Showing papers on "Spatial filter published in 2020"

Spatial Filtering in SSVEP-Based BCIs: Unified Framework and New Improvements

Abstract: Objective: In the steady-state visual evoked potential (SSVEP)-based brain computer interfaces (BCIs), spatial filtering, which combines the multi-channel electroencephalography (EEG) signals in order to reduce the non-SSVEP-related component and thus enhance the signal-to-noise ratio (SNR), plays an important role in target recognition. Recently, various spatial filtering algorithms have been developed employing different prior knowledge and characteristics of SSVEPs, however how these algorithms interconnect and differ is not yet fully explored, leading to difficulties in further understanding, utilizing and improving them. Methods: We propose a unified framework under which the spatial filtering algorithms can be formulated as generalized eigenvalue problems (GEPs) with four different elements: data, temporal filter, orthogonal projection and spatial filter. Based on the framework, we design new spatial filtering algorithms for improvements through the choice of different elements. Results: The similarities, differences and relationships among nineteen mainstream spatial filtering algorithms are revealed under the proposed framework. Particularly, it is found that they originate from the canonical correlation analysis (CCA), principal component analysis (PCA), and multi-set CCA, respectively. Furthermore, three new spatial filtering algorithms are developed with enhanced performance validated on two public SSVEP datasets with 45 subjects. Conclusion: The proposed framework provides insights into the underlying relationships among different spatial filtering algorithms and helps the design of new spatial filtering algorithms. Significance: This is a systematic study to explore, compare and improve the existing spatial filtering algorithms, which would be significant for further understanding and future development of high performance SSVEP-based BCIs.

Spectral control of the orbital angular momentum of a laser beam based on 3D properties of spiral phase plates fabricated for an infrared wavelength

Abstract: This paper examines the spectral properties of a spiral phase plate (SPP) generating orbital angular momentum (OAM) beams. A simple method is proposed for calculating the resulting OAM by measuring only two maximum expansion coefficients. A comparative numerical simulation of the proposed and traditional methods is performed. An SPP is fabricated for generation of an OAM with integer values at infrared and visible wavelengths. Qualitative experimental studies of the changes in a generated OAM with a change in the operating wavelength are performed using the spatial filtering method. The experimental results are found to agree with the results of numerical simulation. Beams with integer and fractional OAM values are obtained experimentally by changing the wavelength.

Stochastic complex transmittance screens for synthesizing general partially coherent sources.

Abstract: We develop a method to synthesize any partially coherent source (PCS) with a genuine cross-spectral density (CSD) function using complex transmittance screens. Prior work concerning PCS synthesis with complex transmittance screens has focused on generating Schell-model (uniformly correlated) sources. Here, using the necessary and sufficient condition for a genuine CSD function, we derive an expression, in the form of a superposition integral, that produces stochastic complex screen realizations. The sample autocorrelation of the screens is equal to the complex correlation function of the desired PCS. We validate our work by generating, in simulation, three PCSs from the literature-none has ever been synthesized using stochastic screens before. Examining planar slices through the four-dimensional CSD functions, we find the simulated results to be in excellent agreement with theory, implying successful realization of all three PCSs. The technique presented herein adds to the existing literature concerning the generation of PCSs and can be physically implemented using a simple optical setup consisting of a laser, spatial light modulator, and spatial filter.

Integrated Sidelobe Cancellation and Linear Prediction Kalman Filter for Joint Multi-Microphone Speech Dereverberation, Interfering Speech Cancellation, and Noise Reduction

Abstract: In multi-microphone speech enhancement, reverberation as well as additive noise and/or interfering speech are commonly suppressed by deconvolution and spatial filtering, e.g., using multi-channel linear prediction (MCLP) on the one hand and beamforming, e.g., a generalized sidelobe canceler (GSC), on the other hand. In this article, we consider several reverberant speech components, whereof some are to be dereverberated and others to be canceled, as well as a diffuse (e.g., babble) noise component to be suppressed. In order to perform both deconvolution and spatial filtering, we integrate MCLP and the GSC into a novel architecture referred to as integrated sidelobe cancellation and linear prediction (ISCLP), where the sidelobe-cancellation (SC) filter and the linear prediction (LP) filter operate in parallel, but on different microphone signal frames. Within ISCLP, we estimate both filters jointly by means of a single Kalman filter. We further propose a spectral Wiener gain post-processor, which is shown to relate to the Kalman filter's posterior state estimate. The presented ISCLP Kalman filter is benchmarked against two state-of-the-art approaches, namely first a pair of alternating Kalman filters respectively performing dereverberation and noise reduction, and second an MCLP+GSC Kalman filter cascade. While the ISCLP Kalman filter is roughly $M^2$ times less expensive than both reference algorithms, where $M$ denotes the number of microphones, it is shown to perform at least similarly as compared to the former, and to outperform the latter. A MATLAB implementation is available.

