l_p-norm optimum filters for image recognition. Part I. Algorithms

摘要

Ordinarily, filters are derived from the optimization of certain expressions with respect to the mean squared metric. We construct a family of linear and nonlinear processors (filters) for image recognition that is l_p-norm optimum in terms of tolerance to input noise and discrimination capabilities. The l_p norm is the generalization of the usual mean squared (l_2) norm, which we obtain by replacing the exponent 2 with any positive constant p (usually p >=1). These processors are developed by minimizing the l_p norm of the filer output that is due to the input scene and the output that is due to input noise. We use the l_p norm to measure the size of the filter output that is due to noise so that we can obtain greater freedom in adjusting the noise robustness and discrimination capabilities. We give a unified theoretical basis for developing these filters. This family of filters includes some of the existing linear and nonlinear filters, giving us a subfamilies of processors, which we denote by H_q~(#sigma#) and H_q. The values of q control the discrimination capabilities and the robustness of the processors. The parameter #sigma# is the standard deviation of the noise process.