Session S5

Session S5: Compressive Sensing

Time:                 Tuesday, May 13, 14:30-15:45
Chair:                 James H. McClellan, Georgia Institute of Technology
Co-Chair:          Douglas Cochran, Arizona State University

S5-1: Compressive Sensing of Underground Structures Using GPR
Ali Cafer Gurbuz, James H. McClellan and Waymond R. Scott Georgia Institute of Technology, Atlanta GA
Detecting parameterized underground structures like pipes or tunnels usually involves two stages. First, the raw data collected by a sensor such as a Ground Penetrating Radar (GPR) is inverted to form an image of the subsurface area. Second, the image is searched for parameterized shapes like lines using an algorithm such as the Hough Transform (HT), which converts the problem of finding spatially spread patterns in the image space to detecting sparse peaks in the parameter space. This paper exploits this same sparsity idea to combine the two stages into one direct processing step using the Compressive Sensing (CS) framework to find the shape parameters directly from the raw sensor measurements. In addition to skipping the image formation step, the CS processing can be done with a minimal number of raw sensor measurements. The utility of this method is demonstrated for finding buried linear structures in both simulated and experimental GPR data.

S5-2: Variable-p Affine Scaling Transformation Algorithms for Improved Compressive Sensing
Sergio Cabrera University of Texas at El Paso, Rufino Dominguez Instituto Tecnologico de Chihuahua, J. Gerardo Rosiles University of Texas at El Paso, and Javier Vega-Pineda Instituto Tecnologico de Chihuahua
In this paper, we investigate the use of the p parameter for improved recovery accuracy and speed in the iterative Affine Scaling Transformation (AST) family of algorithms that solve the compressive sensing problem. The AST family of algorithms is applicable to the minimization of the lp, p-norm-like diversity measure. This includes the numerosity (p=0), and the l1 norm (p=1) as special cases. In our previous work we concluded that any p in [0, 1] can give the sparse solution when exact recovery is possible, however, the best-approximation problem and the behavior of the algorithm is highly dependent on this parameter. We present and evaluate experimentally some simple strategies to vary the values of p as a function of the iteration in the AST algorithm. These variable-p variations of AST capture most of the benefits of the p=0 and the p=1 fixed-p approaches simultaneously.

S5-3: Compressive Sensing and Waveform Design for the Identification of Linear Time-Varying Systems Using Noisy Measurements
Jun Zhang, Antonia Papandreou-Suppappola Arizona State University, Tempe AZ, and Robin L. Murray Naval Undersea Warfare Center, Newport RI
In this paper, we investigate the application of compressive sensing and waveform design for estimating linear time-varying system characteristics using noisy measurements. Based on the facts that the spreading function system representation is sparse in realistic system scenarios, and any real-world sensor or measurement device is subject to at least a small amount of noise, we propose a new method for the identification of narrowband, wideband and dispersive systems using a small set of measurements, which is stable in the presence of noise. Through numerical simulations, we successfully demonstrate the feasibility and the performance of using compressive sensing to estimate the system spreading function.

S5-4: Improved Total Variation-type Regularization Using Higher-order Edge Detectors
Wolfgang Stefan, Rosemary Renaut and Anne Gelb Arizona State University, Tempe AZ
We present a novel deconvolution approach that simultaneously deblurrs and detects the edges in a piecewise smooth signals. Our method preserves edges as well as the smooth regions separated by jump discontinuities. The method uses a two step procedure 1) the higher order polynomial annihilation method is used in combination with total variation (TV) deconvolution to obtain an estimate of the location of the jump discontinuities in blurred noisy data. 2) This information is used to determine the order of a higher order TV regularization resulting in reconstructions with more accurate representations of the true signal in a relative l^2 norm compared to the standard TV reconstructions. The resulting reconstruction can also be used to obtain a more accurate estimation of the jump locations and size in the underlying unblurred signal than possible using standard TV.

S5-5: Performance Limits for Jointly Sparse Signals via Graphical Models
Marco Duarte, Shriram Sarvotham Rice University, Houston TX, Dror Baron Menta Capical LLC, Michael Wakin University of Michigan, Ann Arbor MI and Richard Baraniuk Rice University, Houston TX
The compressed sensing framework has been proposed for efficient acquisition of sparse and compressible signals through incoherent measurements. In our recent work, we introduced a new concept of joint sparsity of a signal ensemble. For several specific joint sparsity models, we demonstrated distributed compressed sensing schemes. This paper considers joint sparsity via graphical models that link the sparse underlying coefficient vector, signal samples, and measurements. Our converse and achievable bounds establish that the number of measurements required in the noiseless measurement setting is closely related to the dimensionality of the sparse coefficient vector. Single signal and joint (single-encoder) compressed sensing are special cases of joint sparsity, and their performance limits fit into our graphical model framework for distributed (multi-encoder) compressed sensing.

S5-6: Preprocessing Measurements and Modifying Sensors to Improve Detection in Sensor Networks
Balakrishnan Narayanaswamy, Rohit Negi and Pradeep Khosla Carnegie Mellon University, Pittsburgh PA
Sequential decoding can be used for detection in sensor networks, where conventional techniques such as optimal detection or belief propagation are infeasible. In this paper, we study the performance of sequential decoding when different kinds of sensors are used. We show that the performance of sequential decoding in a 1-D sensing task depends on certain properties of the sensor physics. We show that data preprocessing can improve the performance of the decoder, and also demonstrate simple practical modifications to sensors that substantially improve their performance with sequential decoding. We outline simple extensions to 2-D sensing tasks.

S5-7: Phase transitions phenomenon in Compressed Sensing
Jared Tanner
Compressed Sensing reconstruction algorithms typically exhibit a zeroth-order phase transition phenomenon for large problem sizes, where there is a domain of problem sizes for which successful recovery occurs with overwhelming probability, and there is a domain of problem sizes for which recovery failure occurs with overwhelming probability. The mathematics underlying this phenomenon will be outlined for L^1 regularization and non-negative feasibility point regions. Both instances employ a large deviation analysis of the associated geometric probability event. These results give precise if and only if conditions on the number of samples needed in Compressed Sensing applications. This work was joint with David L. Donoho.