An ultra-compact particle size analyser using a CMOS image sensor and machine learning.

Abstract: Light scattering is a fundamental property that can be exploited to create essential devices such as particle analysers. The most common particle size analyser relies on measuring the angle-dependent diffracted light from a sample illuminated by a laser beam. Compared to other non-light-based counterparts, such a laser diffraction scheme offers precision, but it does so at the expense of size, complexity and cost. In this paper, we introduce the concept of a new particle size analyser in a collimated beam configuration using a consumer electronic camera and machine learning. The key novelty is a small form factor angular spatial filter that allows for the collection of light scattered by the particles up to predefined discrete angles. The filter is combined with a light-emitting diode and a complementary metal-oxide-semiconductor image sensor array to acquire angularly resolved scattering images. From these images, a machine learning model predicts the volume median diameter of the particles. To validate the proposed device, glass beads with diameters ranging from 13 to 125 µm were measured in suspension at several concentrations. We were able to correct for multiple scattering effects and predict the particle size with mean absolute percentage errors of 5.09% and 2.5% for the cases without and with concentration as an input parameter, respectively. When only spherical particles were analysed, the former error was significantly reduced (0.72%). Given that it is compact (on the order of ten cm) and built with low-cost consumer electronics, the newly designed particle size analyser has significant potential for use outside a standard laboratory, for example, in online and in-line industrial process monitoring.

A-CRNN-Based Method for Coherent DOA Estimation with Unknown Source Number.

Abstract: Estimating directions of arrival (DOA) without knowledge of the source number is regarded as a challenging task, particularly when coherence among sources exists. Researchers have trained deep learning (DL)-based models to attack the problem of DOA estimation. However, existing DL-based methods for coherent sources do not adapt to variable source numbers or require signal independence. Herein, we put forward a new framework combining parallel DOA estimators with Toeplitz matrix reconstruction to address the problem. Each estimator is constructed by connecting a multi-label classifier to a spatial filter, which is based on convolutional-recurrent neural networks. Spatial filters divide the angle domain into several sectors, so that the following classifiers can extract the arrival directions. Assisted with Toeplitz-based method for source-number determination, pseudo or missed angles classified by the estimators will be reduced. Then, the spatial spectrum can be more accurately recovered. In addition, the proposed method is data-driven, so it is naturally immune to signal coherence. Simulation results demonstrate the predominance of the proposed method and show that the trained model is robust to imperfect circumstances such as limited snapshots, colored Gaussian noise, and array imperfections.

AOTF-based hyperspectral imaging phase microscopy

Abstract: Phase imaging microscopy with incoherent object illumination is convenient and affordable for biomedical research and clinics since it provides easy integration with a variety of bright-field optical microscopes. We report the design of a new hyperspectral imaging system based on a combination of a spatial light modulator (SLM) and an acousto-optic tunable filter (AOTF) for phase imaging microscopy. Contrast of phase-only objects originates from matched spectral and spatial filtering performed by the SLM and the AOTF located in Fourier-conjugate optical planes in the back-end of the optical system. The system is designed as an add-on to a standard optical microscope with incoherent diascopic sample illumination.

Optimization of noncollinear AOTF design for laser beam shaping

Abstract: Optimization of a wide-angle paratellurite acousto-optic tunable filter (AOTF) is performed for applications in laser beam shaping systems. The AOTF configuration with annular transfer function is analyzed. It is demonstrated that the optimal AOTF design for single-frequency operation as a narrow-band spatial frequency filter is obtained at acoustic propagation angle of 5.6° relative to the [110] axis. The optimal design for maximization of AOTF resolution in multifrequency laser beam shaping operation mode is obtained at acoustic propagation angle of 13.8°.

