Derivation of Residual Noise of Filtered Poisson and Gaussian Series

Author(s):  
W. Yao ◽  
J. B. Farr
2019 ◽  
Vol 28 (1) ◽  
pp. 114-124
Author(s):  
Linda W. Norrix ◽  
Julie Thein ◽  
David Velenovsky

Purpose Low residual noise (RN) levels are critically important when obtaining electrophysiological recordings of threshold auditory brainstem responses. In this study, we examine the effectiveness and efficiency of Kalman-weighted averaging (KWA) implemented on the Vivosonic Integrity System and artifact rejection (AR) implemented on the Intelligent Hearing Systems SmartEP system for obtaining low RN levels. Method Sixteen adults participated. Electrophysiological measures were obtained using simultaneous recordings by the Vivosonic and Intelligent Hearing Systems for subjects in 2 relaxed conditions and 4 active motor conditions. Three averaging times were used for the relaxed states (1, 1.5, and 3 min) and for the active states (1.5, 3, and 6 min). Repeated-measures analyses of variance were used to examine RN levels as a function of noise reduction strategy (i.e., KWA, AR) and averaging time. Results Lower RN levels were obtained using KWA than AR in both the relaxed and active motor states. Thus, KWA was more effective than was AR under the conditions examined in this study. Using KWA, approximately 3 min of averaging was needed in the relaxed condition to obtain an average RN level of 0.025 μV. In contrast, in the active motor conditions, approximately 6 min of averaging was required using KWA. Mean RN levels of 0.025 μV were not attained using AR. Conclusions When patients are not physiologically quiet, low RN levels are more likely to be obtained and more efficiently obtained using KWA than AR. However, even when using KWA, in active motor states, 6 min of averaging or more may be required to obtain threshold responses. Averaging time needed and whether a low RN level can be attained will depend on the level of motor activity exhibited by the patient.


2018 ◽  
Vol 618 ◽  
pp. A29 ◽  
Author(s):  
T. Trombetti ◽  
C. Burigana ◽  
G. De Zotti ◽  
V. Galluzzi ◽  
M. Massardi

Recent detailed simulations have shown that an insufficiently accurate characterization of the contamination of unresolved polarized extragalactic sources can seriously bias measurements of the primordial cosmic microwave background (CMB) power spectrum if the tensor-to-scalar ratio r ∼ 0.001, as predicted by models currently of special interest (e.g., Starobinsky’s R2 and Higgs inflation). This has motivated a reanalysis of the median polarization fraction of extragalactic sources (radio-loud AGNs and dusty galaxies) using data from the Planck polarization maps. Our approach, exploiting the intensity distribution analysis, mitigates or overcomes the most delicate aspects of earlier analyses based on stacking techniques. By means of simulations, we have shown that the residual noise bias on the median polarization fraction, Πmedian, of extragalactic sources is generally ≲0.1%. For radio sources, we have found Πmedian ≃ 2.83%, with no significant dependence on either frequency or flux density, in good agreement with the earlier estimate and with high-sensitivity measurements in the frequency range 5–40 GHz. No polarization signal is detected in the case of dusty galaxies, implying 90% confidence upper limits of Πdusty ≲ 2.2% at 353 GHz and of ≲3.9% at 217 GHz. The contamination of CMB polarization maps by unresolved point sources is discussed.


2010 ◽  
Vol 28 (1) ◽  
pp. 015010 ◽  
Author(s):  
Christian Röver ◽  
Renate Meyer ◽  
Nelson Christensen

Author(s):  
Apurba Roy ◽  
Santi P. Maity

In many practical situations, magnetic resonance imaging (MRI) needs reconstruction of images at low measurements, far below the Nyquist rate, as sensing process may be very costly and slow enough so that one can measure the coefficients only a few times. Segmentation of such subsampled reconstructed MR images for medical analysis and diagnosis becomes a challenging task due to the inherent complex characteristics of the MR images. This paper considers reconstruction of MR images at compressive sampling (or compressed sensing (CS)) paradigm followed by its segmentation in an integrated platform. Image reconstruction is done from incomplete measurement space with random noise injection iteratively. A weighted linear prediction is done for the unobserved space followed by spatial domain denoising through adaptive recursive filtering. The reconstructed images, however, suffer from imprecise and/or missing edges, boundaries, lines, curvatures etc. and residual noise. Curvelet transform (CT) is purposely used for removal of noise and for edge enhancement through hard thresholding and suppression of approximate subbands, respectively. Then a fuzzy entropy-based clustering, using genetic algorithms (GAs), is done for segmentation of sharpen MR Image. Extensive simulation results are shown to highlight performance improvement of both image reconstruction and segmentation of the reconstructed images along with relative gain over the existing works.


Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 938
Author(s):  
Hyunho Choi ◽  
Jechang Jeong

Ultrasound (US) imaging can examine human bodies of various ages; however, in the process of obtaining a US image, speckle noise is generated. The speckle noise inhibits physicians from accurately examining lesions; thus, a speckle noise removal method is essential technology. To enhance speckle noise elimination, we propose a novel algorithm using the characteristics of speckle noise and filtering methods based on speckle reducing anisotropic diffusion (SRAD) filtering, discrete wavelet transform (DWT) using symmetry characteristics, weighted guided image filtering (WGIF), and gradient domain guided image filtering (GDGIF). The SRAD filter is exploited as a preprocessing filter because it can be directly applied to a medical US image containing speckle noise without a log-compression. The wavelet domain has the advantage of suppressing the additive noise. Therefore, a homomorphic transformation is utilized to convert the multiplicative noise into additive noise. After two-level DWT decomposition is applied, to suppress the residual noise of an SRAD filtered image, GDGIF and WGIF are exploited to reduce noise from seven high-frequency sub-band images and one low-frequency sub-band image, respectively. Finally, a noise-free image is attained through inverse DWT and an exponential transform. The proposed algorithm exhibits excellent speckle noise elimination and edge conservation as compared with conventional denoising methods.


Author(s):  
Yao Cheng ◽  
Dong Zou

Local means decomposition is an adaptive and nonparametric time–frequency decomposition method for nonstationary and nonlinear signals. However, in practice, local means decomposition is susceptible to mode mixing phenomena and produces different scale oscillations in one mode or similar scale oscillations in different modes, rendering the decomposition results difficult to interpret in terms of physical meansing. The noise-assisted ensemble local means decomposition method not only effectively resolved mode mixing but also generated a new problem, which tolerates residual noise in signal reconstruction. Targeting these shortcomings, this article proposes complementary ensemble local means decomposition, a novel noise-assisted time–frequency analysis method. First, an ensemble of white noise is added to the original signal via complementary positive and negative pairs. Second, local means decomposition is applied to decompose the noisy signals into a series of product functions, and the final results are obtained by averaging. The simulation results confirm that complementary ensemble local means decomposition offers an innovative improvement over ensemble local means decomposition in terms of eliminating residual noise. The superiority of the proposed method was further validated on fault signals obtained from faulty railway bearings (rolling element and outer race fault signals).


2020 ◽  
Vol 633 ◽  
pp. A95
Author(s):  
C.-H. Dahlqvist ◽  
F. Cantalloube ◽  
O. Absil

Context. Beyond the choice of wavefront control systems or coronographs, advanced data processing methods play a crucial role in disentangling potential planetary signals from bright quasi-static speckles. Among these methods, angular differential imaging (ADI) for data sets obtained in pupil tracking mode (ADI sequences) is one of the foremost research avenues, considering the many observing programs performed with ADI-based techniques and the associated discoveries. Aims. Inspired by the field of econometrics, here we propose a new detection algorithm for ADI sequences, deriving from the regime-switching model first proposed in the 1980s. Methods. The proposed model is very versatile as it allows the use of PSF-subtracted data sets (residual cubes) provided by various ADI-based techniques, separately or together, to provide a single detection map. The temporal structure of the residual cubes is used for the detection as the model is fed with a concatenated series of pixel-wise time sequences. The algorithm provides a detection probability map by considering two possible regimes for concentric annuli, the first one accounting for the residual noise and the second one for the planetary signal in addition to the residual noise. Results. The algorithm performance is tested on data sets from two instruments, VLT/NACO and VLT/SPHERE. The results show an overall better performance in the receiver operating characteristic space when compared with standard signal-to-noise-ratio maps for several state-of-the-art ADI-based post-processing algorithms.


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