A risk-estimation-based formulation for speech enhancement and its relation to Wiener filtering

The goal of speech enhancement algorithms is to provide an estimate of clean speech starting from noisy observations. The often-employed cost function is the mean square error (MSE). However, the MSE can never be computed in practice. Therefore, it becomes necessary to find practical alternatives to the MSE. In image denoising problems, the cost function (also referred to as risk) is often replaced by an unbiased estimator. Motivated by this approach, we reformulate the problem of speech enhancement from the perspective of risk minimization. Some recent contributions in risk estimation have employed Stein's unbiased risk estimator (SURE) together with a parametric denoising function, which is a linear expansion of threshold/bases (LET). We show that the first-order case of SURE-LET results in a Wiener-filter type solution if the denoising function is made frequency-dependent. We also provide enhancement results obtained with both techniques and characterize the improvement by means of local as well as global SNR calculations.

Spatially Adaptive Kernel Regression Using Risk Estimation

An important question in kernel regression is one of estimating the order and bandwidth parameters from available noisy data. We propose to solve the problem within a risk estimation framework. Considering an independent and identically distributed (i.i.d.) Gaussian observations model, we use Stein's unbiased risk estimator (SURE) to estimate a weighted mean-square error (MSE) risk, and optimize it with respect to the order and bandwidth parameters. The two parameters are thus spatially adapted in such a manner that noise smoothing and fine structure preservation are simultaneously achieved. On the application side, we consider the problem of image restoration from uniform/non-uniform data, and show that the SURE approach to spatially adaptive kernel regression results in better quality estimation compared with its spatially non-adaptive counterparts. The denoising results obtained are comparable to those obtained using other state-of-the-art techniques, and in some scenarios, superior.

Application of nonlinear filtering to credit risk

Merton's model views equity as a call option on the asset of the firm. Thus the asset is partially observed through the equity. Then using nonlinear filtering an explicit expression for likelihood ratio for underlying parameters in terms of the nonlinear filter is obtained. As the evolution of the filter itself depends on the parameters in question, this does not permit direct maximum likelihood estimation, but does pave the way for the `Expectation-Maximization' method for estimating parameters. (C) 2010 Elsevier B.V. All rights reserved.

A generalized Stein's estimation approach to speech enhancement based on perceptual criteria

We address the problem of speech enhancement using a risk- estimation approach. In particular, we propose the use the Stein’s unbiased risk estimator (SURE) for solving the problem. The need for a suitable finite-sample risk estimator arises because the actual risks invariably depend on the unknown ground truth. We consider the popular mean-squared error (MSE) criterion first, and then compare it against the perceptually-motivated Itakura-Saito (IS) distortion, by deriving unbiased estimators of the corresponding risks. We use a generalized SURE (GSURE) development, recently proposed by Eldar for MSE. We consider dependent observation models from the exponential family with an additive noise model,and derive an unbiased estimator for the risk corresponding to the IS distortion, which is non-quadratic. This serves to address the speech enhancement problem in a more general setting. Experimental results illustrate that the IS metric is efficient in suppressing musical noise, which affects the MSE-enhanced speech. However, in terms of global signal-to-noise ratio (SNR), the minimum MSE solution gives better results.

Probable maximum precipitation estimation for catchments in Mahanadi river basin

Probable maximum precipitation (PMP) is a theoretical concept that is widely used by hydrologists to arrive at estimates for probable maximum flood (PMF) that find use in planning, design and risk assessment of high-hazard hydrological structures such as flood control dams upstream of populated areas. The PMP represents the greatest depth of precipitation for a given duration that is meteorologically possible for a watershed or an area at a particular time of year, with no allowance made for long-term climatic trends. Various methods are in use for estimation of PMP over a target location corresponding to different durations. Moisture maximization method and Hershfield method are two widely used methods. The former method maximizes the observed storms assuming that the atmospheric moisture would rise up to a very high value estimated based on the maximum daily dew point temperature. On the other hand, the latter method is a statistical method based on a general frequency equation given by Chow. The present study provides one-day PMP estimates and PMP maps for Mahanadi river basin based on the aforementioned methods. There is a need for such estimates and maps, as the river basin is prone to frequent floods. Utility of the constructed PMP maps in computing PMP for various catchments in the river basin is demonstrated. The PMP estimates can eventually be used to arrive at PMF estimates for those catchments. (C) 2015 The Authors. Published by Elsevier B.V.