Multiscale image denoising using goodness-of-fit test based on EDF statistics.

Two novel image denoising algorithms are proposed which employ goodness of fit (GoF) test at multiple image scales. Proposed methods operate by employing the GoF tests locally on the wavelet coefficients of a noisy image obtained via discrete wavelet transform (DWT) and the dual tree complex wavelet transform (DT-CWT) respectively. We next formulate image denoising as a binary hypothesis testing problem with the null hypothesis indicating the presence of noise and the alternate hypothesis representing the presence of desired signal only. The decision that a given wavelet coefficient corresponds to the null hypothesis or the alternate hypothesis involves the GoF testing based on empirical distribution function (EDF), applied locally on the noisy wavelet coefficients. The performance of the proposed methods is validated by comparing them against the state of the art image denoising methods

Multi-scale image denoising based on goodness of fit (GOF) tests

A novel image denoising method based on discrete wavelet transform (DWT) and goodness of fit (GOF) statistical tests employing empirical distribution function (EDF) statistics is proposed. We formulate the denoising problem into a hypothesis testing problem with a null hypothesis corresponding to the presence of noise, and alternate hypothesis representing the presence of only desired signal in the image samples being tested. The decision process involves GOF tests, employing statistics based on EDF, being applied directly on multiple image scales obtained from DWT. We evaluate the performance of the proposed method against the state of the art in wavelet image denoising through extensive experiments performed on standard images

Geodesics on the manifold of multivariate generalized Gaussian distributions with an application to multicomponent texture discrimination

We consider the Rao geodesic distance (GD) based on the Fisher information as a similarity measure on the manifold of zero-mean multivariate generalized Gaussian distributions (MGGD). The MGGD is shown to be an adequate model for the heavy-tailed wavelet statistics in multicomponent images, such as color or multispectral images. We discuss the estimation of MGGD parameters using various methods. We apply the GD between MGGDs to color texture discrimination in several classification experiments, taking into account the correlation structure between the spectral bands in the wavelet domain. We compare the performance, both in terms of texture discrimination capability and computational load, of the GD and the Kullback-Leibler divergence (KLD). Likewise, both uni- and multivariate generalized Gaussian models are evaluated, characterized by a fixed or a variable shape parameter. The modeling of the interband correlation significantly improves classification efficiency, while the GD is shown to consistently outperform the KLD as a similarity measure

