Estimation Of Noise Standard Deviation Research Articles

Image denoising by low‐rank approximation with estimation of noise energy distribution in SVD domain

Low-rank approximation has shown great potential in various image tasks. It is found that there is a specific functional relationship about singular values between the original image and a series of noisy images, which can be used to construct the singular values of a noise-free image. In this study, the authors propose a novel denoising method based on the above facts and low-rank approximation theory. Firstly, they estimate the noise energy distribution of the group matrix in the singular value decomposition (SVD) domain using the energy characteristics of the image with different noise levels. The energy distribution of the noise is shrunk to obtain the energy distribution of the true signal. Then, based on the optimal energy compaction property of SVD, the low-rank property of matrix is constrained in the SVD domain to obtain the low-rank approximation of the matrix. Moreover, an iterative back projection method is adopted in this study to suppress residual noise. A new noise standard deviation estimation approach, targeted at the back projection process, is proposed to effectively optimise the denoising results during the iteration. Experimental results show that the authors’ method efficiently decreases the noise and achieves comparable denoising performance to the state-of-the-art methods regarding both quantitative measurement and visual effect.

Robust Estimation of Non-Stationary Noise Power Spectrum for Speech Enhancement

We propose a novel method for noise power spectrum estimation in speech enhancement. This method called extended-DATE (E-DATE) extends the $d$ -dimensional amplitude trimmed estimator (DATE), originally introduced for additive white gaussian noise power spectrum estimation in “Robust estimation of noise standard deviation in presence of signals with unknown distributions and occurrences” (D. Pastor and F. Socheleau, IEEE Trans. Signal Processing, vol. 60, no. 4, pp. 1545–1555, Apr. 2012) to the more challenging scenario of non-stationary noise. The key idea is that, in each frequency bin and within a sufficiently short time period, the noise instantaneous power spectrum can be considered as approximately constant and estimated as the variance of a complex gaussian noise process possibly observed in the presence of the signal of interest. The proposed method relies on the fact that the Short-Time Fourier Transform (STFT) of noisy speech signals is sparse in the sense that transformed speech signals can be represented by a relatively small number of coefficients with large amplitudes in the time-frequency domain. The E-DATE estimator is robust in that it does not require prior information about the signal probability distribution except for the weak-sparseness property. In comparison to other state-of-the-art methods, the E-DATE is found to require the smallest number of parameters (only two). The performance of the proposed estimator has been evaluated in combination with noise reduction and compared to alternative methods. This evaluation involves objective as well as pseudo-subjective criteria.

Denoising of Document Images using Discrete Curvelet Transform for OCR Applications

this paper, a denoising and binarization scheme of document images corrupted by white Gaussian noise and Impulse noise is presented using Curvelet Transform. The ability of sparse representation and edge preservation of Curvelet transform is utilized. Impulse noise gets added during document scanning or after binarization of scanned document images. White Gaussian noise corrupts the document images during transmission. The presence of either type of noise or a combination of them can severely degrade the performance of any OCR system. In the proposed denoising scheme, the curvelet transform is used with level dependent threshold calculated by modified sqtwolog method (universal threshold) at each scale with estimation of noise standard deviation. The noisy curvelet coefficients are thresholded by Hard Thresholding method. After curvelet based denoising, the image is binarized using global Otsu method and post processed to smoothen the text boundaries and remove isolated pixels for better OCR performance. The curvelet based scheme is compared with a wavelet transform based scheme and a modified wavelet based scheme with edge preservation. The results show that curvelet based scheme performs better in case of images containing Gaussian, Impulse and a combination of both the noises.

Robust Estimation of Noise Standard Deviation in Presence of Signals With Unknown Distributions and Occurrences

In many applications, d-dimensional observations result from the random presence or absence of random signals in independent and additive white Gaussian noise. An estimate of the noise standard deviation can then be very useful to detect or to estimate these signals, especially when standard likelihood theory cannot be applied because of too little prior knowledge about the signal probability distributions. The present paper introduces a new scale estimator of the noise standard deviation when the noisy signals have unknown probability distributions and unknown probabilities of presence less than or equal to one half. The latter assumption can be regarded as to a weak assumption of sparsity. Applied to the detection of noncooperative radio-communications, this new estimator outperforms the standard MAD and its alternatives as well as the trimmed and winsorized robust scale estimators. The Matlab code corresponding to the proposed estimator is available at http://perso.telecom-bretagne.eu/pastor.