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.

Random noise attenuation using local signal-and-noise orthogonalization

Abstract: We have developed a novel approach to attenuate random noise based on local signal-and-noise orthogonalization. In this approach, we first removed from a seismic section using one of the conventional denoising operators and then applied a weighting operator to the initially denoised section to predict the signal-leakage energy, as well as retrieve it from the initial noise section. The weighting operator was obtained by solving a least-squares minimization problem via shaping regularization with a smoothness constraint. Next, the initially denoised section and the retrieved signal were combined to form the final denoised section. The proposed denoising approach corresponded to orthogonalizing the initially denoised signal and noise in a local manner. We evaluated the denoising performance using local similarity. To test the orthogonalization property of the estimated signal and noise, we calculated the local similarity map between the denoised signal section and removed noise section. Low values o...

Noise2Self: Blind Denoising by Self-Supervision

Abstract: We propose a general framework for denoising high-dimensional measurements which requires no prior on the signal, no estimate of the noise, and no clean training data. The only assumption is that the noise exhibits statistical independence across different dimensions of the measurement, while the true signal exhibits some correlation. For a broad class of functions ("$\mathcal{J}$-invariant"), it is then possible to estimate the performance of a denoiser from noisy data alone. This allows us to calibrate $\mathcal{J}$-invariant versions of any parameterised denoising algorithm, from the single hyperparameter of a median filter to the millions of weights of a deep neural network. We demonstrate this on natural image and microscopy data, where we exploit noise independence between pixels, and on single-cell gene expression data, where we exploit independence between detections of individual molecules. This framework generalizes recent work on training neural nets from noisy images and on cross-validation for matrix factorization.

On noise reduction methods for chaotic data.

Abstract: Recently proposed noise reduction methods for nonlinear chaotic time sequences with additive noise are analyzed and generalized. All these methods have in common that they work iteratively, and that in each step of the iteration the noise is suppressed by requiring locally linear relations among the delay coordinates, i.e., by moving the delay vectors towards some smooth manifold. The different methods can be compared unambiguously in the case of strictly hyperbolic systems corrupted by measurement noise of infinitesimally low level. It was found that all proposed methods converge in this ideal case, but not equally fast. Different problems arise if the system is not hyperbolic, and at higher noise levels. A new scheme which seems to avoid most of these problems is proposed and tested, and seems to give the best noise reduction so far. Moreover, large improvements are possible within the new scheme and the previous schemes if their parameters are not kept fixed during the iteration, and if corrections are included which take into account the curvature of the attracting manifold. Finally, the fact that comparison with simple low‐pass filters tends to overestimate the relative achievements of these nonlinear noise reduction schemes is stressed, and it is suggested that they should be compared to Wiener‐type filters.

Multiplicative Denoising and Deblurring: Theory and Algorithms

Abstract: In [447, 449, 450], a constrained optimization type of numerical algorithm for restoring blurry, noisy images was developed and successfully tested. In this paper we present both theoretical and experimental justification for the method. Our main theoretical results involve constrained nonlinear partial differential equations. Our main experimental results involve blurry images which have been further corrupted with multiplicative noise. As in additive noise case of [447, 450] our numerical algorithm is simple to implement and is nonoscillatory (minimal ringing) and noninvasive (recovers sharp edges).