Kernel Wiener Filter and Its Application to Pattern Recognition

Abstract

The Wiener filter (WF) is widely used for inverse problems. From an observed signal, it provides the best estimated signal with respect to the squared error averaged over the original and the observed signals among linear operators. The kernel WF (KWF), extended directly from WF, has a problem that an additive noise has to be handled by samples. Since the computational complexity of kernel methods depends on the number of samples, a huge computational cost is necessary for the case. By using the first-order approximation of kernel functions, we realize KWF that can handle such a noise not by samples but as a random variable. We also propose the error estimation method for kernel filters by using the approximations. In order to show the advantages of the proposed methods, we conducted the experiments to denoise images and estimate errors. We also apply KWF to classification since KWF can provide an approximated result of the maximum a posteriori classifier that provides the best recognition accuracy. The noise term in the criterion can be used for the classification in the presence of noise or a new regularization to suppress changes in the input space, whereas the ordinary regularization for the kernel method suppresses changes in the feature space. In order to show the advantages of the proposed methods, we conducted experiments of binary and multiclass classifications and classification in the presence of noise.

Wavelet Based Non Local Means Algorithm for Efficient Denoising of MRI Images

“…This filter is the mean squares error-optimal stationary linear filter for images degraded by additive noise and blurring. It is usually applied in the frequency domain (by taking the Fourier transform) [3], due to linear motion or unfocussed optics Wiener filter is the most important technique for removal of blur in images. From a signal processing standpoint.…”

“…In this paper effectiveness of six denoising algorithms viz. median filter [2],wiener filter [3],wavelet filter [4],wavelet based wiener [5],NLM [6],wavelet based NLM [7] using MRI images in the presence of additive white Gaussian noise is compared. Wavelet filter [4] removes noise pretty well in smooth regions but perform poorly along the edges.…”

Spontaneous Rayleigh-Brillouin scattering spectral analysis based on the Wiener filter

“…It works in the frequency domain, attempting to minimize the impact of deconvolved noise at frequencies which have a poor signal-to-noise ratio. The Wiener filter is still widely applied in many fields, such as in the bionic wavelet domain for speech enhancement, 12 pattern recognition 13 and nondestructive evaluation 14 and so on. This paper uses the method of pseudo inverse and the truncated singular value decomposition (TSVD) method to get the Wiener filtering factor.…”

Binary image enhancement based on aperiodic stochastic resonance

“…Considering the complicated environment and random noise in its application field, the research on noisy binary image enhancement algorithms is of great significance. Over the years, most of traditional binary image enhancement methods such as median filter [3] and Wiener filter [4] are mainly focusing on eliminating noise. However, for binary image polluted by strong noise, these methods cannot acquire satisfactory effect.…”