically for different metrological scenarios, is usually not taken into account. We show that for a wide range of tasks in metrology, 2D cluster states (a particular family of states useful for measurement-based quantum computation) can serve as flexible resources that allow one to efficiently prepare any required state for sensing, and perform appropriate (entangled) measurements using only single qubit operations. Crucially, the overhead in the number of qubits is less than quadratic, thus preserving the quantum scaling advantage. This is ensured by using a compression to a logarithmically sized space that contains all relevant information for sensing. We specifically demonstrate how our method can be used to obtain optimal scaling for phase and frequency estimation in local estimation problems, as well as for the Bayesian equivalents with Gaussian priors of varying widths. Furthermore, we show that in the paradigmatic case of local phase estimation 1D cluster states are sufficient for optimal state preparation and measurement.Comment: 9+18 pages, many figure