3,580 research outputs found
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
MDL Denoising Revisited
We refine and extend an earlier MDL denoising criterion for wavelet-based
denoising. We start by showing that the denoising problem can be reformulated
as a clustering problem, where the goal is to obtain separate clusters for
informative and non-informative wavelet coefficients, respectively. This
suggests two refinements, adding a code-length for the model index, and
extending the model in order to account for subband-dependent coefficient
distributions. A third refinement is derivation of soft thresholding inspired
by predictive universal coding with weighted mixtures. We propose a practical
method incorporating all three refinements, which is shown to achieve good
performance and robustness in denoising both artificial and natural signals.Comment: Submitted to IEEE Transactions on Information Theory, June 200
Monte Carlo-based Noise Compensation in Coil Intensity Corrected Endorectal MRI
Background: Prostate cancer is one of the most common forms of cancer found
in males making early diagnosis important. Magnetic resonance imaging (MRI) has
been useful in visualizing and localizing tumor candidates and with the use of
endorectal coils (ERC), the signal-to-noise ratio (SNR) can be improved. The
coils introduce intensity inhomogeneities and the surface coil intensity
correction built into MRI scanners is used to reduce these inhomogeneities.
However, the correction typically performed at the MRI scanner level leads to
noise amplification and noise level variations. Methods: In this study, we
introduce a new Monte Carlo-based noise compensation approach for coil
intensity corrected endorectal MRI which allows for effective noise
compensation and preservation of details within the prostate. The approach
accounts for the ERC SNR profile via a spatially-adaptive noise model for
correcting non-stationary noise variations. Such a method is useful
particularly for improving the image quality of coil intensity corrected
endorectal MRI data performed at the MRI scanner level and when the original
raw data is not available. Results: SNR and contrast-to-noise ratio (CNR)
analysis in patient experiments demonstrate an average improvement of 11.7 dB
and 11.2 dB respectively over uncorrected endorectal MRI, and provides strong
performance when compared to existing approaches. Conclusions: A new noise
compensation method was developed for the purpose of improving the quality of
coil intensity corrected endorectal MRI data performed at the MRI scanner
level. We illustrate that promising noise compensation performance can be
achieved for the proposed approach, which is particularly important for
processing coil intensity corrected endorectal MRI data performed at the MRI
scanner level and when the original raw data is not available.Comment: 23 page
Analysis and Synthesis Prior Greedy Algorithms for Non-linear Sparse Recovery
In this work we address the problem of recovering sparse solutions to non
linear inverse problems. We look at two variants of the basic problem, the
synthesis prior problem when the solution is sparse and the analysis prior
problem where the solution is cosparse in some linear basis. For the first
problem, we propose non linear variants of the Orthogonal Matching Pursuit
(OMP) and CoSamp algorithms; for the second problem we propose a non linear
variant of the Greedy Analysis Pursuit (GAP) algorithm. We empirically test the
success rates of our algorithms on exponential and logarithmic functions. We
model speckle denoising as a non linear sparse recovery problem and apply our
technique to solve it. Results show that our method outperforms state of the
art methods in ultrasound speckle denoising
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