Adaptive-optics-enabled quantum communication: A technique for daytime space-to-Earth links

Abstract: Previous demonstrations of free-space quantum communication in daylight have been touted as significant for the development of global-scale quantum networks. Until now, no one has carefully tuned their atmospheric channel to reproduce the daytime sky radiance and slant-path turbulence conditions as they exist between space and Earth. In this article we report a quantum communication field experiment under conditions representative of daytime downlinks from space. Higher-order adaptive optics increased quantum channel efficiencies far beyond those possible with tip/tilt correction alone while spatial filtering at the diffraction limit rejected optical noise without the need for an ultra-narrow spectral filter. High signal-to-noise probabilities and low quantum-bit-error rates were demonstrated over a wide range of channel radiances and turbulence conditions associated with slant-path propagation in daytime. The benefits to satellite-based quantum key distribution are quantified and discussed.

Automatic cross filtering for off-axis digital holographic microscopy

Abstract: Off-axis digital holographic microscopy (DHM) is a significant quantitative phase imaging (QPI) modality in a single shot. However, the reconstructed quality of the image in the off-axis DHM is governed by the spatial filtering in the spectral domain of a hologram. In this study, we develop an automatic cross filtering method to automatically extract the 1st order term, thus achieving more useful high frequency information but less interference information from components of zero and -1st order. In contrast to the state-of-the-art filter, the proposed filter can realize high image quality at high speed by incorporating the division algorithm. Some experiments are conducted to prove the feasibility and validity of the proposed method.

Laboratory characterization of FIRSTv2 photonic chip for the study of substellar companions

Abstract: FIRST (Fibered Imager foR a Single Telescope instrument) is a post-AO instrument that enables high contrast imaging and spectroscopy at spatial scales below the diffraction limit. FIRST achieves sensitivity and accuracy by a unique combination of sparse aperture masking, spatial filtering by single-mode fibers and cross-dispersion in the visible. The telescope pupil is divided into sub-pupils by an array of microlenses, coupling the light into single-mode fibers. The output of the fibers are rearranged in a non redundant configuration, allowing the measurement of the complex visibility for every baseline over the 600-900 nm spectral range. A first version of this instrument is currently integrated to the Subaru Extreme AO bench (SCExAO). This paper focuses on the on-going instrument upgrades and testings, which aim at increasing the instrument’s stability and sensitivity, thus improving the dynamic range. FIRSTv2’s interferometric scheme is based on a photonic chip beam combiner. We report on the laboratory characterization of two different types of 5-input beam combiner with enhanced throughput. The interferometric recombination of each pair of sub-pupils is encoded on a single output. Thus, to sample the fringes we implemented a temporal phase modulation by pistoning the segmented mirrors of a Micro-ElectroMechanical System (MEMS). By coupling high angular resolution and spectral resolution in the visible, FIRST offers unique capabilities in the context of the detection and spectral characterization of close companions, especially on 30m-class telescopes.

3.9 THz spatial filter based on a back-to-back Si-lens system.

Abstract: We present a terahertz spatial filter consisting of two back-to-back (B2B) mounted elliptical silicon lenses and an opening aperture defined on a thin gold layer between the lenses. The beam filtering efficiency of the B2B lens system is investigated by simulation and experiment. Using a unidirectional antenna coupled 3rd-order distributed feedback (DFB) quantum cascade laser (QCL) at 3.86 THz as the source, the B2B lens system shows 72% transmissivity experimentally with a fundamental Gaussian mode as the input, in reasonably good agreement with the simulated value of 80%. With a proper aperture size, the B2B lens system is capable of filtering the non-Gaussian beam from the QCL to a nearly fundamental Gaussian beam, where Gaussicity increases from 74% to 99%, and achieves a transmissivity larger than 30%. Thus, this approach is proven to be an effective beam shaping technique for QCLs, making them to be suitable local oscillators in the terahertz range with a Gaussian beam. Besides, the B2B lens system is applicable to a wide frequency range if the wavelength dependent part is properly scaled.

