Sparse Recovery from Linear Observations

Encoding and transmitting multimedia data over low-cost wireless sensors require a trade-off between energy and quality. Compressive Sensing (CS) has been proposed to transfer encoder complexity to the decoder and save energy at the sender, so it has been beneficial for recently developed Internet of Things (IoT) technologies. On the other hand, in practical applications of IoT, such as Low Power and Lossy Networks (LLNs), data is prone to error, which affects the quality at the receiver side. In order to solve this issue, error control mechanisms have been employed, while they are energy-consuming. Therefore, finding an efficient method for error protection in CS encoded videos is crucial in IoT lossy networks. This paper investigates the impact of Unequal Error Protection (UEP) on different frame types for a CS video setting in IoT lossy networks. Experimental results show that making a less complex and energy-efficient encoder can be done by not treating all frames with the same error control mechanism. Instead, having no or less complicated error control methods for non-key (P and B) frames but protecting I-frames is a better solution. Compared to equal error protection for all frame types, our method results in around 20% better SSIM (Structural Similarity Index) for CS video delivery over IoT LLNs.

In recent years, a compressive sensing based underwater imaging system has been under investigation: the Compressive Line Sensing (CLS) imaging system. In the CLS system, each line segment is sensed independently; with regard to signal reconstruction, the correlation among the adjacent lines is exploited via the joint sparsity in the distributed compressive sensing model. Interestingly, the dynamic compressive sensing signal model is also capable of exploiting the correlated nature of the adjacent lines through a Bayesian framework. This paper proposes a new CLS reconstruction technique through the integration of these different models, and includes an evaluation of the proposed technique using the experiment dataset obtained from an underwater imaging test setup.

The past decade has witnessed the emergence of compressed sensing as a way of acquiring sparsely representable signals in a compressed form. These developments have greatly motivated research in sparse signal recovery, which lies at the heart of compressed sensing, and which has recently found its use in altogether new applications. In the first part of this thesis we study the theoretical aspects of jointsparse recovery by means of sum-of-norms minimization, and the ReMBo-`1 algorithm, which combines boosting techniques with `1-minimization. For the sum-of-norms approach we derive necessary and sufficient conditions for recovery, by extending existing results to the joint-sparse setting. We focus in particular on minimization of the sum of `1, and `2 norms, and give concrete examples where recovery succeeds with one formulation but not with the other. We base our analysis of ReMBo-`1 on its geometrical interpretation, which leads to a study of orthant intersections with randomly oriented subspaces. This work establishes a clear picture of the mechanics behind the method, and explains the different aspects of its performance. The second part and main contribution of this thesis is the development of a framework for solving a wide class of convex optimization problems for sparse recovery. We provide a detailed account of the application of the framework on several problems, but also consider its limitations. The framework has been implemented in the spgl1 algorithm, which is already well established as an effective solver. Numerical results show that our algorithm is state-of-the-art, and compares favorably even with solvers for the easier—but less natural— Lagrangian formulations. The last part of this thesis discusses two supporting software packages: sparco, which provides a suite of test problems for sparse recovery, and spot, a Matlab toolbox for the creation and manipulation of linear operators. spot greatly facilitates rapid prototyping in sparse recovery and compressed sensing, where linear operators form the elementary building blocks. Following the practice of reproducible research, all code used for the experiments and generation of figures is available online at http://www.cs.ubc.ca/labs/scl/thesis/09vandenBerg/

Compressive sampling (CS), or Compressed Sensing , has generated a tremendous amount of excitement in the signal processing community. Compressive sampling, which involves non-traditional samples in the form of randomized projections, can capture most of the salient information in a signal with a relatively small number of samples, often far fewer samples than required using traditional sampling schemes. Adaptive sampling (AS), also called Active Learning , uses information gleaned from previous observations (e.g. , feedback) to focus the sampling process. Theoretical and experimental results have shown that adaptive sampling can dramatically outperform conventional (non-adaptive) sampling schemes. This paper compares the theoretical performance of compressive and adaptive sampling for regression in noisy conditions, and it is shown that for certain classes of piecewise constant signals and high SNR regimes both CS and AS are near optimal. This result is remarkable since it is the first evidence that shows that compressive sampling, which is non-adaptive, cannot be significantly outperformed by any other method (including adaptive sampling procedures), even in the presence of noise. The performance of CS schemes for signal detection is also investigated.© (2006) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Compressive sampling (CS), or Compressed Sensing, has generated a tremendous amount of excitement in the signal processing community. Compressive sampling, which involves non-traditional samples in the form of randomized projections, can capture most of the salient information in a signal with a relatively small number of samples, often far fewer samples than required using traditional sampling schemes. Adaptive sampling (AS), also called Active Learning, uses information gleaned from previous observations (e.g., feedback) to focus the sampling process. Theoretical and experimental results have shown that adaptive sampling can dramatically outperform conventional (non-adaptive) sampling schemes. This paper compares the theoretical performance of compressive and adaptive sampling in noisy conditions, and it is shown that for certain classes of piecewise constant signals and high SNR regimes both CS and AS are near-optimal. This result is remarkable since it is the first evidence that shows that compressive sampling, which is non-adaptive, cannot be significantly outperformed by any other method (including adaptive sampling procedures), even in presence of noise.