Reduced Cycle Spinning Method for the Undecimated Wavelet Transform

[EN] The Undecimated Wavelet Transform is commonly used for signal processing due to its advantages over other wavelet techniques, but it is limited for some applications because of its computational cost. One of the methods utilized for the implementation of the Undecimated Wavelet Transform is the one known as Cycle Spinning. This paper introduces an alternative Cycle Spinning implementation method that divides the computational cost by a factor close to 2. This work develops the mathematical background of the proposed method, shows the block diagrams for its implementation and validates the method by applying it to the denoising of ultrasonic signals. The evaluation of the denoising results shows that the new method produces similar denoising qualities than other Cycle Spinning implementations, with a reduced computational cost.This research was funded by grants number PGC2018-09415-B-I00 (MCIU/AEI/FEDER, UE) and TEC2015-71932-REDT.Rodríguez-Hernández, MA. (2019). Reduced Cycle Spinning Method for the Undecimated Wavelet Transform. Sensors. 19(12):1-16. https://doi.org/10.3390/s19122777S1161912Signal Processing Fourier and Wavelet Representationshttp://www.fourierandwavelets.org/SPFWR_a3.1_2012.pdfZhao, H., Zuo, S., Hou, M., Liu, W., Yu, L., Yang, X., & Deng, W. (2018). A Novel Adaptive Signal Processing Method Based on Enhanced Empirical Wavelet Transform Technology. Sensors, 18(10), 3323. doi:10.3390/s18103323Gradolewski, D., Magenes, G., Johansson, S., & Kulesza, W. (2019). A Wavelet Transform-Based Neural Network Denoising Algorithm for Mobile Phonocardiography. Sensors, 19(4), 957. doi:10.3390/s19040957Shikhsarmast, F., Lyu, T., Liang, X., Zhang, H., & Gulliver, T. (2018). Random-Noise Denoising and Clutter Elimination of Human Respiration Movements Based on an Improved Time Window Selection Algorithm Using Wavelet Transform. Sensors, 19(1), 95. doi:10.3390/s19010095Shensa, M. J. (1992). The discrete wavelet transform: wedding the a trous and Mallat algorithms. IEEE Transactions on Signal Processing, 40(10), 2464-2482. doi:10.1109/78.157290Li, M., & Ghosal, S. (2015). Fast Translation Invariant Multiscale Image Denoising. IEEE Transactions on Image Processing, 24(12), 4876-4887. doi:10.1109/tip.2015.2470601Hazarika, D., Nath, V. K., & Bhuyan, M. (2016). SAR Image Despeckling Based on a Mixture of Gaussian Distributions with Local Parameters and Multiscale Edge Detection in Lapped Transform Domain. Sensing and Imaging, 17(1). doi:10.1007/s11220-016-0141-8Sakhaee, E., & Entezari, A. (2017). Joint Inverse Problems for Signal Reconstruction via Dictionary Splitting. IEEE Signal Processing Letters, 24(8), 1203-1207. doi:10.1109/lsp.2017.2701815Ong, F., Uecker, M., Tariq, U., Hsiao, A., Alley, M. T., Vasanawala, S. S., & Lustig, M. (2014). Robust 4D flow denoising using divergence-free wavelet transform. Magnetic Resonance in Medicine, 73(2), 828-842. doi:10.1002/mrm.25176Rehman, N. ur, Abbas, S. Z., Asif, A., Javed, A., Naveed, K., & Mandic, D. P. (2017). Translation invariant multi-scale signal denoising based on goodness-of-fit tests. Signal Processing, 131, 220-234. doi:10.1016/j.sigpro.2016.08.019Mota, H. de O., Vasconcelos, F. H., & de Castro, C. L. (2016). A comparison of cycle spinning versus stationary wavelet transform for the extraction of features of partial discharge signals. IEEE Transactions on Dielectrics and Electrical Insulation, 23(2), 1106-1118. doi:10.1109/tdei.2015.005300Li, D., Wang, Y., Lin, J., Yu, S., & Ji, Y. (2016). Electromagnetic noise reduction in grounded electrical‐source airborne transient electromagnetic signal using a stationarywavelet‐based denoising algorithm. Near Surface Geophysics, 15(2), 163-173. doi:10.3997/1873-0604.2017003San Emeterio, J. L., & Rodriguez-Hernandez, M. A. (2014). Wavelet Cycle Spinning Denoising of NDE Ultrasonic Signals Using a Random Selection of Shifts. Journal of Nondestructive Evaluation, 34(1). doi:10.1007/s10921-014-0270-8Rodriguez-Hernandez, M. A., & Emeterio, J. L. S. (2015). Noise reduction using wavelet cycle spinning: analysis of useful periodicities in the z-transform domain. Signal, Image and Video Processing, 10(3), 519-526. doi:10.1007/s11760-015-0762-8Rodriguez-Hernandez, M. A. (2016). Shift selection influence in partial cycle spinning denoising of biomedical signals. Biomedical Signal Processing and Control, 26, 64-68. doi:10.1016/j.bspc.2015.12.002Beylkin, G., Coifman, R., & Rokhlin, V. (1991). Fast wavelet transforms and numerical algorithms I. Communications on Pure and Applied Mathematics, 44(2), 141-183. doi:10.1002/cpa.3160440202Beylkin, G. (1992). On the Representation of Operators in Bases of Compactly Supported Wavelets. SIAM Journal on Numerical Analysis, 29(6), 1716-1740. doi:10.1137/0729097Donoho, D. 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Constraints on CPT violation from WMAP three year polarization data: a wavelet analysis

We perform a wavelet analysis of the temperature and polarization maps of the Cosmic Microwave Background (CMB) delivered by the WMAP experiment in search for a parity violating signal. Such a signal could be seeded by new physics beyond the standard model, for which the Lorentz and CPT symmetries may not hold. Under these circumstances, the linear polarization direction of a CMB photon may get rotated during its cosmological journey, a phenomenon also called cosmological birefringence. Recently, Feng et al. have analyzed a subset the WMAP and BOOMERanG 2003 angular power spectra of the CMB, deriving a constraint that mildly favors a non zero rotation. By using wavelet transforms we set a tighter limit on the CMB photon rotation angle \Delta\alpha= -2.5 \pm 3.0 (\Delta\alpha= -2.5 \pm 6.0) at the one (two) \sigma level, consistent with a null detection.Comment: 7 pages, 4 figures, some modifications to match accepted (PRD) version, results unchange

A Multiscale Approach for Statistical Characterization of Functional Images

Increasingly, scientific studies yield functional image data, in which the observed data consist of sets of curves recorded on the pixels of the image. Examples include temporal brain response intensities measured by fMRI and NMR frequency spectra measured at each pixel. This article presents a new methodology for improving the characterization of pixels in functional imaging, formulated as a spatial curve clustering problem. Our method operates on curves as a unit. It is nonparametric and involves multiple stages: (i) wavelet thresholding, aggregation, and Neyman truncation to effectively reduce dimensionality; (ii) clustering based on an extended EM algorithm; and (iii) multiscale penalized dyadic partitioning to create a spatial segmentation. We motivate the different stages with theoretical considerations and arguments, and illustrate the overall procedure on simulated and real datasets. Our method appears to offer substantial improvements over monoscale pixel-wise methods. An Appendix which gives some theoretical justifications of the methodology, computer code, documentation and dataset are available in the online supplements