Recent results on electro-optic visible multi-telescope beam combiner for next generation FIRST/SUBARU instruments: hybrid and passive devices

Abstract: FIRST (Fibered Imager foR a Single Telescope instrument) is an instrument that enables high contrast imaging and spectroscopy, thanks to a unique combination of sparse aperture masking, spatial filtering by single-mode waveguides and cross-dispersion in the visible. In order to increase the instrument’s stability and sensitivity, we proposed a new series of photonic beam combiners. The idea is to achieve phase modulation inside an optical chip and get rid of external delay lines, and improve the transmission by using novel techniques that will allow for beam combination in 3D, avoiding planar X-crossings and large bending radii observed in planar integrated optics instruments, between first and last inputs to combine, when the inputs separation is large (i.e. in 9 telescopes beam combiners). In a previous paper [4] we presented first prototypes of beam combiners for FIRST/SUBARU 9T. Planar 2D concepts were studied, but transmission was low due to the high number of crossings and the sharp bending angles needed to achieve beam combination within the length of the wafer. In this paper we will present our recent results on improved designs concerning: A) A hybrid Lithium-Niobate active beam splitter and phase modulator (9T, 1x8), coupled to a passive glass beam combiner (72x36, by pairs). B) A full passive device (5T splitter+beam combiner) and C) a narrow 5T splitter + phase modulator based on lithium niobate, to reduce the bending losses and optimize the overall transmission once coupled to the passive combiner. A comparative analysis of different performances will be presented.

Radial polarizing phase-shifting interferometry with applications to single-shot n interferogram measurements and potential usage for white light interferogram analysis

Abstract: In this research, we present an interferometric system to analyze transparent samples using interferograms generated by a phase-shifting radial shear grating interferometer for two cases: the first obtaining n simultaneous phase-shifting interferograms using a coherent light source and the second one using sequential phase steps with a white light source. For the first case, the simultaneous interferograms are generated using two optical systems: the first one generates the polarized pattern while the second one consists of a 4f system creating replicas of the output interferograms. By using a 2D sinusoidal phase grating, we have the advantage of obtaining up to nine replicated interferograms, all of them with comparable intensities and having amplitudes modulated by the 2D sinusoidal phase grating diffraction orders as zero-order Bessel’s functions. To obtain the optical phase map, several phase shifts are generated by placing a polarizing filter covering each replicated interferogram. We highlight the advantage of using n simultaneous interferograms by comparing resulting optical phases processed by a conventional four-step algorithm against those obtained by an implemented n=N+1 method, reducing errors with noisy interferograms. Results for n=7 and n=9 cases are presented. In addition, we have tested the setup with white light interference techniques by employing the polarizer radial shearing interferometer; for this case, the optical phase is calculated with the four-step and the three-step algorithms. Results of testing the developed system to examine static and dynamic phase objects are also included.

Low-pass filtering compensation in common-path digital holographic microscopy

Abstract: A low-pass filtering compensation (LPFC) method is proposed to compensate for phase aberrations in point diffraction-based common-path digital holographic microscopy. This method estimates the phase aberration from the object hologram by Fourier transform and low-pass spatial filtering. The estimated phase aberration is subtracted from the object phase image to achieve single-hologram phase compensation. The accuracy and capability of LPFC for phase compensation were demonstrated by experiments on a Ronchi grating and a human blood smear. LPFC provides phase compensation for both smooth objects and objects containing abrupt edges, in the special case of a system with relatively high-frequency objects and low-frequency slight phase aberrations. LPFC operates without the need for fitting procedures, iterative steps, or prior knowledge of the optical parameters, which substantially simplifies the process of phase compensation in quantitative phase imaging.

Analysis and Design of Multi-Agent Systems in Spatial Frequency Domain: Application to Distributed Spatial Filtering in Sensor Networks

Abstract: This study attempts to analyze and design multi-agent systems in the spatial frequency domain and demonstrates that the spatial frequency-based approach is useful for distributed spatial filtering in sensor networks. First, we take the consensus of multi-agent systems ( i.e., letting the states of all agents converge to an identical value) as an example and analyze it using the concept of spatial frequencies. We then show that consensus by typical controllers corresponds to lowpass filtering in the spatial frequency domain. This demonstrates that spatial frequencies can characterize the behavior of multi-agent systems. Second, we present a controller design method in the spatial frequency domain. The designed controllers provide the feedback system with a desired spatial frequency characteristic given in advance. We further derive a sufficient condition for the spatial frequency characteristic to ensure that the designed controllers are distributed. Finally, the effectiveness and applicability of our design method are demonstrated through an example of distributed denoising in a sensor network.

