Deterministic Sensing Research Articles

Spectral Universality in Regularized Linear Regression With Nearly Deterministic Sensing Matrices

Spectral Universality in Regularized Linear Regression With Nearly Deterministic Sensing Matrices

Deterministic Bipolar Compressed Sensing Matrices from Binary Sequence Family

Deterministic Bipolar Compressed Sensing Matrices from Binary Sequence Family

A Class of Deterministic Sensing Matrices and Their Application in Harmonic Detection

In this paper, a class of deterministic sensing matrices are constructed by selecting rows from Fourier matrices. These matrices have better performance in sparse recovery than random partial Fourier matrices. The coherence and restricted isometry property of these matrices are given to evaluate their capacity as compressive sensing matrices. In general, compressed sensing requires random sampling in data acquisition, which is difficult to implement in hardware. By using these sensing matrices in harmonic detection, a deterministic sampling method is provided. The frequencies and amplitudes of the harmonic components are estimated from under-sampled data. The simulations show that this under-sampled method is feasible and valid in noisy environments.

Multiple Target Localization in WSNs Based on Compressive Sensing Using Deterministic Sensing Matrices

Accurate and low-cost localization of multiple targets or nodes is one of fundamental and challenging technical issues in wireless sensor networks (WSNs). Furthermore, compressive sensing allows that a sparse signal can be reconstructed from few measurements, and choosing a suitable sensing matrix is also important. For this purpose, random sensing matrices have been studied, while a few researches on deterministic sensing matrices have been considered. In this paper, we use compressive sensing for multiple target localization in WSNs. We formulate multiple target locations as a sparse matrix in the discrete time domain. Then, we exploit received signal strength information to recover noisy measurements, while utilizing deterministic sensing matrices and greedy algorithm to locate each target. The proposal approach reduces the number of measurements in localization process, takes low-cost, and maintains the accuracy as compared to the conventional approach which is noncompressive sensing. Further simulation shows that the proposed approach is practical in use, while being favorably comparable to the existing random sensing matrices in reconstruction performance. This cooperation between the compressive sensing using deterministic sensing matrices and multiple target localization provides a new point of view in WSN localization.

Stability of Efficient Deterministic Compressed Sensing for Images with Chirps and Reed-Muller Sequences

We explore the stability of image reconstruction algorithms under deterministic compressed sensing. Recently, we have proposed [1-3] deterministic compressed sensing algorithms for 2D images. These algorithms are suitable when Daubechies wavelets are used as the sparsifying basis. In the initial work, we have shown that the algorithms perform well for images with sparse wavelets coefficients. In this work, we address the question of robustness and stability of the algorithms, specifically, if the image is not sparse and/or if noise is present. We show that our algorithms perform very well in the presence of a certain degree of noise. This is especially important for MRI and other real world applications where some level of noise is always present.

Construction of a Large Class of Deterministic Sensing Matrices That Satisfy a Statistical Isometry Property

Compressed Sensing aims to capture attributes of $k$-sparse signals using very few measurements. In the standard Compressed Sensing paradigm, the $\m\times \n$ measurement matrix $\A$ is required to act as a near isometry on the set of all $k$-sparse signals (Restricted Isometry Property or RIP). Although it is known that certain probabilistic processes generate $\m \times \n$ matrices that satisfy RIP with high probability, there is no practical algorithm for verifying whether a given sensing matrix $\A$ has this property, crucial for the feasibility of the standard recovery algorithms. In contrast this paper provides simple criteria that guarantee that a deterministic sensing matrix satisfying these criteria acts as a near isometry on an overwhelming majority of $k$-sparse signals; in particular, most such signals have a unique representation in the measurement domain. Probability still plays a critical role, but it enters the signal model rather than the construction of the sensing matrix. We require the columns of the sensing matrix to form a group under pointwise multiplication. The construction allows recovery methods for which the expected performance is sub-linear in $\n$, and only quadratic in $\m$; the focus on expected performance is more typical of mainstream signal processing than the worst-case analysis that prevails in standard Compressed Sensing. Our framework encompasses many families of deterministic sensing matrices, including those formed from discrete chirps, Delsarte-Goethals codes, and extended BCH codes.