A singular vector perspective of 4D-Var: Filtering and interpolation

Four-dimensional variational data assimilation (4D-Var) combines the information from a time sequence of observations with the model dynamics and a background state to produce an analysis. In this paper, a new mathematical insight into the behaviour of 4D-Var is gained from an extension of concepts that are used to assess the qualitative information content of observations in satellite retrievals. It is shown that the 4D-Var analysis increments can be written as a linear combination of the singular vectors of a matrix which is a function of both the observational and the forecast model systems. This formulation is used to consider the filtering and interpolating aspects of 4D-Var using idealized case-studies based on a simple model of baroclinic instability. The results of the 4D-Var case-studies exhibit the reconstruction of the state in unobserved regions as a consequence of the interpolation of observations through time. The results also exhibit the filtering of components with small spatial scales that correspond to noise, and the filtering of structures in unobserved regions. The singular vector perspective gives a very clear view of this filtering and interpolating by the 4D-Var algorithm and shows that the appropriate specification of the a priori statistics is vital to extract the largest possible amount of useful information from the observations. Copyright © 2005 Royal Meteorological Society

Comparison of subspace and ARX models of a waveguide's terahertz transient response after optimal wavelet filtering

A quasi-optical deembedding technique for characterizing waveguides is demonstrated using wide-band time-resolved terahertz spectroscopy. A transfer function representation is adopted for the description of the signal in the input and output port of the waveguides. The time-domain responses were discretized and the waveguide transfer function was obtained through a parametric approach in the z-domain after describing the system with an AutoRegressive with eXogenous input (ARX), as well as with a state-space model. Prior to the identification procedure, filtering was performed in the wavelet domain to minimize both signal distortion, as well as the noise propagating in the ARX and subspace models. The optimal filtering procedure used in the wavelet domain for the recorded time-domain signatures is described in detail. The effect of filtering prior to the identification procedures is elucidated with the aid of pole-zero diagrams. Models derived from measurements of terahertz transients in a precision WR-8 waveguide adjustable short are presented.

Background-noise reduction

Interference by siren background-noise with speech transmitted from radio equipment (3) of an emergency-service vehicle, is reduced by apparatus (1) that subtracts (43) an estimate nk of the correlated siren-noise component from the contaminated signal yk supplied by the cab-microphone (2). The estimate nk is computed by FIR (finite impulse response) filtering of a siren-reference signal xk supplied by a unit (4) from one or more microphones located on or near the siren, or from the electric waveform driving the siren. The filter-coefficients wk are adjusted according to an LMS (least mean square) adaptive algorithm that is applied to the correlated-noise component ek of the fed-back noise-reduced signal, so as to bring about iterative cancellation with close frequency-tracking, of the siren noise.

Separating heart and brain: on the reduction of physiological noise from multichannel functional near-infrared spectroscopy (fNIRS) signals

Objective. Functional near-infrared spectroscopy (fNIRS) is an emerging technique for the in vivo assessment of functional activity of the cerebral cortex as well as in the field of brain–computer interface (BCI) research. A common challenge for the utilization of fNIRS in these areas is a stable and reliable investigation of the spatio-temporal hemodynamic patterns. However, the recorded patterns may be influenced and superimposed by signals generated from physiological processes, resulting in an inaccurate estimation of the cortical activity. Up to now only a few studies have investigated these influences, and still less has been attempted to remove/reduce these influences. The present study aims to gain insights into the reduction of physiological rhythms in hemodynamic signals (oxygenated hemoglobin (oxy-Hb), deoxygenated hemoglobin (deoxy-Hb)). Approach. We introduce the use of three different signal processing approaches (spatial filtering, a common average reference (CAR) method; independent component analysis (ICA); and transfer function (TF) models) to reduce the influence of respiratory and blood pressure (BP) rhythms on the hemodynamic responses. Main results. All approaches produce large reductions in BP and respiration influences on the oxy-Hb signals and, therefore, improve the contrast-to-noise ratio (CNR). In contrast, for deoxy-Hb signals CAR and ICA did not improve the CNR. However, for the TF approach, a CNR-improvement in deoxy-Hb can also be found. Significance. The present study investigates the application of different signal processing approaches to reduce the influences of physiological rhythms on the hemodynamic responses. In addition to the identification of the best signal processing method, we also show the importance of noise reduction in fNIRS data.

Enzymatic Logic Gates with Noise-Reducing Sigmoid Response

Biochemical computing is an emerging field of unconventional computing that attempts to process information with biomolecules and biological objects using digital logic. In this work we survey filtering in general, in biochemical computing, and summarize the experimental realization of an and logic gate with sigmoid response in one of the inputs. The logic gate is realized with electrode-immobilized glucose-6-phosphate dehydrogenase enzyme that catalyzes a reaction corresponding to the Boolean and functions. A kinetic model is also developed and used to evaluate the extent to which the performance of the experimentally realized logic gate is close to optimal.

