3,158 research outputs found
Generalized SURE for Exponential Families: Applications to Regularization
Stein's unbiased risk estimate (SURE) was proposed by Stein for the
independent, identically distributed (iid) Gaussian model in order to derive
estimates that dominate least-squares (LS). In recent years, the SURE criterion
has been employed in a variety of denoising problems for choosing
regularization parameters that minimize an estimate of the mean-squared error
(MSE). However, its use has been limited to the iid case which precludes many
important applications. In this paper we begin by deriving a SURE counterpart
for general, not necessarily iid distributions from the exponential family.
This enables extending the SURE design technique to a much broader class of
problems. Based on this generalization we suggest a new method for choosing
regularization parameters in penalized LS estimators. We then demonstrate its
superior performance over the conventional generalized cross validation
approach and the discrepancy method in the context of image deblurring and
deconvolution. The SURE technique can also be used to design estimates without
predefining their structure. However, allowing for too many free parameters
impairs the performance of the resulting estimates. To address this inherent
tradeoff we propose a regularized SURE objective. Based on this design
criterion, we derive a wavelet denoising strategy that is similar in sprit to
the standard soft-threshold approach but can lead to improved MSE performance.Comment: to appear in the IEEE Transactions on Signal Processin
Empirical Bayes and Full Bayes for Signal Estimation
We consider signals that follow a parametric distribution where the parameter
values are unknown. To estimate such signals from noisy measurements in scalar
channels, we study the empirical performance of an empirical Bayes (EB)
approach and a full Bayes (FB) approach. We then apply EB and FB to solve
compressed sensing (CS) signal estimation problems by successively denoising a
scalar Gaussian channel within an approximate message passing (AMP) framework.
Our numerical results show that FB achieves better performance than EB in
scalar channel denoising problems when the signal dimension is small. In the CS
setting, the signal dimension must be large enough for AMP to work well; for
large signal dimensions, AMP has similar performance with FB and EB.Comment: This work was presented at the Information Theory and Application
workshop (ITA), San Diego, CA, Feb. 201
Improving the performance of translation wavelet transform using BMICA
Research has shown Wavelet Transform to be one of the best methods for denoising biosignals. Translation-Invariant
form of this method has been found to be the best performance. In this paper however we utilize this method and merger with our newly created Independent Component Analysis method – BMICA. Different EEG signals are used to verify the method within the MATLAB environment. Results are then compared with those of the actual Translation-Invariant algorithm and evaluated using the performance measures Mean Square Error (MSE), Peak Signal to Noise Ratio (PSNR), Signal to Distortion Ratio (SDR), and Signal to Interference Ratio (SIR). Experiments revealed that the BMICA Translation-Invariant Wavelet Transform out performed in all four measures. This indicates that it performed superior to the basic Translation- Invariant Wavelet Transform algorithm producing cleaner EEG signals which can influence diagnosis as well as clinical studies of the brain
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