Noise measurement

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

Compressed Sensing With Quantized Measurements

Abstract: We consider the problem of estimating a sparse signal from a set of quantized, Gaussian noise corrupted measurements, where each measurement corresponds to an interval of values. We give two methods for (approximately) solving this problem, each based on minimizing a differentiable convex function plus an l 1 regularization term. Using a first order method developed by Hale et al, we demonstrate the performance of the methods through numerical simulation. We find that, using these methods, compressed sensing can be carried out even when the quantization is very coarse, e.g., 1 or 2 bits per measurement.

The Noise-Sensitivity Phase Transition in Compressed Sensing

Abstract: Consider the noisy underdetermined system of linear equations: y = Ax0 + z, with A an n × N measurement matrix, n <; N, and z ~ N(0, σ2I) a Gaussian white noise. Both y and A are known, both x0 and z are unknown, and we seek an approximation to x0. When x0 has few nonzeros, useful approximations are often obtained by l1-penalized l2 minimization, in which the reconstruction x1,λ solves min{||y - Ax||22/2 + λ||x||1}. Consider the reconstruction mean-squared error MSE = E|| x1,λ - x0||22/N, and define the ratio MSE/σ2 as the noise sensitivity. Consider matrices A with i.i.d. Gaussian entries and a large-system limit in which n, N → ∞ with n/N → δ and k/n → ρ. We develop exact expressions for the asymptotic MSE of x1,λ , and evaluate its worst-case noise sensitivity over all types of k-sparse signals. The phase space 0 ≤ 8, ρ ≤ 1 is partitioned by the curve ρ = ρMSE(δ) into two regions. Formal noise sensitivity is bounded throughout the region ρ = ρMSE(δ) and is unbounded throughout the region ρ = ρMSE(δ). The phase boundary ρ = ρMSE(δ) is identical to the previously known phase transition curve for equivalence of l1 - l0 minimization in the k-sparse noiseless case. Hence, a single phase boundary describes the fundamental phase transitions both for the noise less and noisy cases. Extensive computational experiments validate these predictions, including the existence of game-theoretical structures underlying it (saddlepoints in the payoff, least-favorable signals and maximin penalization). Underlying our formalism is an approximate message passing soft thresholding algorithm (AMP) introduced earlier by the authors. Other papers by the authors detail expressions for the formal MSE of AMP and its close connection to l1-penalized reconstruction. The focus of the present paper is on computing the minimax formal MSE within the class of sparse signals x0.

A Multi-Path Gated Ring Oscillator TDC With First-Order Noise Shaping

Abstract: An 11-bit, 50-MS/s time-to-digital converter (TDC) using a multipath gated ring oscillator with 6 ps of effective delay per stage demonstrates 1st-order noise shaping. At frequencies below 1 MHz, the TDC error integrates to 80 fs (rms) for a dynamic range of 95 dB with no calibration required. The 157 times 258 mum TDC is realized in 0.13 mum CMOS and, depending on the time difference between input edges, consumes 2.2 to 21 mA from a 1.5 V supply.

Image Denoising Using the Higher Order Singular Value Decomposition

Abstract: In this paper, we propose a very simple and elegant patch-based, machine learning technique for image denoising using the higher order singular value decomposition (HOSVD). The technique simply groups together similar patches from a noisy image (with similarity defined by a statistically motivated criterion) into a 3D stack, computes the HOSVD coefficients of this stack, manipulates these coefficients by hard thresholding, and inverts the HOSVD transform to produce the final filtered image. Our technique chooses all required parameters in a principled way, relating them to the noise model. We also discuss our motivation for adopting the HOSVD as an appropriate transform for image denoising. We experimentally demonstrate the excellent performance of the technique on grayscale as well as color images. On color images, our method produces state-of-the-art results, outperforming other color image denoising algorithms at moderately high noise levels. A criterion for optimal patch-size selection and noise variance estimation from the residual images (after denoising) is also presented.

Radiometric detection of spread-spectrum signals in noise of uncertain power

Abstract: The standard analysis of the radiometric detectability of a spread-spectrum signal assumes a background of stationary, white Gaussian noise whose power spectral density can be measured very accurately. This assumption yields a fairly high probability of interception, even for signals of short duration. By explicitly considering the effect of uncertain knowledge of the noise power density, it is demonstrated that detection of these signals by a wideband radiometer can be considerably more difficult in practice than is indicated by the standard result. Worst-case performance bounds are provided as a function of input signal-to-noise ratio (SNR), time-bandwidth (TW) product and peak-to-peak noise uncertainty. The results are illustrated graphically for a number of situations of interest. It is also shown that asymptotically, as the TW product becomes large, the SNR required for detection becomes a function of noise uncertainty only and is independent of the detection parameters and the observation interval. >