A Multiscale Denoising Framework using Detection Theory with Application to Images from CMOS/CCD Sensors

Output from imaging sensors based on CMOS and CCD devices is prone to noise due to inherent electronic fluctuations and low photon count. The resulting noise in the acquired image could be effectively modelled as signal dependent Poisson noise or as a mixture of Poisson and Gaussian noise. To that end, we propose a generalized framework based on detection theory of hypothesis testing coupled with the variance stability transformation (VST) for Poisson or Poisson-Gaussian denoising. VST transforms signal dependent Poisson noise to a signal independent Gaussian noise with stable variance. Subsequently, multiscale transforms are employed on the noisy image to segregate signal and noise into separate coefficients. That facilitates the application of local binary hypothesis testing on multiple scales using empirical distribution function (EDF) for the purpose of detection and removal of noise. We demonstrate the effectiveness of the proposed framework with different multiscale transforms and on a wide variety of input datasets

A novel framework for high-quality voice source analysis and synthesis

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.The analysis, parameterization and modeling of voice source estimates obtained via inverse filtering of recorded speech are some of the most challenging areas of speech processing owing to the fact humans produce a wide range of voice source realizations and that the voice source estimates commonly contain artifacts due to the non-linear time-varying source-filter coupling. Currently, the most widely adopted representation of voice source signal is Liljencrants-Fant's (LF) model which was developed in late 1985. Due to the overly simplistic interpretation of voice source dynamics, LF model can not represent the fine temporal structure of glottal flow derivative realizations nor can it carry the sufficient spectral richness to facilitate a truly natural sounding speech synthesis. In this thesis we have introduced Characteristic Glottal Pulse Waveform Parameterization and Modeling (CGPWPM) which constitutes an entirely novel framework for voice source analysis, parameterization and reconstruction. In comparative evaluation of CGPWPM and LF model we have demonstrated that the proposed method is able to preserve higher levels of speaker dependant information from the voice source estimates and realize a more natural sounding speech synthesis. In general, we have shown that CGPWPM-based speech synthesis rates highly on the scale of absolute perceptual acceptability and that speech signals are faithfully reconstructed on consistent basis, across speakers, gender. We have applied CGPWPM to voice quality profiling and text-independent voice quality conversion method. The proposed voice conversion method is able to achieve the desired perceptual effects and the modified speech remained as natural sounding and intelligible as natural speech. In this thesis, we have also developed an optimal wavelet thresholding strategy for voice source signals which is able to suppress aspiration noise and still retain both the slow and the rapid variations in the voice source estimate

Deriving probabilistic short-range forecasts from a deterministic high-resolution model

In order to take full advantage of short-range forecasts from deterministic high-resolution NWP models, the direct model output must be addressed in a probabilistic framework. A promising approach is mesoscale ensemble prediction. However, its operational use is still hampered by conceptual deficiencies and large computational costs. This study tackles two relevant issues: (1) the representation of model-related forecast uncertainty in mesoscale ensemble prediction systems and (2) the development of post-processing procedures that retrieve additional probabilistic information from a single model simulation. Special emphasis is laid on mesoscale forecast uncertainty of summer precipitation and 2m-temperature in Europe. Source of forecast guidance is the deterministic high-resolution model Lokal-Modell (LM) of the German Weather Service. This study gains more insight into the effect and usefulness of stochastic parametrisation schemes in the representation of short-range forecast uncertainty. A stochastic parametrisation scheme is implemented into the LM in an attempt to simulate the stochastic effect of sub-grid scale processes. Experimental ensembles show that the scheme has a substantial effect on the forecast of precipitation amount. However, objective verification reveals that the ensemble does not attain better forecast goodness than a single LM simulation. Urgent issues for future research are identified. In the context of statistical post-processing, two schemes are designed: the neighbourhood method and wavelet smoothing. Both approaches fall under the framework of estimating a large array of statistical parameters on the basis of a single realisation on each parameter. The neighbourhood method is based on the notion of spatio-temporal ergodicity including explicit corrections for enhanced predictability from topographic forcing. The neighbourhood method derives estimates of quantiles, exceedance probabilities and expected values at each grid point of the LM. If the post-processed precipitation forecast is formulated in terms of probabilities or quantiles, it attains clear superiority in comparison to the raw model output. Wavelet smoothing originates from the field of image denoising and includes concepts of multiresolution analysis and non-parametric regression. In this study, the method is used to produce estimates of the expected value, but it may be easily extended to the additional estimation of exceedance probabilities. Wavelet smoothing is not only computationally more efficient than the neighbourhood method, but automatically adapts the amount of spatial smoothing to local properties of the underlying data. The method apparently detects deterministically predictable temperature patterns on the basis of statistical guidance only