Apodisation, denoising and system identification techniques for THz transients in the wavelet domain

This work describes the use of a quadratic programming optimization procedure for designing asymmetric apodization windows to de-noise THz transient interferograms and compares these results to those obtained when wavelet signal processing algorithms are adopted. A systems identification technique in the wavelet domain is also proposed for the estimation of the complex insertion loss function. The proposed techniques can enhance the frequency dependent dynamic range of an experiment and should be of particular interest to the THz imaging and tomography community. Future advances in THz sources and detectors are likely to increase the signal-to-noise ratio of the recorded THz transients and high quality apodization techniques will become more important, and may set the limit on the achievable accuracy of the deduced spectrum.

Real-time image denoising algorithm in teleradiology systems - art.no.606304

Denoising of medical images in wavelet domain has potential application in transmission technologies such as teleradiology. This technique becomes all the more attractive when we consider the progressive transmission in a teleradiology system. The transmitted images are corrupted mainly due to noisy channels. In this paper, we present a new real time image denoising scheme based on limited restoration of bit-planes of wavelet coefficients. The proposed scheme exploits the fundamental property of wavelet transform - its ability to analyze the image at different resolution levels and the edge information associated with each sub-band. The desired bit-rate control is achieved by applying the restoration on a limited number of bit-planes subject to the optimal smoothing. The proposed method adapts itself to the preference of the medical expert; a single parameter can be used to balance the preservation of (expert-dependent) relevant details against the degree of noise reduction. The proposed scheme relies on the fact that noise commonly manifests itself as a fine-grained structure in image and wavelet transform allows the restoration strategy to adapt itself according to directional features of edges. The proposed approach shows promising results when compared with unrestored case, in context of error reduction. It also has capability to adapt to situations where noise level in the image varies and with the changing requirements of medical-experts. The applicability of the proposed approach has implications in restoration of medical images in teleradiology systems. The proposed scheme is computationally efficient.

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

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.

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.

Image Denoising Using Sure-Based Adaptive Thresholding In Directionlet Domain

The standard separable two dimensional wavelet transform has achieved a great success in image denoising applications due to its sparse representation of images. However it fails to capture efficiently the anisotropic geometric structures like edges and contours in images as they intersect too many wavelet basis functions and lead to a non-sparse representation. In this paper a novel de-noising scheme based on multi directional and anisotropic wavelet transform called directionlet is presented. The image denoising in wavelet domain has been extended to the directionlet domain to make the image features to concentrate on fewer coefficients so that more effective thresholding is possible. The image is first segmented and the dominant direction of each segment is identified to make a directional map. Then according to the directional map, the directionlet transform is taken along the dominant direction of the selected segment. The decomposed images with directional energy are used for scale dependent subband adaptive optimal threshold computation based on SURE risk. This threshold is then applied to the sub-bands except the LLL subband. The threshold corrected sub-bands with the unprocessed first sub-band (LLL) are given as input to the inverse directionlet algorithm for getting the de-noised image. Experimental results show that the proposed method outperforms the standard wavelet-based denoising methods in terms of numeric and visual quality

Spatially Adaptive Image Denoising Techniques Using Directionlets

The aim of the thesis was to design and develop spatially adaptive denoising techniques with edge and feature preservation, for images corrupted with additive white Gaussian noise and SAR images affected with speckle noise. Image denoising is a well researched topic. It has found multifaceted applications in our day to day life. Image denoising based on multi resolution analysis using wavelet transform has received considerable attention in recent years. The directionlet based denoising schemes presented in this thesis are effective in preserving the image specific features like edges and contours in denoising. Scope of this research is still open in areas like further optimization in terms of speed and extension of the techniques to other related areas like colour and video image denoising. Such studies would further augment the practical use of these techniques.

An effective wavelet method to detect and mitigate low-frequency multipath effects

To ensure high accuracy results from GPS relative positioning, the multipath effects have to be mitigated. Although the careful selection of antenna site and the use of especial antennas and receivers can minimize multipath, it cannot always be eliminated and frequently the residual multipath disturbance remains as the major error in GPS results. The high-frequency multipath from large delays can be attenuated by double difference (DD) denoising methods. But the low-frequency multipath from short delays is very difficult to be reduced or modeled. In this paper, it is proposed a method based on wavelet regression (WR), which can effectively detect and reduce the low-frequency multipath. The wavelet technique is firstly applied to decompose the DD residuals into the low-frequency bias and high-frequency noise components. The extracted bias components by WR are then directly applied to the DD observations to correct them from the trend. The remaining terms, largely characterized by the high-frequency measurement noise, are expected to give the best linear unbiased solutions from a least-squares (LS) adjustment. An experiment was carried out using objects placed close to the receiver antenna to cause, mainly, low-frequency multipath. The data were collected for two days to verify the multipath repeatability. The ground truth coordinates were computed with data collected in the absence of the reflector objects. The coordinates and ambiguity solution were compared with and without the multipath mitigation using WR. After mitigating the multipath, ambiguity resolution became more reliable and the coordinates were more accurate.