EDGE-PRESERVING SPECKLE TEXTURE REMOVAL BY INTERFERENCE-BASED SPECKLE FILTERING FOLLOWED BY ANISOTROPIC DIFFUSION

Ultrasonography has an inherent noise pattern, called speckle, which is known to hamper object recognition for both humans and computers. Speckle noise is produced by the mutual interference of a set of scattered wavefronts. Depending on the phase of the wavefronts, the interference may be constructive or destructive, which results in brighter or darker pixels, respectively. We propose a filter that minimizes noise fluctuation while simultaneously preserving local gray level information. It is based on steps to attenuate the destructive and constructive interference present in ultrasound images. This filter, called interference-based speckle filter followed by anisotropic diffusion (ISFAD), was developed to remove speckle texture from B-mode ultrasound images, while preserving the edges and the gray level of the region. The ISFAD performance was compared with 10 other filters. The evaluation was based on their application to images simulated by Field II (developed by Jensen et al.) and the proposed filter presented the greatest structural similarity, 0.95. Functional improvement of the segmentation task was also measured, comparing rates of true positive, false positive and accuracy. Using three different segmentation techniques, ISFAD also presented the best accuracy rate (greater than 90% for structures with well-defined borders). (E-mail: fernando.okara@gmail.com) (C) 2012 World Federation for Ultrasound in Medicine & Biology.

USING AUTO- AND CROSS-CORRELATIONS FROM SEISMIC NOISE TO MONITOR VELOCITY CHANGES AT VILLARRICA VOLCANO, CHILE

We used the Green's functions from auto-correlations and cross-correlations of seismic ambient noise to monitor temporal velocity changes in the subsurface at Villarrica volcano in the Southern Andes of Chile. Campaigns were conducted from March to October 2010 and February to April 2011 with 8 broadband and 6 short-period stations, respectively. We prepared the data by removing the instrument response, normalizing with a root-mean-square method, whitening the spectra, and filtering from 1 to 10 Hz. This frequency band was chosen based on the relatively high background noise level in that range. Hour-long auto- and cross-correlations were computed and the Green's functions stacked by day and total time. To track the temporal velocity changes we stretched a 24 hour moving window of correlation functions from 90% to 110% of the original and cross correlated them with the total stack. All of the stations' auto-correlations detected what is interpreted as an increase in velocity in 2010, with an average increase of 0.13%. Cross-correlations from station V01, near the summit, to the other stations show comparable changes that are also interpreted as increases in velocity. We attribute this change to the closing of cracks in the subsurface due either to seasonal snow loading or regional tectonics. In addition to the common increase in velocity across the stations, there are excursions in velocity on the same order lasting several days. Amplitude decreases as the station's distance from the vent increases suggesting these excursions may be attributed to changes within the volcanic edifice. In at least two occurrences the amplitudes at stations V06 and V07, the stations farthest from the vent, are smaller. Similar short temporal excursions were seen in the auto-correlations from 2011, however, there was little to no increase in the overall velocity.

Graphics Processor Unit Based Parallelization of Optimized Baseline Wander Filtering Algorithms for Long-term Electrocardiography

Long-term electrocardiogram (ECG) often suffers from relevant noise. Baseline wander in particular is pronounced in ECG recordings using dry or esophageal electrodes, which are dedicated for prolonged registration. While analog high-pass filters introduce phase distortions, reliable offline filtering of the baseline wander implies a computational burden that has to be put in relation to the increase in signal-to-baseline ratio (SBR). Here we present a graphics processor unit (GPU) based parallelization method to speed up offline baseline wander filter algorithms, namely the wavelet, finite, and infinite impulse response, moving mean, and moving median filter. Individual filter parameters were optimized with respect to the SBR increase based on ECGs from the Physionet database superimposed to auto-regressive modeled, real baseline wander. A Monte-Carlo simulation showed that for low input SBR the moving median filter outperforms any other method but negatively affects ECG wave detection. In contrast, the infinite impulse response filter is preferred in case of high input SBR. However, the parallelized wavelet filter is processed 500 and 4 times faster than these two algorithms on the GPU, respectively, and offers superior baseline wander suppression in low SBR situations. Using a signal segment of 64 mega samples that is filtered as entire unit, wavelet filtering of a 7-day high-resolution ECG is computed within less than 3 seconds. Taking the high filtering speed into account, the GPU wavelet filter is the most efficient method to remove baseline wander present in long-term ECGs, with which computational burden can be strongly reduced.

Dual-Domain Filtering

We propose dual-domain filtering, an image processing paradigm that couples spatial domain with frequency domain filtering. Our dual-domain defined filter removes artifacts like residual noise of other image denoising methods and compression artifacts. Moreover, iterating the filter achieves state-of-the-art image denoising results, but with a much simpler algorithm than competing approaches. The simplicity and versatility of the dual-domain filter makes it an attractive tool for image processing.