Exploring information retrieval using image sparse representations

Effective algorithm for optimizing compressive sensing in IoT and periodic monitoring applications

The support for high data rate applications with the cognitive radio technology necessitates wideband spectrum sensing. However, it is costly to apply long-term wideband sensing and is especially difficult in the presence of uncertainty, such as high noise, interference, outliers, and channel fading. In this work, we propose scheduling of sequential compressed spectrum sensing which jointly exploits compressed sensing (CS) and sequential periodic detection techniques to achieve more accurate and timely wideband sensing. Instead of invoking CS to reconstruct the signal in each period, our proposed scheme performs backward grouped-compressed-data sequential probability ratio test (backward GCD-SPRT) using compressed data samples in sequential detection, while CS recovery is only pursued when needed. This method on one hand significantly reduces the CS recovery overhead, and on the other takes advantage of sequential detection to improve the sensing quality. Furthermore, we propose (a) an in-depth sensing scheme to accelerate sensing decision-making when a change in channel status is suspected, (b) a block-sparse CS reconstruction algorithm to exploit the block sparsity properties of wide spectrum, and (c) a set of schemes to fuse results from the recovered spectrum signals to further improve the overall sensing accuracy. Extensive performance evaluation results show that our proposed schemes can significantly outperform peer schemes under sufficiently low SNR settings.

Compressive sensing (CS) is a new technique that give an approach to reconstruct the signal with few numbers of observations or measurements. The CS is based on L1 -norm minimizations to find the sparse solutions and it is known as basis pursuit. In this investigation, CS scheme with different transforms is proposed. The three utilized transform techniques are: Discrete Fourier Transform(DFT), Discrete Cosine Transform(DCT) and Discrete Wavelet Transform(DWT) with daubechies1(DB1) and coiflets1(coif1) basis. The proposed system is tested by employing the following signals: Blocks, Heavy Sine, ‘Bumps’ and ‘Doppler’ which cover wide range of applications. The four testing signals are represented in sparse domain using different transforms. In order to threshold the coefficients of the signals in sparse domain, the universal threshold is utilized in the case of CS with FFT and DWT whereas, the universal threshold is modified to prune the DCT coefficients. The main aim of this study is to investigate the differences among CS with DFT, CS with DCT and CS with DWT, and consequently a suitable transform domain used with CS to be selected. The comparative study is established by assessing the performance of the proposed system using Root Mean Square Error (RMSE), output SNR, and the time required to reconstruct approximated signals. Simulation results have shown that the CS with DWT outperforms the CS with FFT and DCT. CS with DWT has achieved good RMSE values about (0.0014 to 3.359e-8) even when half of the signal elements are removed. CS with FFT and DCT enhanced the noisy Blocks and Bumps signals by 3dB and 1dB respectively, while it is failed to enhance noisy Heavy Sine and Doppler signals. CS with DWT of two basis and for single decomposition level have improved the noisy Blocks, Bumps, Heavy Sine and Doppler signals by 5dB, 4dB, 3dB, and 3dB respectively.

