An Unbiased Risk Estimator for Multiplicative Noise - Application to 1-D Signal Denoising

The effect of multiplicative noise on a signal when compared with that of additive noise is very large. In this paper, we address the problem of suppressing multiplicative noise in one-dimensional signals. To deal with signals that are corrupted with multiplicative noise, we propose a denoising algorithm based on minimization of an unbiased estimator (MURE) of meansquare error (MSE). We derive an expression for an unbiased estimate of the MSE. The proposed denoising is carried out in wavelet domain (soft thresholding) by considering time-domain MURE. The parameters of thresholding function are obtained by minimizing the unbiased estimator MURE. We show that the parameters for optimal MURE are very close to the optimal parameters considering the oracle MSE. Experiments show that the SNR improvement for the proposed denoising algorithm is competitive with a state-of-the-art method.

Patch-based and multiresolution optimum bilateral filters for denoising images corrupted by Gaussian noise

We propose optimal bilateral filtering techniques for Gaussian noise suppression in images. To achieve maximum denoising performance via optimal filter parameter selection, we adopt Stein's unbiased risk estimate (SURE)-an unbiased estimate of the mean-squared error (MSE). Unlike MSE, SURE is independent of the ground truth and can be used in practical scenarios where the ground truth is unavailable. In our recent work, we derived SURE expressions in the context of the bilateral filter and proposed SURE-optimal bilateral filter (SOBF). We selected the optimal parameters of SOBF using the SURE criterion. To further improve the denoising performance of SOBF, we propose variants of SOBF, namely, SURE-optimal multiresolution bilateral filter (SMBF), which involves optimal bilateral filtering in a wavelet framework, and SURE-optimal patch-based bilateral filter (SPBF), where the bilateral filter parameters are optimized on small image patches. Using SURE guarantees automated parameter selection. The multiresolution and localized denoising in SMBF and SPBF, respectively, yield superior denoising performance when compared with the globally optimal SOBF. Experimental validations and comparisons show that the proposed denoisers perform on par with some state-of-the-art denoising techniques. (C) 2015 SPIE and IS&T

Joint Bilateral Filtering based Non-local Means Image Denoising

This paper proposes a denoising algorithm which performs non-local means bilateral filtering. As existing literature suggests, non-local means (NLM) is one of the widely used denoising techniques, but has a critical drawback of smoothing of edges. In order to improve this, we perform fast and efficient NLM using Approximate Nearest Neighbour Fields and improve the edge content in denoising by formulating a joint-bilateral filter. Using the proposed joint bilateral, we are able to denoise smooth regions using the NLM approach and efficient edge reconstruction is obtained from the bilateral filter. Furthermore, to avoid tedious parameter selection, we carry out a noise estimation before performing joint bilateral filtering. The proposed approach is observed to perform well on high noise images.

IMAGE DENOISING USING OPTIMALLY WEIGHTED BILATERAL FILTERS: A SURE AND FAST APPROACH

The bilateral filter is known to be quite effective in denoising images corrupted with small dosages of additive Gaussian noise. The denoising performance of the filter, however, is known to degrade quickly with the increase in noise level. Several adaptations of the filter have been proposed in the literature to address this shortcoming, but often at a substantial computational overhead. In this paper, we report a simple pre-processing step that can substantially improve the denoising performance of the bilateral filter, at almost no additional cost. The modified filter is designed to be robust at large noise levels, and often tends to perform poorly below a certain noise threshold. To get the best of the original and the modified filter, we propose to combine them in a weighted fashion, where the weights are chosen to minimize (a surrogate of) the oracle mean-squared-error (MSE). The optimally-weighted filter is thus guaranteed to perform better than either of the component filters in terms of the MSE, at all noise levels. We also provide a fast algorithm for the weighted filtering. Visual and quantitative denoising results on standard test images are reported which demonstrate that the improvement over the original filter is significant both visually and in terms of PSNR. Moreover, the denoising performance of the optimally-weighted bilateral filter is competitive with the computation-intensive non-local means filter.

IMAGE DENOISING IN MULTIPLICATIVE NOISE

We address the problem of denoising images corrupted by multiplicative noise. The noise is assumed to follow a Gamma distribution. Compared with additive noise distortion, the effect of multiplicative noise on the visual quality of images is quite severe. We consider the mean-square error (MSE) cost function and derive an expression for an unbiased estimate of the MSE. The resulting multiplicative noise unbiased risk estimator is referred to as MURE. The denoising operation is performed in the wavelet domain by considering the image-domain MURE. The parameters of the denoising function (typically, a shrinkage of wavelet coefficients) are optimized for by minimizing MURE. We show that MURE is accurate and close to the oracle MSE. This makes MURE-based image denoising reliable and on par with oracle-MSE-based estimates. Analogous to the other popular risk estimation approaches developed for additive, Poisson, and chi-squared noise degradations, the proposed approach does not assume any prior on the underlying noise-free image. We report denoising results for various noise levels and show that the quality of denoising obtained is on par with the oracle result and better than that obtained using some state-of-the-art denoisers.

Wavelet denoising and feature extraction of seismic signal for footstep detection

Seismic sensors are widely used to detect moving target in ground sensor networks. Footstep detection is very important for security surveillance and other applications. Because of non-stationary characteristic of seismic signal and complex environment conditions, footstep detection is a very challenging problem. A novel wavelet denoising method based on singular value decomposition is used to solve these problems. The signal-to-noise ratio (SNR) of raw footstep signal is greatly improved using this strategy. The feature extraction method is also discussed after denosing procedure. Comparing, with kurtosis statistic feature, the wavelet energy feature is more promising for seismic footstep detection, especially in a long distance surveillance.

Discrete wavelets transform for signal denoising in capillary electrophoresis with electrochemiluminescence detection

Discrete wavelets transform (DWT). was applied to noise on removal capillary electrophoresis-electrochemiluminescence (CE-ECL) electropherograms. Several typical wavelet transforms, including Haar, Daublets, Coiflets, and Symmlets, were evaluated. Four types of determining threshold methods, fixed form threshold, rigorous Stein's unbiased estimate of risk (rigorous SURE), heuristic SURE and minimax, combined with hard and soft thresholding methods were compared. The denoising study on synthetic signals showed that wave Symmlet 4 with a level decomposition of 5 and the thresholding method of heuristic SURE-hard provide the optimum denoising strategy. Using this strategy, the noise on CE-ECL electropherograms could be removed adequately. Compared with the Savitzky-Golay and Fourier transform denoising methods, DWT is an efficient method for noise removal with a better preservation of the shape of peaks.