Research And Design Of Sparse Two-dimensional FIR Notch Filter

The 2-D(Two-dimensional)FIR notch filter has a good filtering effect on the noise interference of a specific frequency existing in the 2-D signal,and thus has been widely concerned and applied.However,the number of tap coefficients of a 2-D filter is generally large,which results in the enormous computation and the high hardware power consumption.In this dissertation,the design of sparse 2-D FIR notch filter is studied in order to reduce the number of non-zero coefficients in the tap coefficients matrix.Three methods for designing spares 2-D FIR notch filters are as follows:(1)A design method of sparse 2-D FIR notch filters based on iterative weighted orthogonal matching pursuit(IROMP)algorithm is proposed.First,a sparse 2-D FIR filter with notch frequency at the origin is developed as the prototype filter.Second,a spectrum shifting procedure is applied to the sparse 2-D prototype filter to produce the sparse 2-D notch filter with the given notch frequency.And then the linear optimization procedure is applied to ensure a solution that meets the given design specifications.The application examples demonstrate the usefilness of the proposed scheme both in the quality of the solutions obtained and the image processing.(2)A design method of sparse 2-D FIR notch filter based on linear neural network is proposed.Firstly,the position set of non-ze,ro coefficients in the 2-D FTR filter coefficient matrix is obtained by IROMP algorithm.Then,the columns of the frequency sampling matrix corresponding to the non-zero coefficients positions is used as the input of the neural network,and the idal frequency response,e used as the ideal output of the linear neural network.The input parameters are trained by the neural network.The weights and thresh olds are adjusted continuously to minimize the.error between the output of the neural network and the ideal output.The coefficient matrix of the sparse 2-D FIR notch filter can be obtained by extracting the weights and thresholds of the linear neural network and apply the zero padding procedure according to the set of non-zero coefficients.Simulation results demonstrate that the proposed scheme can obtain sparse solutions and is effective in image processing.(3)A design method of sparse 2-D FIR notch filter based on Hopfield neural network is proposed.Firstly,according to the design parameters of the 2-D FIR notch filter and the structure of Hopfield neural network,the Lyapunov energy function of the neural network is bonded to the error function of the 2-D FIR notch filter.Then,the non-zero coefficient position set in the coefficient matrix of the 2-D FIR filter is obtained by orthogonal matching pursuit(OMP)algorithm.The coefficients corresponding to the positions of non-zero coefficients are inputted into the Hopfield neural network for training.When the Lyapunov energy function of the neural network converges,the error function of the designed filter reaches the minimum value.At this time,the output of the neural network is the optimal non-zero coefficients,and it is padded with zero according to the position set of non-zero coefficients.Simulation results demonstrate that the proposed scheme can obtain sparse solutions and is effective in image processing.