Polynomial and rational filters for image enhancement, edge preserving noise smoothing, and interpolation of encoded images are usually designed as a weighted combination of nonlinear filters having lowpass or highpass behaviour. The choice of the filter components and of the coefficients is performed heuristically, though. In this paper general design constraints for polynomial and rational fi...

This paper is concerned with the regularization of linear ill-posed problems by a combination of data smoothing and fractional filter methods. For the data smoothing, a wavelet shrinkage denoising is applied to the noisy data with known error level δ. For the reconstruction, an approximation to the solution of the operator equation is computed from the data estimate by fractional filter methods...

INTRODUCTION Post processing of MR images is omnipresent: for fMRI in particular, smoothing of the raw images is frequently applied to gain SNR on the spatial scale of the BOLD response (‘matched filter’). This shaping of the point spread function (PSF) acts complementary to sampling itself, where the choice of a k-space trajectory imposes an intrinsic filter onto the data. We combine both appr...

Abstract: A smoothing finite impulse response (FIR) filter is addressed for discrete time-invariant state-space polynomial models commonly used to represent signals over finite data. A general gain is derived for the relevant p-lag unbiased smoothing FIR filter. Applications are given for the time interval errors of a local crystal clock and the United States Naval Observatory Master Clock. An ...

The aim of this paper is to propose a new approach to probability density function (PDF) estimation which is based on the fuzzy transform (F-transform) introduced by Perfilieva in [10]. Firstly, a smoothing filter based on the combination of the discrete direct and continuous inverse F-transform is introduced and some of the basic properties are investigated. Next, an alternative approach to PD...

Gaussian filter is widely used for image smoothing but it is well known that this type of filters blur the image features (e.g., edges). Two extensions of Gaussian filters will be discussed in this survey. One is the anisotropic filtering (bilateral filtering or PDE-based anisotropic diffusion) for feature-preserving smoothing and the other is the recursive implementation of various filters tha...

This paper presents a smoothing data association algorithm for a single target tracking in clutter. The proposed algorithm fuses the forward estimates and all the available measurement information retrodictions (but not backward track estimates) within the smoothing window to obtain the smoothed estimates. The measurement information retrodictions are obtained using the one-step-backward inform...

This paper proposes a double-talk-robust echo canceller using a smoothed-coefficient filter (SCF). The SCF’s tap coefficients are obtained by smoothing those of a pilot adaptive filter (PAF) for better accuracy and stability. The smoothing time constant is controlled by comparing mean squared high-pass errors of the SCF and the PAF. The high-pass filters enable precise control of the SCF by eli...

The smoothing problem for continuous systems is treated in a state space representation by means of variational calculus techniques. The smoothing problem is introduced in an criterion by means of an artificial discontinuity that splits the problem in term of forward and backward filtering problems. Hence, the smoother design is realized in three steps. First, a forward filter is developed. Sec...

This paper focuses on sequential Monte Carlo approximations of smoothing distributions in conditionally linear and Gaussian state spaces. To reduce Monte Carlo variance of smoothers, it is typical in these models to use Rao-Blackwellization: particle approximation is used to sample sequences of hidden regimes while the Gaussian states are explicitly integrated conditional on the sequence of reg...