Non white gaussian noise reduction on microstructure data using wavelet denoising

INSTRUMENTATION VIEWPOINT Sessions 89 3. Conclusions Excitation spectra from diff erent cultures were measured, and were processed with the Self-Organizing Map. These preliminary results show the SOM methodology as a feasible way to achieve phytoplankton discrimination. Furthermore, they are encouraging enough in order to expand the current work into an automated system for phytoplankton’s EEM classifi cation. 4. Acknowledgements The project VARITEC-SAMPLER (CTM2004-04442-C02-2/MAR) is funded from the Spanish Ministry of Education and Science. 5. References [1] M. Beutler, “Spectral fl uorescence of chlorophyll and phycobilins as an in-situ tool of phytoplankton analysis –models, algorithms and instruments”, PhD Thesis, University of Kiel , 2003. [2] T. Kohonen, The Self-Organizing Map,Proceedings of the IEEE, 78(9):14641480, 1990. Figure 3. SOM label representation. NON WHITE GAUSSIAN NOISE REDUCTION ON MICROSTRUCTURE DATA USING WAVELET DENOISING R. Quesada López (1) , J. Piera Fernàndez (2) (1) Technical University of Catalonia. Av. Canal Olímpic s/n 08860 Castelldefels, Spain. 934137120 [email protected] (2) Marine Technology Unit (CMIMA-CSIC), Passeig Marítim 37-49, Barcelona 08003, Spain 1. Introduction The characterization of the turbulent fl ow in the ocean dynamics has many implications in environmental modelling. The biological and physical processes characterization [1] [2] or the turbulent analyses of the energetic part of the vertical microstructure records [3] [4] are some of the fi elds on which we can focus the turbulent characterization. A common procedure for detecting turbulent regions from CTD data is by computing the Thorpe displacements (dT) profi les [5].The Turbulent patches are calculated from the density profi les δ (z) and are identifi ed as regions with non-null values of Thorpe displacements. The presence of noise is a critical problem when processing or analyzing the CTD data profi les. A method was proposed in [6] to improve patch detection at low-density gradients. The method, pointed out the infl uence of wavelet mother selection and the noise characterization on the fi nal denoising results. This article introduces a procedure to obtain the optimal wavelet fi lters selection to reduce noise eff ects. In the literature the studies based in wavelet denoising are focused on reduce the eff ects of white Gaussian noise. In turn, in this study, the signal representing the noise is synthetically created and modelled by both fl icker and white Gaussian noise. 2. Noise Instrument Model In this section we present the procedure considered to determine noise features in the Self Contained Autonomous Micro Profi ler (SCAMP) measurements. This noise model will be used to optimize the Wavelet family to denoise the fi eld profi les. A set of laboratory test measurements were carried out for modelling the SCAMP noise. In these tests, the temperature was kept constant providing a reference to link the temperature fl uctuations to the instrumental noise. Fig 1. To model the noise present in the data profi le we need to know the power spectrum density. This signal is used to obtain the fi lter coeffi cients to generate the synthetic noise. An autoregressive model was applied to the experimental data tests to obtain a noise model. This model provided the fi lter coeffi cients to implement a synthetic signal. The graphics Fig1 and Fig2 show the agreement between the power spectral density estimation of the experimental test signal and the synthetic noise model. The resultant synthesized noise model is used to simulate the real instrumentation and environmental noise and analyze the denoising process to obtain the improvement for each wavelet family. To select the optimal mother wavelet, a computed test was developed. This test is a trial and error method which report us a matrix with the RMS error of the Thorpe displacement histogram between INSTRUMENTATION VIEWPOINT Sessions 90 the original signal and the obtained after the denoising process. The output matrix for each family is analyzed to determine the optimal selection. 4. Results From the obtained results, Battle-Lemarié with order 5 has been selected as a mother wavelet to use for denoising microstructure data. The Daubechies 20 report similar results that Battle-Lemarié 5, but Fig 2. This noise model is computed with the original noise signal and modeled as a white Gaussian noise and the fl icker noise contribution. Fig 3. (RMS) Root mean square error calculated between Thorpe displacement histogram of the original patch and the denoised one. Fig 4 Daubechies 20 and Battle-Lemarie 5 mother wavelet and spectra representation needs more coeffi cients (20) than the Battle selected (5). Wavelets with higher order require more computational power and are more problematic when applying in the boundary limits of the data profi les. In order to analyze the results, the fi gure 4 shows us the mother wavelet and the spectral representation of dB20 and B-L 5. The spectral Daubechies 20 have a small component near the principal response. The Battle-Lemarié 5 erases all secondary lobes. When we apply the diff erent wavelet families to the denoising process, the secondary lobes obstruct the scale separation and in consequence on the denoising process. 5. Conclusions The model described in this article is an experimental procedure to analyze and select the optimal wavelet family to use with denoising technique. The tests applied to obtain the optimal wavelet, are a recursive procedure to test the most common wavelet families. The applied signal to test the method is composed by: (1) theoretical profi les where we can modify the temperature gradient and the turbulent patch size, (2) synthetic noise. A synthetic noise signal is computed from real noise data to emulate. The preliminary numerical results determine that the Battle-Lemarié 5 is a good selection to denoise microstructure test profi les. A future tests will be developed to use the synthetically noise model on more complex simulations and real data profi les. 4. References [1]Reynols, C.S. “Dynamics, selection and composition of phytoplankton in relation to vertical structure in lakes” Arch. Hidrobiol. Beih. Ergebn. Limnol., 35:13-31, 1992 [2]Haury, L.R. et al. “Eff ects of turbulent shear fl ow on zooplankton distribution. Deep Sea Res., 37(3):447-461, 1990 [3]Gregg, M.C. “Diapycnal mixing in the thermocline: a review. J. Geophys. Res., 92:5249-5286, 1987 [4]Moum, J.N “Effi ciency of mixing in the main thermocline. J. Geophy. Res., 101:12057-12069, 1996 [5]Thorpe, S. A. “Turbulence and mixing in a Scottish Loch”. Philos. Trans. R. Soc., 286:125-181, 1977 [6]Piera, J. et al. “Turbulent Patch Identifi cation in Microstructure Profi les: A Method Base don Wavelet Denoising and Thorpe Displacement Analysis” J.Atmos. Oceanic Technol., 19:1390-1402, 2002 M9