Kernel adaptive filter

About: Kernel adaptive filter is a research topic. Over the lifetime, 8771 publications have been published within this topic receiving 142711 citations.

Adaptive trimmed mean filters for image restoration

Abstract: An adaptive smoothing filter is proposed for reducing noise in digital signals of any dimensionality. The adaptive procedure is based on the selection of an appropriate inner or outer trimmed mean filter according to local measurements of the tail behavior (impulsivity) of the noise process. The set of trimmed means used provides robustness against a wide range of noise possibilities ranging from very shallow tailed to very heavy tailed. A Monte Carlo analysis using a family of generalized exponential distributions supports the choice of the trimmed mean selected for measured values of an impulsivity statistic. The assumption underlying the definition of the filter is that the signal to be filtered is locally smoothly varying, and that the noise process is uncorrelated and derives from an unknown, unimodal symmetric distribution. For image-processing applications, a second statistic is used to mark the location of abrupt intensity changes, or edges; in the vicinity of an edge, the trend-preserving median filter is used. Since the impulsivity and edge statistics used in defining the adaptive filter are both functions of order statistics, the extra computation required for their calculation is minimal. Examples are provided of the filter as applied to images corrupted by a variety of noises. >

Kernel Risk-Sensitive Loss: Definition, Properties and Application to Robust Adaptive Filtering

Abstract: Nonlinear similarity measures defined in kernel space, such as correntropy, can extract higher order statistics of data and offer potentially significant performance improvement over their linear counterparts especially in non Gaussian signal processing and machine learning. In this paper, we propose a new similarity measure in kernel space, called the kernel risk-sensitive loss (KRSL), and provide some important properties. We apply the KRSL to adaptive filtering and investigate the robustness, and then develop the MKRSL algorithm and analyze the mean square convergence performance. Compared with correntropy, the KRSL can offer a more efficient performance surface, thereby enabling a gradient-based method to achieve faster convergence speed and higher accuracy while still maintaining the robustness to outliers. Theoretical analysis results and superior performance of the new algorithm are confirmed by simulation.

Data record-based criteria for the selection of an auxiliary vector estimator of the MMSE/MVDR filter

Abstract: When the auxiliary vector (AV) filter generation algorithm utilizes sample average estimated input data statistics, it provides a sequence of estimates of the ideal minimum mean-square error or minimum-variance distortionless-response filter for the given signal processing/receiver design application. Evidently, early nonasymptotic elements of the sequence offer favorable bias/variance balance characteristics and outperform in mean-square filter estimation error the unbiased sample matrix inversion (SMI) estimator as well as the (constraint) least-mean square, recursive least-squares, "multistage nested Wiener filter", and diagonally-loaded SMI filter estimators. Selecting the most successful (in some appropriate sense) AV filter estimator in the sequence for a given data record is a critical problem that has not been addressed so far. We deal exactly with this problem and we propose two data-driven selection criteria. The first criterion minimizes the cross-validated sample average variance of the AV filter output and can be applied to general filter estimation problems; the second criterion maximizes the estimated J-divergence of the AV filter output conditional distributions and is tailored to binary phase-shift-keying-type detection problems.

Digital filter bank design quadratic-constrained formulation

Abstract: Formulate the filter bank design problem as an quadratic-constrained least-squares minimization problem. The solution of the minimization problem converges very quickly since the cost function as well as the constraints are quadratic functions with respect to the unknown parameters. The formulations of the perfect-reconstruction cosine-modulated filter bank, of the near-perfect-reconstruction pseudo-QMF bank, and of the two-channel biorthogonal linear-phase filter bank are derived using the proposed approach. Compared with other design methods, the proposed technique yields PR filter banks with much higher stopband attenuation. The proposed technique can also be extended to design multidimensional filter banks. >

Encoding and decoding video signals using adaptive filter switching criteria

Abstract: Reference frames are generated by selectively filtering blocks of decoded video frames. The decision whether to filter a block is based on a comparison of an energy measure value generated for the block and an energy measure threshold value corresponding to the quantization level used to encode the block. The energy measure threshold value for a given quantization level is selected by analyzing the results of encoding and decoding training video frames using that quantization level. The reference frames are used in encoding and decoding video frames using interframe processing.