SONAR Images Denoising

International audienc

Sparse and Redundant Representations for Inverse Problems and Recognition

Sparse and redundant representation of data enables the description of signals as linear combinations of a few atoms from a dictionary. In this dissertation, we study applications of sparse and redundant representations in inverse problems and object recognition. Furthermore, we propose two novel imaging modalities based on the recently introduced theory of Compressed Sensing (CS). This dissertation consists of four major parts. In the first part of the dissertation, we study a new type of deconvolution algorithm that is based on estimating the image from a shearlet decomposition. Shearlets provide a multi-directional and multi-scale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets. We develop a deconvolution algorithm that allows for the approximation inversion operator to be controlled on a multi-scale and multi-directional basis. Furthermore, we develop a method for the automatic determination of the threshold values for the noise shrinkage for each scale and direction without explicit knowledge of the noise variance using a generalized cross validation method. In the second part of the dissertation, we study a reconstruction method that recovers highly undersampled images assumed to have a sparse representation in a gradient domain by using partial measurement samples that are collected in the Fourier domain. Our method makes use of a robust generalized Poisson solver that greatly aids in achieving a significantly improved performance over similar proposed methods. We will demonstrate by experiments that this new technique is more flexible to work with either random or restricted sampling scenarios better than its competitors. In the third part of the dissertation, we introduce a novel Synthetic Aperture Radar (SAR) imaging modality which can provide a high resolution map of the spatial distribution of targets and terrain using a significantly reduced number of needed transmitted and/or received electromagnetic waveforms. We demonstrate that this new imaging scheme, requires no new hardware components and allows the aperture to be compressed. Also, it presents many new applications and advantages which include strong resistance to countermesasures and interception, imaging much wider swaths and reduced on-board storage requirements. The last part of the dissertation deals with object recognition based on learning dictionaries for simultaneous sparse signal approximations and feature extraction. A dictionary is learned for each object class based on given training examples which minimize the representation error with a sparseness constraint. A novel test image is then projected onto the span of the atoms in each learned dictionary. The residual vectors along with the coefficients are then used for recognition. Applications to illumination robust face recognition and automatic target recognition are presented

Extraction of anthropological data with ultrasound

This thesis was submitted for the degree of Doctor of Philosophy and was awarded by Brunel University.Human body scanners used to extract anthropological data have a significant drawback, the subject is required to undress or wear tight fitting clothing. This thesis demonstrates an ultrasonic based alternative to the current optical systems, that can potentially operate on a fully clothed subject. To validate the concept several experiments were performed to determine the acoustic properties of multiple garments. The results indicated that such an approach was possible. Beamforming is introduced as a method by which the ultrasonic scanning area can be increased, the concept is thoroughly studied and a clear theoretical analysis is performed. Additionally, Matlab has been used to demonstrate graphically, the results of such analysis, providing an invaluable tool during the simulation, experimental and results stages of the thesis. To evaluate beamfoming as a composite part of ultrasonic body imaging, a hardware solution was necessary. During the concept phase, both FPGA and digital signal processors were evaluated to determine their suitability for the role. An FPGA approach was finally chosen, which allows highly parallel operation, essential to the high acquisition speeds required by some beamforming methodologies. In addition, analogue circuitry was also designed to provide an interface with the ultrasonic transducers, which, included variable gain amplifiers, charge amplifiers and signal conditioning. Finally, a digital acquisition card was used to transfer data between the FPGA and a desktop computer, on which, the sampled data was processed and displayed in a coherent graphical manner. The beamforming results clearly demonstrate that imaging multiple layers in air, with ultrasound, is a viable technique for anthroplogical data collection. Furthermore, a wavelet based method of improving the axial resolution is also proposed and demonstrated

Progressively communicating rich telemetry from autonomous underwater vehicles via relays

