Noise reduction

About: Noise reduction is a research topic. Over the lifetime, 25121 publications have been published within this topic receiving 300815 citations. The topic is also known as: denoising & noise removal.

From Denoising to Compressed Sensing

Abstract: A denoising algorithm seeks to remove noise, errors, or perturbations from a signal. Extensive research has been devoted to this arena over the last several decades, and as a result, today's denoisers can effectively remove large amounts of additive white Gaussian noise. A compressed sensing (CS) reconstruction algorithm seeks to recover a structured signal acquired using a small number of randomized measurements. Typical CS reconstruction algorithms can be cast as iteratively estimating a signal from a perturbed observation. This paper answers a natural question: How can one effectively employ a generic denoiser in a CS reconstruction algorithm? In response, we develop an extension of the approximate message passing (AMP) framework, called Denoising-based AMP (D-AMP), that can integrate a wide class of denoisers within its iterations. We demonstrate that, when used with a high performance denoiser for natural images, D-AMP offers state-of-the-art CS recovery performance while operating tens of times faster than competing methods. We explain the exceptional performance of D-AMP by analyzing some of its theoretical features. A key element in D-AMP is the use of an appropriate Onsager correction term in its iterations, which coerces the signal perturbation at each iteration to be very close to the white Gaussian noise that denoisers are typically designed to remove.

Diffusion Weighted Image Denoising Using Overcomplete Local PCA

Abstract: Diffusion Weighted Images (DWI) normally shows a low Signal to Noise Ratio (SNR) due to the presence of noise from the measurement process that complicates and biases the estimation of quantitative diffusion parameters. In this paper, a new denoising methodology is proposed that takes into consideration the multicomponent nature of multi-directional DWI datasets such as those employed in diffusion imaging. This new filter reduces random noise in multicomponent DWI by locally shrinking less significant Principal Components using an overcomplete approach. The proposed method is compared with state-of-the-art methods using synthetic and real clinical MR images, showing improved performance in terms of denoising quality and estimation of diffusion parameters.

A globally convergent frequency estimator

Abstract: Online estimation of the frequency of a sinusoidal signal is a classical problem in systems theory that has many practical applications. In this paper the authors provide a solution to the problem of ensuring a globally convergent estimation. More specifically, they propose a new adaptive notch filter whose dynamic equations exhibit the following remarkable features: 1) all signals are globally bounded and the estimated frequency is asymptotically correct for all initial conditions and all frequency values; 2) the authors obtain a simple tuning procedure for the estimator design parameters, which trades-off the adaptation tracking capabilities with noise sensitivity, ensuring (exponential) stability of the desired orbit; and 3) transient performance is considerably enhanced, even for small or large frequencies, as witnessed by extensive simulations. To reveal some of the stability-instability mechanisms of the existing algorithms and motivate our modifications the authors make appeal to a novel nonlinear (state-dependent) time scaling. The main advantage of working in the new time scale is that they remove the coupling between the parameter update law and the filter itself, decomposing the system into a feedback form where the required modifications to ensure stability become apparent. Even though they limit their attention here to the simplest case of a single constant frequency without noise the algorithm is able to track time-varying frequencies, preserve local stability in the presence of multiple sinusoids, and is robust with respect to noise.

Speckle filtering of SAR images: a comparative study between complex-wavelet-based and standard filters

Abstract: We present a comparative study between a complex Wavelet Coefficient Shrinkage (WCS) filter and several standard speckle filters that are widely used in the radar imaging community. The WCS filter is based on the use of Symmetric Daubechies wavelets which share the same properties as the real Daubechies wavelets but with an additional symmetry property. The filtering operation is an elliptical soft- thresholding procedure with respect to the principal axes of the 2D complex wavelet coefficient distributions. Both qualitative and quantitative results (signal to mean square error ratio, equivalent number of looks, edgemap figure of merit) are reported. Tests have been performed using simulated speckle noise as well as real radar images. It is found that the WCS filter performs equally well as the standard filters for low-level noise and slightly outperforms them for higher-level noise.© (1997) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.