Abstract
We propose an adaptive, data-driven thresholding method based on a recently developed idea of Minimum Noiseless Description Length (MNDL). MNDL Subspace Selection (MNDL-SS) is a novel method of selecting an optimal subspace among the competing subspaces of the transformed noisy data. Here we extend the application of MNDL-SS for thresholding purposes. The approach searches for the optimum threshold for the data coefficients in an orthonormal basis. It is shown that the optimum threshold can be extracted from the noisy coefficients themselves. While the additive noise in the available data is assumed to be independent, the main challenge in MNDL thresholding is caused by the dependence of the additive noise in the sorted coefficients. The approach provides new hard and soft thresholds. Simulation results are presented for orthonormal wavelet transforms. While the method is comparable with the existing thresholding methods and in some cases outperforms them, the main advantage of the new approach is that it provides not only the optimum threshold but also an estimate of the associated mean-square error (MSE) for that threshold simultaneously.
Highlights
We can recognize different phenomena by collecting data from them
We first demonstrate the performance of Minimum Noiseless Description Length (MNDL) hard and soft thresholding by using two well-known examples in wavelet denoising
We proposed thresholding method based on the MNDLSS approach
Summary
We can recognize different phenomena by collecting data from them. defective instruments, problems with the data acquisition process, and the interference of natural factors can all degrade the data of interest. Denoising is often a necessary step in data processing and various approaches have been introduced for this purpose Some of these methods, such as Wiener filters, are grouped as linear techniques. Researchers have improved the performance of denoising methods by developing nonlinear approaches such as [1,2,3,4,5,6] These approaches have succeeded in providing better results, they are usually computationally exhaustive, hard to implement, or use particular assumptions either on the noisy data or on the class of the data estimator. The fundamentals of MSE estimation are similar to the method proposed in Minimum Noiseless Description Length (Codelength) Subspace Selection (MNDL-SS) [10]. Each subspace in this approach keeps a subset of the coefficients and discards the rest.
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