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution June 2012As analysis of imagery and environmental data plays a greater role in mission construction and execution, there is an increasing need for autonomous marine vehicles to transmit this data to the surface. Without access to the data acquired by a vehicle, surface operators cannot fully understand the state of the mission. Communicating imagery and high-resolution sensor readings to surface observers remains a significant challenge – as a result, current telemetry from free-roaming autonomous marine vehicles remains limited to ‘heartbeat’ status messages, with minimal scientific data available until after recovery. Increasing the challenge, longdistance communication may require relaying data across multiple acoustic hops between vehicles, yet fixed infrastructure is not always appropriate or possible. In this thesis I present an analysis of the unique considerations facing telemetry systems for free-roaming Autonomous Underwater Vehicles (AUVs) used in exploration. These considerations include high-cost vehicle nodes with persistent storage and significant computation capabilities, combined with human surface operators monitoring each node. I then propose mechanisms for interactive, progressive communication of data across multiple acoustic hops. These mechanisms include wavelet-based embedded coding methods, and a novel image compression scheme based on texture classification and synthesis. The specific characteristics of underwater communication channels, including high latency, intermittent communication, the lack of instantaneous end-to-end connectivity, and a broadcast medium, inform these proposals. Human feedback is incorporated by allowing operators to identify segments of data thatwarrant higher quality refinement, ensuring efficient use of limited throughput. I then analyze the performance of these mechanisms relative to current practices. Finally, I present CAPTURE, a telemetry architecture that builds on this analysis. CAPTURE draws on advances in compression and delay tolerant networking to enable progressive transmission of scientific data, including imagery, across multiple acoustic hops. In concert with a physical layer, CAPTURE provides an endto- end networking solution for communicating science data from autonomous marine vehicles. Automatically selected imagery, sonar, and time-series sensor data are progressively transmitted across multiple hops to surface operators. Human operators can request arbitrarily high-quality refinement of any resource, up to an error-free reconstruction. The components of this system are then demonstrated through three field trials in diverse environments on SeaBED, OceanServer and Bluefin AUVs, each in different software architectures.Thanks to the National Science Foundation, and the National Oceanic and Atmospheric Administration for their funding of my education and this work

Measure What Should be Measured: Progress and Challenges in Compressive Sensing

Is compressive sensing overrated? Or can it live up to our expectations? What will come after compressive sensing and sparsity? And what has Galileo Galilei got to do with it? Compressive sensing has taken the signal processing community by storm. A large corpus of research devoted to the theory and numerics of compressive sensing has been published in the last few years. Moreover, compressive sensing has inspired and initiated intriguing new research directions, such as matrix completion. Potential new applications emerge at a dazzling rate. Yet some important theoretical questions remain open, and seemingly obvious applications keep escaping the grip of compressive sensing. In this paper I discuss some of the recent progress in compressive sensing and point out key challenges and opportunities as the area of compressive sensing and sparse representations keeps evolving. I also attempt to assess the long-term impact of compressive sensing

Signal processing with Fourier analysis, novel algorithms and applications

Fourier analysis is the study of the way general functions may be represented or approximated by sums of simpler trigonometric functions, also analogously known as sinusoidal modeling. The original idea of Fourier had a profound impact on mathematical analysis, physics and engineering because it diagonalizes time-invariant convolution operators. In the past signal processing was a topic that stayed almost exclusively in electrical engineering, where only the experts could cancel noise, compress and reconstruct signals. Nowadays it is almost ubiquitous, as everyone now deals with modern digital signals. Medical imaging, wireless communications and power systems of the future will experience more data processing conditions and wider range of applications requirements than the systems of today. Such systems will require more powerful, efficient and flexible signal processing algorithms that are well designed to handle such needs. No matter how advanced our hardware technology becomes we will still need intelligent and efficient algorithms to address the growing demands in signal processing. In this thesis, we investigate novel techniques to solve a suite of four fundamental problems in signal processing that have a wide range of applications. The relevant equations, literature of signal processing applications, analysis and final numerical algorithms/methods to solve them using Fourier analysis are discussed for different applications in the electrical engineering/computer science. The first four chapters cover the following topics of central importance in the field of signal processing: • Fast Phasor Estimation using Adaptive Signal Processing (Chapter 2) • Frequency Estimation from Nonuniform Samples (Chapter 3) • 2D Polar and 3D Spherical Polar Nonuniform Discrete Fourier Transform (Chapter 4) • Robust 3D registration using Spherical Polar Discrete Fourier Transform and Spherical Harmonics (Chapter 5) Even though each of these four methods discussed may seem completely disparate, the underlying motivation for more efficient processing by exploiting the Fourier domain signal structure remains the same. The main contribution of this thesis is the innovation in the analysis, synthesis, discretization of certain well known problems like phasor estimation, frequency estimation, computations of a particular non-uniform Fourier transform and signal registration on the transformed domain. We conduct propositions and evaluations of certain applications relevant algorithms such as, frequency estimation algorithm using non-uniform sampling, polar and spherical polar Fourier transform. The techniques proposed are also useful in the field of computer vision and medical imaging. From a practical perspective, the proposed algorithms are shown to improve the existing solutions in the respective fields where they are applied/evaluated. The formulation and final proposition is shown to have a variety of benefits. Future work with potentials in medical imaging, directional wavelets, volume rendering, video/3D object classifications, high dimensional registration are also discussed in the final chapter. Finally, in the spirit of reproducible research we release the implementation of these algorithms to the public using Github