Adaptive local threshold segmentation for Fourier spatial filtering in automatic analysis of digital speckle interferogram

Abstract: Automated extraction of the +1 term spectrum can greatly benefit the real-time measurement of dynamic deformation in the digital speckle pattern interferometry (DSPI). However, most spatial filtering methods are not satisfactory for automatic analysis because they need manual intervention or are unable to accurately extract multiple +1 term spectrums in one frequency distribution image. We propose an adaptive local threshold segmentation method for the Fourier spatial filtering of a three-dimensional DSPI system. This method first uses global thresholding to coarsely recognize the spectral regions and then adopts local thresholding to accurately determine the spatial filtering windows for each spectrum. Experimental result shows that the proposed adaptive local threshold segmentation can accurately extract multiple desired +1 term spectrums even if the intensities of different spectral regions differ greatly. In addition, experiments of the comparison between the automatic and manual spatial filtering and automatic analysis of dynamic deformation demonstrate that the proposed method can be used for the real-time measurement.

A Graph-Theoretic Approach for Spatial Filtering and Its Impact on Mixed-type Spatial Pattern Recognition in Wafer Bin Maps.

Abstract: Statistical quality control in semiconductor manufacturing hinges on effective diagnostics of wafer bin maps, wherein a key challenge is to detect how defective chips tend to spatially cluster on a wafer--a problem known as spatial pattern recognition. Recently, there has been a growing interest in mixed-type spatial pattern recognition--when multiple defect patterns, of different shapes, co-exist on the same wafer. Mixed-type spatial pattern recognition entails two central tasks: (1) spatial filtering, to distinguish systematic patterns from random noises; and (2) spatial clustering, to group filtered patterns into distinct defect types. Observing that spatial filtering is instrumental to high-quality mixed-type pattern recognition, we propose to use a graph-theoretic method, called adjacency-clustering, which leverages spatial dependence among adjacent defective chips to effectively filter the raw wafer maps. Tested on real-world data and compared against a state-of the-art approach, our proposed method achieves at least 46% gain in terms of internal cluster validation quality (i.e., validation without external class labels), and about ~5% gain in terms of Normalized Mutual Information--an external cluster validation metric based on external class labels. Interestingly, the margin of improvement appears to be a function of the pattern complexity, with larger gains achieved for more complex-shaped patterns.

A space-frequency localized approach of spatial filtering for motor imagery classification

Abstract: Classification of Motor Imagery (MI) signals is the heart of Brain-Computer Interface (BCI) based applications. Spatial filtering is an important step in this process that produce new set of signals for better discrimination of two classes of EEG signals. In this work, a new approach of spatial filtering called Space-Frequency Localized Spatial Filtering (SFLSF) is proposed to enhance the performances of MI classification. The SFLSF method initially divides the scalp-EEG channels into local overlapping spatial windows. Then a filter bank is used to divide the signals into local frequency bands. The group of channels, localized in space and frequency, are then processed with spatial filter, and features are subsequently extracted for classification task. Experimental results corroborate that the proposed space localization helps to increase the classification accuracy when compared to the existing methods using spatial filters. The classification performance is further improved when frequency localization is incorporated. Thus, the proposed space-frequency localized approach of spatial filtering helps to deliver better classification result which is consistently 3–5% higher than traditional methods.

Spatio-Temporal Filtering: Precise Beam Control Using Fast Beam Switching

Abstract: This paper presents a spatio-temporal filtering approach for beamforming with phased arrays. The approach takes advantage of fast beam switching in modern Si-integrated phased arrays enabled by integrated digital circuits. The key technique involves fast switching among spatial beams created using the phased array. The resulting time-averaged beam represents a new spatial filter that might not have been feasible using the phase and gain control resolution available in the phased array. We present the underlying theory, and perform extensive system measurements on a software defined phased array radio based on state-of-the-art 28GHz phased array ICs. We demonstrate three use cases of spatio-temporal beam control in measurement: a) side lobe reduction, b) multi-armed beam formation and c) null pointing. We demonstrate how this approach can enable high precision beam control even in systems with limited phase shifter resolution and/or systems without any gain control per antenna element.

