Many important problems in engineering and science are well-modeled by Poisson processes. A common technique for noise reduction is to use a filter. Wiener filter, which utilizes the second-order statistics of the Fourier decomposition, and the median filter which is based on the theory of order statistion, are normally used to denoise degraded images. Wavelet-based methods are powerful tools f...

A wildfire model is formulated based on balance equations for energy and fuel, where the fuel loss due to combustion corresponds to the fuel reaction rate. The resulting coupled partial differential equations have coefficients that can be approximated from prior measurements of wildfires. An ensemble Kalman filter technique with regularization is then used to assimilate temperatures measured at...

Estimation of the heat flux for a quenched solid tungsten sphere is demonstrated using a filter formulation. Even though the values of the thermal properties significantly change during quenching, nearly as accurate heat flux estimates as with a temperature-variable analyses are possible using the proposed filter method. The filter algorithm is very efficient for the repeated analyses of simila...

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...

In this paper we present a general formalism for the establishment of the family of selective partial update affine projection algorithms (SPU-APA). The SPU-APA, the SPU regularized APA (SPU-R-APA), the SPU partial rank algorithm (SPU-PRA), the SPU binormalized data reusing least mean squares (SPU-BNDR-LMS), and the SPU normalized LMS with orthogonal correction factors (SPU-NLMS-OCF) algorithms...

The area of mathematical inverse problems is quite broad and involves the qualitative and quantitative analysis of a wide variety of physical models. Applications include, for example, the problem of inverse heat conduction, image reconstruction, tomography, the inverse scattering problem, and the determination of unknown coefficients or boundary parameters appearing in partial differential equ...