Magnetic resonance cholangiopancreatography (MRCP) is an established technique in routine magnetic resonance examination. By applying the compressed sensing (CS) acceleration technique to conventional MRCP sequences, scan time can be markedly reduced. With promising results at 3 T, there is a necessity to evaluate the performance at 1.5 T due to wide scanner availabilities. Aim of this study is to test the feasibility of accelerated 3-dimensional (3D) MRCP with extended sampling perfection with application-optimized contrasts using different flip angle evolution (SPACE) using CS in navigator triggering and in a single breath-hold in a clinical setting at 1.5 T and 3 T and compare it with a conventional navigator-triggered 3D SPACE-MRCP. Phantom measurements were performed to adapt sequence parameters. Conventional 3D SPACE-MRCP in navigator triggering (STD_MRCP) as well as CS-accelerated 3D SPACE-MRCP acquired in navigator triggering and in a single breath-hold (CS_MRCP and CS_BH_MRCP) was performed in 66 patients undergoing clinically induced MRI of the pancreatobiliary system at 1.5 T and 3 T. Image quality evaluation was performed by 2 independent radiologists. Dedicated statistics were performed (P < 0.05 considered significant). In patient imaging, CS_MRCP was superior to STD_MRCP and CS_BH_MRCP in aspects of overall image quality at 1.5 T (P = 0.01; P < 0.001) and 3 T (P = 0.002; P = 0.013). Overall image quality in CS_BH_MRCP was inferior compared with STD_MRCP and CS_MRCP at 1.5 T. At 3 T, overall image quality in CS_BH_MRCP was superior to STD_MRCP (P = 0.001). Scan time was reduced by 25% to 46% covering 5% of k-space (CS_MRCP at 1.5 and 3 T) and 97% covering 3.6% of k-space (CS_BH_MRCP at 1.5 and 3 T). Compressed sensing-accelerated MRCP is feasible in clinical routine at 1.5 and 3 T offering major reduction of acquisition time. When applying a single breath-hold CS imaging, field strengths of 3 T are recommended.

BackgroundWe aimed to determine the capabilities of compressed sensing (CS) and deep learning reconstruction (DLR) with those of conventional parallel imaging (PI) for improving image quality while reducing examination time on female pelvic 1.5-T magnetic resonance imaging (MRI).MethodsFifty-two consecutive female patients with various pelvic diseases underwent MRI with T1- and T2-weighted sequences using CS and PI. All CS data was reconstructed with and without DLR. Signal-to-noise ratio (SNR) of muscle and contrast-to-noise ratio (CNR) between fat tissue and iliac muscle on T1-weighted images (T1WI) and between myometrium and straight muscle on T2-weighted images (T2WI) were determined through region-of-interest measurements. Overall image quality (OIQ) and diagnostic confidence level (DCL) were evaluated on 5-point scales. SNRs and CNRs were compared using Tukey’s test, and qualitative indexes using the Wilcoxon signed-rank test.ResultsSNRs of T1WI and T2WI obtained using CS with DLR were higher than those using CS without DLR or conventional PI (p < 0.010). CNRs of T1WI and T2WI obtained using CS with DLR were higher than those using CS without DLR or conventional PI (p < 0.003). OIQ of T1WI and T2WI obtained using CS with DLR were higher than that using CS without DLR or conventional PI (p < 0.001). DCL of T2WI obtained using CS with DLR was higher than that using conventional PI or CS without DLR (p < 0.001).ConclusionCS with DLR provided better image quality and shorter examination time than those obtainable with PI for female pelvic 1.5-T MRI.Relevance statementCS with DLR can be considered effective for attaining better image quality and shorter examination time for female pelvic MRI at 1.5 T compared with those obtainable with PI.Key PointsPatients underwent MRI with T1- and T2-weighted sequences using CS and PI.All CS data was reconstructed with and without DLR.CS with DLR allowed for examination times significantly shorter than those of PI and provided significantly higher signal- and CNRs, as well as OIQ.Graphical

Non-contrast enhancement of brachial plexus magnetic resonance imaging with compressed sensing

Compressed sensing (CS) is a technique which uses fewer measurements than dictated by the Nyquist sampling theorem. The traditional CS with linear measurements achieves efficient recovery performances, but it suffers from the large bit consumption due to the huge storage occupied by those measurements. Then, the one-bit CS with binary measurements is proposed and saves the bit budget, but it is infeasible when the energy information of signals is not available as a prior knowledge. Subsequently, the hybrid CS which combines the traditional CS and one-bit CS appears, striking a balance between the pros and cons of both types of CS. Considering the fact that the one-bit CS is optimal for the direction estimation of signals under noise with a fixed bit budget and that the traditional CS is able to provide residue information and estimated signals, we focus on the design of greedy algorithms, which consist of the main steps of support detection and recovered signal update, for the hybrid CS in this paper. We first propose a theorem on the random uniform tessellations for sparse signals to further investigate the properties of one-bit CS. Afterwards, we propose two greedy algorithms for the hybrid CS, with the one-bit CS responsible for support detection and traditional CS offering updated residues and signal estimates. For each of the proposed algorithms, we provide the corresponding theorem with proof to analyze their capabilities theoretically. Simulation results have demonstrated the efficacy of the proposed greedy algorithms under a limited bit budget in noisy environments.

Improving the image quality in compressed sensing MRI by the exploitation of data properties

Rapid acquisition of magnetic resonance imaging of the shoulder using three-dimensional fast spin echo sequence with compressed sensing