Spatial filtering of structured light

Abstract: Spatial filtering is a commonly deployed technique to improve the quality of laser beams by optically filtering the noise. In the “textbook” example, the noise is usually assumed to be high frequency and the laser beam, Gaussian. In this case, the filtering is achieved by a simple pinhole placed at the common focal plane of two lenses. Here, we explain how to generalize the concept of spatial filtering to arbitrary beam profiles: spatial filtering of structured light. We show how to construct the spatial filters using a range of structured light examples and highlight under what conditions spatial filtering works. In the process, we address some misconceptions in the community as to how and when spatial filters can be applied, extend the concept of spatial filtering to arbitrary beam types, and provide a theoretical and experimental framework for further study at both the undergraduate and graduate level.

Nanoscale x-ray holotomography of human brain tissue with phase retrieval based on multienergy recordings

Abstract: X-ray cone-beam holotomography of unstained tissue from the human central nervous system reveals details down to subcellular length scales. This visualization of variations in the electron density of the sample is based on phase-contrast techniques using intensities formed by self-interference of the beam between object and detector. Phase retrieval inverts diffraction and overcomes the phase problem by constraints such as several measurements at different Fresnel numbers for a single projection. Therefore, the object-to-detector distance (defocus) can be varied. However, for cone-beam geometry, changing defocus changes magnification, which can be problematic in view of image processing and resolution. Alternatively, the photon energy can be altered (multi-E). Far from absorption edges, multi-E data yield the wavelength-independent electron density. We present the multi-E holotomography at the Gottingen Instrument for Nano-Imaging with X-Rays (GINIX) setup of the P10 beamline at Deutsches Elektronen-Synchrotron. The instrument is based on a combined optics of elliptical mirrors and an x-ray waveguide positioned in the focal plane for further coherence, spatial filtering, and high numerical aperture. Previous results showed the suitability of this instrument for nanoscale tomography of unstained brain tissue. We demonstrate that upon energy variation, the focal spot is stable enough for imaging. To this end, a double-crystal monochromator and automated alignment routines are required. Three tomograms of human brain tissue were recorded and jointly analyzed using phase retrieval based on the contrast transfer function formalism generalized to multiple photon energies. Variations of the electron density of the sample are successfully reconstructed.

Low-pass spatial filter based on 3D metamaterial rasorber with wideband absorption at high frequency

Abstract: This paper presents the design and analysis of a low-pass spatial filter which has wideband absorption at high frequency using a 3D metamaterial rasorber (MR). The unit cell of the 3D MR is composed of several stacked layers of square patches with tapered dimensions, which are separated by thin lossy dielectric laminas. Every two adjacent layers’ metallic patches constitute a resonance cavity, and the inside lossy dielectric substrate results in absorption at the resonance frequency. The stacked metal–dielectric laminas construct a frustum pyramid. With the dimensions of the resonance cavities tapering from the bottom layer to the top layer, the pyramid absorbs over their resonance frequencies so that wideband absorption can be achieved. Besides, the incident wave at the frequencies below all these resonance frequencies can transmit through these cavities. Hence, the pyramid also constructs a low-pass spatial filter. The operation mechanism of this 3D MR structure is analyzed from several aspects by numerical simulation, and experimental measurement has also been executed to verify the design. The 3D metamaterial rasorber performs as an absorber in the Ku-band and a low-pass filter below the X-band. The absorption band with absorptivity higher than 80% spans from 12.3 GHz to 18.2 GHz, and the insertion loss at the frequency below 11.1 GHz is less than 0.9 dB.

Nonlinear Spatial Filtering for Multichannel Speech Enhancement in Inhomogeneous Noise Fields

Abstract: A common processing pipeline for multichannel speech enhancement is to combine a linear spatial filter with a single-channel postfilter. In fact, it can be shown that such a combination is optimal in the minimum mean square error (MMSE) sense if the noise follows a multivariate Gaussian distribution. However, for non-Gaussian noise, this serial concatenation is generally suboptimal and may thus also lead to suboptimal results. For instance, in our previous work, we showed that a joint spatial-spectral nonlinear estimator achieves a performance gain of 2.6 dB segmental signal-to-noise ratio (SNR) improvement for heavy-tailed large-kurtosis multivariate noise compared to the traditional combination of a linear spatial beamformer and a postfilter.In this paper, we show that a joint spatial-spectral nonlinear filter is not only advantageous for noise distributions that are significantly more heavy-tailed than a Gaussian but also for distributions that model inhomogeneous noise fields while having rather low kurtosis. In experiments with artificially created noise we measure a gain of 1 dB for inhomogenous noise with low kurtosis and up to 2 dB for inhomogeneous noise fields with moderate kurtosis.