Novel method to improve the signal-to-noise ratio in the far-field results obtained from planar near-field measurements

A method to reduce the noise power in far-field pattern without modifying the desired signal is proposed. Therefore, an important signal-to-noise ratio improvement may be achieved. The method is used when the antenna measurement is performed in planar near-field, where the recorded data are assumed to be corrupted with white Gaussian and space-stationary noise, because of the receiver additive noise. Back-propagating the measured field from the scan plane to the antenna under test (AUT) plane, the noise remains white Gaussian and space-stationary, whereas the desired field is theoretically concentrated in the aperture antenna. Thanks to this fact, a spatial filtering may be applied, cancelling the field which is located out of the AUT dimensions and which is only composed by noise. Next, a planar field to far-field transformation is carried out, achieving a great improvement compared to the pattern obtained directly from the measurement. To verify the effectiveness of the method, two examples will be presented using both simulated and measured near-field data.

Methods for noise reduction in far-field patterns obtained from cylindrical near-field antenna measurements

Two different methods to reduce the noise power in the far-field pattern of an antenna as measured in cylindrical near-field (CNF) are proposed. Both methods are based on the same principle: the data recorded in the CNF measurement, assumed to be corrupted by white Gaussian and space-stationary noise, are transformed into a new domain where it is possible to filter out a portion of noise. Those filtered data are then used to calculate a far-field pattern with less noise power than that one obtained from the measured data without applying any filtering. Statistical analyses are carried out to deduce the expressions of the signal-to-noise ratio improvement achieved with each method. Although the idea of the two alternatives is the same, there are important differences between them. The first one applies a modal filtering, requires an oversampling and improves the far-field pattern in all directions. The second method employs a spatial filtering on the antenna plane, does not require oversampling and the far-field pattern is only improved in the forward hemisphere. Several examples are presented using both simulated and measured near-field data to verify the effectiveness of the methods.

Spatio-temporal filtering with morphological operators for robust cell migration estimation in "in-vivo" images

The understanding of the embryogenesis in living systems requires reliable quantitative analysis of the cell migration throughout all the stages of development. This is a major challenge of the "in-toto" reconstruction based on different modalities of "in-vivo" imaging techniques -spatio-temporal resolution and image artifacts and noise. Several methods for cell tracking are available, but expensive manual interaction -time and human resources- is always required to enforce coherence. Because of this limitation it is necessary to restrict the experiments or assume an uncontrolled error rate. Is it possible to obtain automated reliable measurements of migration? can we provide a seed for biologists to complete cell lineages efficiently? We propose a filtering technique that considers trajectories as spatio-temporal connected structures that prunes out those that might introduce noise and false positives by using multi-dimensional morphological operators.

Application of postprocessing techniques methods for noise reduction in cylindrical near field antenna measurements

Three different methods to reduce the noise power in the far-field pattern of an antenna when it is measured in a cylindrical near field system are presented and compared. The first one is based on a modal filtering while the other two are based on spatial filtering, either on an antenna plane or either on a cylinder of smaller radius. Simulated and measured results will be presented.

Image Noise Removal on Heterogeneous CPU-GPU Configurations

A parallel algorithm to remove impulsive noise in digital images using heterogeneous CPU/GPU computing is proposed. The parallel denoising algorithm is based on the peer group concept and uses an Euclidean metric. In order to identify the amount of pixels to be allocated in multi-core and GPUs, a performance analysis using large images is presented. A comparison of the parallel implementation in multi-core, GPUs and a combination of both is performed. Performance has been evaluated in terms of execution time and Megapixels/second. We present several optimization strategies especially effective for the multi-core environment, and demonstrate significant performance improvements. The main advantage of the proposed noise removal methodology is its computational speed, which enables efficient filtering of color images in real-time applications.

Power line interference filtering on surface electromyography based on the stationary wavelet packet transform

Power line interference is one of the main problems in surface electromyogram signals (EMG) analysis. In this work, a new method based on the stationary wavelet packet transform is proposed to estimate and remove this kind of noise from EMG data records. The performance has been quantitatively evaluated with synthetic noisy signals, obtaining good results independently from the signal to noise ratio (SNR). For the analyzed cases, the obtained results show that the correlation coefficient is around 0.99, the energy respecting to the pure EMG signal is 98–104%, the SNR is between 16.64 and 20.40 dB and the mean absolute error (MAE) is in the range of −69.02 and −65.31 dB. It has been also applied on 18 real EMG signals, evaluating the percentage of energy respecting to the noisy signals. The proposed method adjusts the reduction level to the amplitude of each harmonic present in the analyzed noisy signals (synthetic and real), reducing the harmonics with no alteration of the desired signal.