Noise measurement

About: Noise measurement is a research topic. Over the lifetime, 19776 publications have been published within this topic receiving 308180 citations.

Exact signal recovery from sparsely corrupted measurements through the Pursuit of Justice

Abstract: Compressive sensing provides a framework for recovering sparse signals of length N from M ≪ N measurements. If the measurements contain noise bounded by ∈, then standard algorithms recover sparse signals with error at most C∈. However, these algorithms perform suboptimally when the measurement noise is also sparse. This can occur in practice due to shot noise, malfunctioning hardware, transmission errors, or narrowband interference. We demonstrate that a simple algorithm, which we dub Justice Pursuit (JP), can achieve exact recovery from measurements corrupted with sparse noise. The algorithm handles unbounded errors, has no input parameters, and is easily implemented via standard recovery techniques.

Robust 1-bit Compressive Sensing Using Adaptive Outlier Pursuit

Abstract: In compressive sensing (CS), the goal is to recover signals at reduced sample rate compared to the classic Shannon-Nyquist rate. However, the classic CS theory assumes the measurements to be real-valued and have infinite bit precision. The quantization of CS measurements has been studied recently and it has been shown that accurate and stable signal acquisition is possible even when each measurement is quantized to only one single bit. There are many algorithms proposed for 1-bit compressive sensing and they work well when there is no noise in the measurements, e.g., there are no sign flips, while the performance is worsened when there are a lot of sign flips in the measurements. In this paper, we propose a robust method for recovering signals from 1-bit measurements using adaptive outlier pursuit. This method will detect the positions where sign flips happen and recover the signals using “correct” measurements. Numerical experiments show the accuracy of sign flips detection and high performance of signal recovery for our algorithms compared with other algorithms.

A New Wavelet Denoising Method for Selecting Decomposition Levels and Noise Thresholds

Abstract: A new method is presented to denoise 1-D experimental signals using wavelet transforms. Although the state-of-the-art wavelet denoising methods perform better than other denoising methods, they are not very effective for experimental signals. Unlike images and other signals, experimental signals in chemical and biophysical applications, for example, are less tolerant to signal distortion and under-denoising caused by the standard wavelet denoising methods. The new method: 1) provides a method to select the number of decomposition levels to denoise; 2) uses a new formula to calculate noise thresholds that does not require noise estimation; 3) uses separate noise thresholds for positive and negative wavelet coefficients; 4) applies denoising to the approximation component; and 5) allows the flexibility to adjust the noise thresholds. The new method is applied to continuous wave electron spin resonance spectra and it is found that it increases the signal-to-noise ratio (SNR) by more than 32 dB without distorting the signal, whereas standard denoising methods improve the SNR by less than 10 dB and with some distortion. In addition, its computation time is more than six times faster.

Framelet Algorithms for De-Blurring Images Corrupted by Impulse Plus Gaussian Noise

Abstract: This paper studies a problem of image restoration that observed images are contaminated by Gaussian and impulse noise. Existing methods for this problem in the literature are based on minimizing an objective functional having the l1 fidelity term and the Mumford-Shah regularizer. We present an algorithm on this problem by minimizing a new objective functional. The proposed functional has a content-dependent fidelity term which assimilates the strength of fidelity terms measured by the l1 and l2 norms. The regularizer in the functional is formed by the l1 norm of tight framelet coefficients of the underlying image. The selected tight framelet filters are able to extract geometric features of images. We then propose an iterative framelet-based approximation/sparsity deblurring algorithm (IFASDA) for the proposed functional. Parameters in IFASDA are adaptively varying at each iteration and are determined automatically. In this sense, IFASDA is a parameter-free algorithm. This advantage makes the algorithm more attractive and practical. The effectiveness of IFASDA is experimentally illustrated on problems of image deblurring with Gaussian and impulse noise. Improvements in both PSNR and visual quality of IFASDA over a typical existing method are demonstrated. In addition, Fast_IFASDA, an accelerated algorithm of IFASDA, is also developed.

A recursive multiple model approach to noise identification

Abstract: Correct knowledge of noise statistics is essential for an estimator or controller to have reliable performance. In practice, however, the noise statistics are unknown or not known perfectly and thus need to be identified. Previous work on noise identification is limited to stationary noise and noise with slowly varying statistics only. An approach is presented here that is valid for nonstationary noise with rapidly or slowly varying statistics as well as stationary noise. This approach is based on the estimation with multiple hybrid system models. As one of the most cost-effective estimation schemes for hybrid system, the interacting multiple model (IMM) algorithm is used in this approach. The IMM algorithm has two desirable properties: it is recursive and has fixed computational requirements per cycle. The proposed approach is evaluated via a number of representative examples by both Monte Carlo simulations and a nonsimulation technique of performance prediction developed by the authors recently. The application of the proposed approach to failure detection is also illustrated. >