RECONSTRUCTION OF COMPRESSIVELY SAMPLED TEXTURE IMAGES IN THE GRAPH-BASED TRANSFORM DOMAIN

ABSTRACT This paper addresses the problem of texture images recovery from compressively sampled measurements. Texture images hardly present a sparse, or even compressible, representation in transformed domains (e.g. wavelet) and are therefore difficult to deal with in the Compressive Sampling (CS) framework. Herein, we resort to the recently defined Graph-based transform (GBT), formerly introduced for depth map coding, as a sparsifying transform for classes of textures sharing the similar spatial patterns. Since GBT proves to be a good candidate for compact representation of some classes of texture, we leverage it for CS texture recovery. To this aim, we resort to a modified version of a state-of-the-art recovery algorithm to reconstruct the texture representation in the GBT domain. Numerical simulation results show that this approach outperforms state-of-the-art CS recovery algorithms on texture images

Hierarchical CoSaMP for compressively sampled sparse signals with nested structure

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Green compressive sampling reconstruction in IoT networks

In this paper, we address the problem of green Compressed Sensing (CS) reconstruction within Internet of Things (IoT) networks, both in terms of computing architecture and reconstruction algorithms. The approach is novel since, unlike most of the literature dealing with energy efficient gathering of the CS measurements, we focus on the energy efficiency of the signal reconstruction stage given the CS measurements. As a first novel contribution, we present an analysis of the energy consumption within the IoT network under two computing architectures. In the first one, reconstruction takes place within the IoT network and the reconstructed data are encoded and transmitted out of the IoT network; in the second one, all the CS measurements are forwarded to off-network devices for reconstruction and storage, i.e., reconstruction is off-loaded. Our analysis shows that the two architectures significantly differ in terms of consumed energy, and it outlines a theoretically motivated criterion to select a green CS reconstruction computing architecture. Specifically, we present a suitable decision function to determine which architecture outperforms the other in terms of energy efficiency. The presented decision function depends on a few IoT network features, such as the network size, the sink connectivity, and other systems’ parameters. As a second novel contribution, we show how to overcome classical performance comparison of different CS reconstruction algorithms usually carried out w.r.t. the achieved accuracy. Specifically, we consider the consumed energy and analyze the energy vs. accuracy trade-off. The herein presented approach, jointly considering signal processing and IoT network issues, is a relevant contribution for designing green compressive sampling architectures in IoT networks

Structure-Constrained Basis Pursuit for Compressively Sensing Speech

Compressed Sensing (CS) exploits the sparsity of many signals to enable sampling below the Nyquist rate. If the original signal is sufficiently sparse, the Basis Pursuit (BP) algorithm will perfectly reconstruct the original signal. Unfortunately many signals that intuitively appear sparse do not meet the threshold for sufficient sparsity . These signals require so many CS samples for accurate reconstruction that the advantages of CS disappear. This is because Basis Pursuit/Basis Pursuit Denoising only models sparsity. We developed a Structure-Constrained Basis Pursuit that models the structure of somewhat sparse signals as upper and lower bound constraints on the Basis Pursuit Denoising solution. We applied it to speech, which seems sparse but does not compress well with CS, and gained improved quality over Basis Pursuit Denoising. When a single parameter (i.e. the phone) is encoded, Normalized Mean Squared Error (NMSE) decreases by between 16.2% and 1.00% when sampling with CS between 1/10 and 1/2 the Nyquist rate, respectively. When bounds are coded as a sum of Gaussians, NMSE decreases between 28.5% and 21.6% in the same range. SCBP can be applied to any somewhat sparse signal with a predictable structure to enable improved reconstruction quality with the same number of samples

An Adaptive Optimal Bandwidth Sensor for Video Imaging and Sparsifying Basis

Many compressive sensing architectures have shown promise towards reducingthe bandwidth for image acquisition significantly. In order to use these architectures for video acquisition we need a scheme that is able to effectively exploit temporal redundancies in a sequence. In this thesis we study a method to efficiently sample and reconstruct specific video sequences. The method is suitable for implementation using a single pixel detector along with a digital micromirror device (DMD) or other forms of spatial light modulators (SLMs). Conventional implementations of single pixel cameras are able to spatially compress the signal but the compressed measurements make it difficult to exploit temporal redundancies directly. Moreover a single pixel camera needs to make measurements in a sequential manner before the scene changes making it inefficient for video imaging. In this thesis we discuss a measurement scheme that exploits sparsity along the time axis for video imaging. After acquiring all measurements required for the first frame, measurements are only acquired from the areas which change in subsequent frames. We segment the first frame and detect magnitude and direction of change for each segment and acquire compressed measurements for the changing segments in the predicted direction. TV minimization is used to reconstruct the dynamic areas and PSNR variation is studied against different parameters of proposed scheme. We show the reconstruction results for a few test sequences commonly used for performance analysis and demonstrate the practical utility of the scheme. A comparison is made with existing algorithms to show the eeffectiveness of proposed method for specific video sequences. We also discuss use of customized transform to improve reconstruction of submililimeter wave single pixel imager. We use a sparseness inducing transformation onthe measurements and optimize the result using l1 minimization algorithms. We demonstrate improvement in result of several images acquired and reconstructed using this technique

