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Register a new userRobustness of Two-Dimensional Line Spectral Estimation Against Spiky Noise
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Added by
Iman Valiulahi
Publication date
2018
fields
Informatics Engineering
and research's language is
English
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The aim of two-dimensional line spectral estimation is to super-resolve the spectral point sources of the signal from time samples. In many associated applications such as radar and sonar, due to cut-off and saturation regions in electronic devices, some of the numbers of samples are corrupted by spiky noise. To overcome this problem, we present a new convex program to simultaneously estimate spectral point sources and spiky noise in two dimensions. To prove uniqueness of the solution, it is sufficient to show that a dual certificate exists. Construction of the dual certificate imposes a mild condition on the separation of the spectral point sources. Also, the number of spikes and detectable sparse sources are shown to be a logarithmic function of the number of time samples. Simulation results confirm the conclusions of our general theory.
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We study the trade-offs between storage/bandwidth and prediction accuracy of neural networks that are stored in noisy media. Conventionally, it is assumed that all parameters (e.g., weight and biases) of a trained neural network are stored as binary arrays and are error-free. This assumption is based upon the implementation of error correction codes (ECCs) that correct potential bit flips in storage media. However, ECCs add storage overhead and cause bandwidth reduction when loading the trained parameters during the inference. We study the robustness of deep neural networks when bit errors exist but ECCs are turned off for different neural network models and datasets. It is observed that more sophisticated models and datasets are more vulnerable to errors in their trained parameters. We propose a simple detection approach that can universally improve the robustness, which in some cases can be improved by orders of magnitude. We also propose an alternative binary representation of the parameters such that the distortion brought by bit flips is reduced and even theoretically vanishing when the number of bits to represent a parameter increases.
Recently, efforts have been made to improve ptychography phase retrieval algorithms so that they are more robust against noise. Often the algorithm is adapted by changing the cost functional that needs to be minimized. In particular, it has been suggested that the cost functional should be obtained using a maximum-likelihood approach that takes the noise statistics into account. Here, we consider the different choices of cost functional, and to how they affect the reconstruction results. We find that seemingly the only consistently reliable way to improve reconstruction results in the presence of noise is to reduce the step size of the update function. In addition, a noise-robust ptychographic reconstruction method has been proposed that relies on adapting the intensity constraints
This work investigates the parameter estimation performance of super-resolution line spectral estimation using atomic norm minimization. The focus is on analyzing the algorithms accuracy of inferring the frequencies and complex magnitudes from noisy observations. When the Signal-to-Noise Ratio is reasonably high and the true frequencies are separated by $O(frac{1}{n})$, the atomic norm estimator is shown to localize the correct number of frequencies, each within a neighborhood of size $O(sqrt{{log n}/{n^3}} sigma)$ of one of the true frequencies. Here $n$ is half the number of temporal samples and $sigma^2$ is the Gaussian noise variance. The analysis is based on a primal-dual witness construction procedure. The obtained error bound matches the Cramer-Rao lower bound up to a logarithmic factor. The relationship between resolution (separation of frequencies) and precision or accuracy of the estimator is highlighted. Our analysis also reveals that the atomic norm minimization can be viewed as a convex way to solve a $ell_1$-norm regularized, nonlinear and nonconvex least-squares problem to global optimality.
The fundamental multidimensional line spectral estimation problem is addressed utilizing the Bayesian methods. Motivated by the recently proposed variational line spectral estimation (VALSE) algorithm, multidimensional VALSE (MDVALSE) is developed. MDVALSE inherits the advantages of VALSE such as automatically estimating the model order, noise variance and providing uncertain degrees of frequency estimates. Compared to VALSE, the multidimensional frequencies of a single component is treated as a whole, and the probability density function is projected as independent univariate von Mises distribution to perform tractable inference. Besides, for the initialization, efficient fast Fourier transform (FFT) is adopted to significantly reduce the computation complexity of MDVALSE. Numerical results demonstrate the effectiveness of the MDVALSE, compared to state-of-art methods.
We consider the problem of direction-of-arrival (DOA) estimation in unknown partially correlated noise environments where the noise covariance matrix is sparse. A sparse noise covariance matrix is a common model for a sparse array of sensors consisted of several widely separated subarrays. Since interelement spacing among sensors in a subarray is small, the noise in the subarray is in general spatially correlated, while, due to large distances between subarrays, the noise between them is uncorrelated. Consequently, the noise covariance matrix of such an array has a block diagonal structure which is indeed sparse. Moreover, in an ordinary nonsparse array, because of small distance between adjacent sensors, there is noise coupling between neighboring sensors, whereas one can assume that nonadjacent sensors have spatially uncorrelated noise which makes again the array noise covariance matrix sparse. Utilizing some recently available tools in low-rank/sparse matrix decomposition, matrix completion, and sparse representation, we propose a novel method which can resolve possibly correlated or even coherent sources in the aforementioned partly correlated noise. In particular, when the sources are uncorrelated, our approach involves solving a second-order cone programming (SOCP), and if they are correlated or coherent, one needs to solve a computationally harder convex program. We demonstrate the effectiveness of the proposed algorithm by numerical simulations and comparison to the Cramer-Rao bound (CRB).
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