UNBIASED RISK ESTIMATES FOR SINGULAR VALUE THRESHOLDING AND SPECTRAL ESTIMATORS By
نویسندگان
چکیده
In an increasing number of applications, it is of interest to recover an approximately low-rank data matrix from noisy observations. This paper develops an unbiased risk estimate—holding in a Gaussian model—for any spectral estimator obeying some mild regularity assumptions. In particular, we give an unbiased risk estimate formula for singular value thresholding (SVT), a popular estimation strategy which applies a soft-thresholding rule to the singular values of the noisy observations. Among other things, our formulas offer a principled and automated way of selecting regularization parameters in a variety of problems. In particular, we demonstrate the utility of the unbiased risk estimation for SVT-based denoising of real clinical cardiac MRI series data. We also give new results concerning the differentiability of certain matrix-valued functions.
منابع مشابه
An Optimised SVD with SFLA & ABC for Spectrum Sensing in Cognitive Radio
The aim of this study is to focus on spectrum sensing in cognitive radio which is a recently introduced technology in order to increase the spectrum efficiency. We studied the Singular value decomposition based signal detector and its advantages over the energy based signal detection. Soft thresholding technique for spectrum sensing is optimized using SFLA (Shuffled Frog Leaping) and Ant Bee Co...
متن کاملAdaptive Thresholding for Sparse Covariance Matrix Estimation
In this article we consider estimation of sparse covariance matrices and propose a thresholding procedure that is adaptive to the variability of individual entries. The estimators are fully data-driven and demonstrate excellent performance both theoretically and numerically. It is shown that the estimators adaptively achieve the optimal rate of convergence over a large class of sparse covarianc...
متن کاملNonlinear spectral density estimation: thresholding the correlogram
Traditional kernel spectral density estimators are linear as a function of the sample autocovariance sequence. The purpose of the present paper is to propose and analyze two new spectral estimation methods that are based on the sample autocovariances in a nonlinear way. The rate of convergence of the new estimators is quantified, and practical issues such as bandwidth and/or threshold choice ar...
متن کاملMri Medical Image Denoising by Combined Spectral Subtraction and Wavelet Based Methods
Image denoising is a compromise between the removal of the largest possible amount of noise and the preservation of signal integrity and image resolution. To address this issue, a new hybrid approach is proposed by fusing dual band spectral subtraction and wavelet packet based thresholding method. The dual band spectral subtraction method (SS) is used for preprocessing of noisy MRI images in or...
متن کاملMathematical methods for spectral image reconstruction
We present a method for recovery of damaged parts of old paintings (frescoes), caused by degradation of the pigments contained in the paint layer. The original visible colour information in the damaged parts can be faithfully recovered from measurements of absorption spectra in the invisible region (IR and UV) and from the full spectral data of the well preserved parts of the image. We use the ...
متن کامل