Autoregressive process parameters estimation from Compressed Sensing measurements and Bayesian dictionary learning

The main contribution of this thesis is the introduction of new techniques which allow to perform signal processing operations on signals represented by means of compressed sensing. Exploiting autoregressive modeling of the original signal, we obtain a compact yet representative description of the signal which can be estimated directly in the compressed domain. This is the key concept on which the applications we introduce rely on. In fact, thanks to proposed the framework it is possible to gain information about the original signal given compressed sensing measurements. This is done by means of autoregressive modeling which can be used to describe a signal through a small number of parameters. We develop a method to estimate these parameters given the compressed measurements by using an ad-hoc sensing matrix design and two different coupled estimators that can be used in different scenarios. This enables centralized and distributed estimation of the covariance matrix of a process given the compressed sensing measurements in a efficient way at low communication cost. Next, we use the characterization of the original signal done by means of few autoregressive parameters to improve compressive imaging. In particular, we use these parameters as a proxy to estimate the complexity of a block of a given image. This allows us to introduce a novel compressive imaging system in which the number of allocated measurements is adapted for each block depending on its complexity, i.e., spatial smoothness. The result is that a careful allocation of the measurements, improves the recovery process by reaching higher recovery quality at the same compression ratio in comparison to state-of-the-art compressive image recovery techniques. Interestingly, the parameters we are able to estimate directly in the compressed domain not only can improve the recovery but can also be used as feature vectors for classification. In fact, we also propose to use these parameters as more general feature vectors which allow to perform classification in the compressed domain. Remarkably, this method reaches high classification performance which is comparable with that obtained in the original domain, but with a lower cost in terms of dataset storage. In the second part of this work, we focus on sparse representations. In fact, a better sparsifying dictionary can improve the Compressed Sensing recovery performance. At first, we focus on the original domain and hence no dimensionality reduction by means of Compressed Sensing is considered. In particular, we develop a Bayesian technique which, in a fully automated fashion, performs dictionary learning. More in detail, using the uncertainties coming from atoms selection in the sparse representation step, this technique outperforms state-of-the-art dictionary learning techniques. Then, we also address image denoising and inpainting tasks using the aforementioned technique with excellent results. Next, we move to the compressed domain where a better dictionary is expected to provide improved recovery. We show how the Bayesian dictionary learning model can be adapted to the compressive case and the necessary assumptions that must be made when considering random projections. Lastly, numerical experiments confirm the superiority of this technique when compared to other compressive dictionary learning techniques

Sparse Reconstruction of Compressive Sensing Magnetic Resonance Imagery using a Cross Domain Stochastic Fully Connected Conditional Random Field Framework

Prostate cancer is a major health care concern in our society. Early detection of prostate cancer is crucial in the successful treatment of the disease. Many current methods used in detecting prostate cancer can either be inconsistent or invasive and discomforting to the patient. Magnetic resonance imaging (MRI) has demonstrated its ability as a non-invasive and non-ionizing medical imaging modality with a lengthy acquisition time that can be used for the early diagnosis of cancer. Speeding up the MRI acquisition process can greatly increase the number of early detections for prostate cancer diagnosis. Compressive sensing has exhibited the ability to reduce the imaging time for MRI by sampling a sparse yet sufficient set of measurements. Compressive sensing strategies are usually accompanied by strong reconstruction algorithms. This work presents a comprehensive framework for a cross-domain stochastically fully connected conditional random field (CD-SFCRF) reconstruction approach to facilitate compressive sensing MRI. This approach takes into account original k-space measurements made by the MRI machine with neighborhood and spatial consistencies of the image in the spatial domain. This approach facilitates the difference in domain between MRI measurements made in the k-space, and the reconstruction results in spatial domain. An adaptive extension of the CD-SFCRF approach that takes into account regions of interest in the image and changes the CD-SFCRF neighborhood connectivity based on importance is presented and tested as well. Finally, a compensated CD-SFCRF approach that takes into account MRI machine imaging apparatus properties to correct for degradations and aberrations from the image acquisition process is presented and tested. Clinical MRI data were collected from twenty patients with ground truth data examined and con firmed by an expert radiologist with multiple years of prostate cancer diagnosis experience. Compressive sensing simulations were performed and the reconstruction results show the CD-SFCRF and extension frameworks having noticeable improvements over state of the art methods. Tissue structure and image details are well preserved while sparse sampling artifacts were reduced and eliminated. Future work on this framework include extending the current work in multiple ways. Extensions including integration into computer aided diagnosis applications as well as improving on the compressive sensing strategy