Automatic Kalman-filter-based wavelet shrinkage denoising of 1D stellar spectra

We propose a non-parametric method to denoise 1D stellar spectra based on wavelet shrinkage followed by adaptive Kalman thresholding. Wavelet shrinkage denoising involves applying the discrete wavelet transform (DWT) to the input signal, 'shrinking' certain frequency components in the transform domain, and then applying inverse DWT to the reduced components. The performance of this procedure is influenced by the choice of base wavelet, the number of decomposition levels, and the thresholding function. Typically, these parameters are chosen by 'trial and error', which can be strongly dependent on the properties of the data being denoised. We here introduce an adaptive Kalman-filter-based thresholding method that eliminates the need for choosing the number of decomposition levels. We use the 'Haar' wavelet basis, which we found to provide excellent filtering for 1D stellar spectra, at a low computational cost. We introduce various levels of Poisson noise into synthetic PHOENIX spectra, and test the performance of several common denoising methods against our own. It proves superior in terms of noise suppression and peak shape preservation. We expect it may also be of use in automatically and accurately filtering low signal-to-noise galaxy and quasar spectra obtained from surveys such as SDSS, Gaia, LSST, PESSTO, VANDELS, LEGA-C, and DESI

An Iterative Wavelet Threshold for Signal Denoising

This paper introduces an adaptive filtering process based on shrinking wavelet coefficients from the corresponding signal wavelet representation. The filtering procedure considers a threshold method determined by an iterative algorithm inspired by the control charts application, which is a tool of the statistical process control (SPC). The proposed method, called SpcShrink, is able to discriminate wavelet coefficients that significantly represent the signal of interest. The SpcShrink is algorithmically presented and numerically evaluated according to Monte Carlo simulations. Two empirical applications to real biomedical data filtering are also included and discussed. The SpcShrink shows superior performance when compared with competing algorithms.Comment: 19 pages, 10 figures, 2 table

Fault feature extraction method based on EWT-SMF and MF-DFA for valve fault of reciprocating compressor

According to the nonlinearity and nonstationarity characteristics of reciprocating compressor vibration signal, a fault feature extraction method of reciprocating compressor based on the empirical wavelet transform (EWT) and state-adaptive morphological filtering (SMF) is proposed. Firstly, an adaptive empirical wavelet transform was used to divide the Fourier spectrum by constructing a scale-space curve, and an appropriate orthogonal wavelet filter bank was constructed to extract the AM-FM component with a tightly-supported Fourier spectrum. Then according to the impact characteristic of the reciprocating compressor vibration signal, the morphological structural elements were constructed with the characteristics of the signal to perform state-adaptive morphological filtering on the partitioned modal functions. Finally, the MF-DFA method of the modal function was quantitatively analyzed and the fault identification was performed. By analyzing the experimental data, it can be shown that the method can effectively identify the fault type of reciprocating compressor valve

A STUDY OF POWER LINE INTERFERENCE CANCELLATION USING IIR, AAPTIVE AND WAVELET FILTERING IN ECG

Background: It is essential to reduce these disturbances in ECG signal to improve accuracy and reliability. The bandwidth of the noise overlaps that of wanted signals, so that simple filtering cannot sufficiently enhance the signal to noise ratio. The present paper deals with the digital filtering method to reduce 50 Hz power line noise artifacts in the ECG signal. 4th order Butterworth notch filters(BW=.5 Hz) is used to reduce 50 Hz power line noise interference(PLI) from ECG signals and its performance is compared with Adaptve filters. Method: ECG signal is taken from physionet database. ECG signal (with PLI noise of different frequencies) were processed by Butterworth notch filters of bandwidths of 0.5 Hz. Ringing Artifact is observed in the output. ECG signal (with PLI noise of different frequencies) were processed by Adaptive filters no ringing effect seen. Wavelet filtering applied clean ECG were observed. Result: Performance is compared based on SNR and MSE of Butterworth notch filter and adaptive filters and output of wallet filtering were observed. Conclusion: RLS adaptive filter give better performance as compared to IIR Butterworth and LMS. Clean ECG were seen when filtering using symlet8 wavelet was done

Wavelet-based denoising for 3D OCT images

Optical coherence tomography produces high resolution medical images based on spatial and temporal coherence of the optical waves backscattered from the scanned tissue. However, the same coherence introduces speckle noise as well; this degrades the quality of acquired images. In this paper we propose a technique for noise reduction of 3D OCT images, where the 3D volume is considered as a sequence of 2D images, i.e., 2D slices in depth-lateral projection plane. In the proposed method we first perform recursive temporal filtering through the estimated motion trajectory between the 2D slices using noise-robust motion estimation/compensation scheme previously proposed for video denoising. The temporal filtering scheme reduces the noise level and adapts the motion compensation on it. Subsequently, we apply a spatial filter for speckle reduction in order to remove the remainder of noise in the 2D slices. In this scheme the spatial (2D) speckle-nature of noise in OCT is modeled and used for spatially adaptive denoising. Both the temporal and the spatial filter are wavelet-based techniques, where for the temporal filter two resolution scales are used and for the spatial one four resolution scales. The evaluation of the proposed denoising approach is done on demodulated 3D OCT images on different sources and of different resolution. For optimizing the parameters for best denoising performance fantom OCT images were used. The denoising performance of the proposed method was measured in terms of SNR, edge sharpness preservation and contrast-to-noise ratio. A comparison was made to the state-of-the-art methods for noise reduction in 2D OCT images, where the proposed approach showed to be advantageous in terms of both objective and subjective quality measures

Combined wavelet domain and motion compensated filtering compliant with video codecs

In this paper, we introduce the idea of using motion estimation resources from a video codec for video denoising. This is not straightforward because the motion estimators aimed for video compression and coding, tolerate errors in the estimated motion field and hence are not directly applicable to video denoising. To solve this problem, we propose a novel motion field filtering step that refines the accuracy of the motion estimates to a degree that is required for denoising. We illustrate the use of the proposed motion estimation method within a wavelet-based video denoising scheme. The resulting video denoising method is of low-complexity and receives comparable results with respect to the latest video denoising methods

A Primal-Dual Proximal Algorithm for Sparse Template-Based Adaptive Filtering: Application to Seismic Multiple Removal

Unveiling meaningful geophysical information from seismic data requires to deal with both random and structured "noises". As their amplitude may be greater than signals of interest (primaries), additional prior information is especially important in performing efficient signal separation. We address here the problem of multiple reflections, caused by wave-field bouncing between layers. Since only approximate models of these phenomena are available, we propose a flexible framework for time-varying adaptive filtering of seismic signals, using sparse representations, based on inaccurate templates. We recast the joint estimation of adaptive filters and primaries in a new convex variational formulation. This approach allows us to incorporate plausible knowledge about noise statistics, data sparsity and slow filter variation in parsimony-promoting wavelet frames. The designed primal-dual algorithm solves a constrained minimization problem that alleviates standard regularization issues in finding hyperparameters. The approach demonstrates significantly good performance in low signal-to-noise ratio conditions, both for simulated and real field seismic data