Nonlinear Matched Filtering Research Articles

Robust multicarrier CDMA receiver for coded power-line communications

Existing indoor power-line grids are a potential solution to the last mile problem for broadband communication providers. However, power-line communication (PLC) channels suffer from deep frequency notches and severe impulsive noise making powerful signal processing essential if these channels are to be utilized. Broadband communications using Multicarrier Code Division Multiple Access(MC-CDMA) with channel coding is considered. Although resilient to frequency-selective fading, the coding gain from turbo signal processing is substantially compromised in the presence of impulsive noise. To overcome this, we propose a low complexity non-linear matched filter utilizing M-estimation technique. We will show that this matched M-estimate filter is indispensable in providing efficient baseband filtering in impulsive channels.

Photon-counting passive 3D image sensing for reconstruction and recognition of partially occluded objects

In this paper, we discuss the reconstruction and the recognition of partially occluded objects using photon counting integral imaging (II). Irradiance scenes are numerically reconstructed for the reference target in three-dimensional (3D) space. Photon counting scenes are estimated for unknown input objects using maximum likelihood estimation (MLE) of Poisson parameter. We propose nonlinear matched filtering in 3D space to recognize partially occluded targets. The recognition performance is substantially improved from the nonlinear matched filtering of elemental images without 3D reconstruction. The discrimination capability is analyzed in terms of Fisher ratio (FR) and receiver operating characteristic (ROC) curves.

Photon counting passive 3D image sensing for automatic target recognition

In this paper, we propose photon counting three-dimensional (3D) passive sensing and object recognition using integral imaging. The application of this approach to 3D automatic target recognition (ATR) is investigated using both linear and nonlinear matched filters. We find there is significant potential of the proposed system for 3D sensing and recognition with a low number of photons. The discrimination capability of the proposed system is quantified in terms of discrimination ratio, Fisher ratio, and receiver operating characteristic (ROC) curves. To the best of our knowledge, this is the first report on photon counting 3D passive sensing and ATR with integral imaging.

Real-time target recognition and tracking of vehicles moving on a street by matched filtering that uses quantization of modulated function to complexes of a quadrupole.

Vehicles moving on a street were monitored by a CCD digital TV camera and recognized in real time by a nonlinear matched filtering method, quantization of modulated function to complexes of a quadrupole, with a personal computer. In the nonlinear matched filtering method an input scene containing the vehicles is modulated in the frequency domain by matched filters, the modulated functions are quantized to complex numbers representing a quadrupole, and then quantized functions are inverse-Fourier transformed. In the frame time of an NTSC-TV system, autocorrelation signals of four vehicles were calculated and discriminated, and their peak positions were determined. Their correct loci in real time were tracked in sequential frames.

Binary encoding of gray-scale nonlinearly transformed filters for optical pattern recognition

A binary-encoded nonlinear matched filter for optical correlation is described. The gray-scale matchedfilter function, transformed by a general type of nonlinearity, is represented in a binary format by a threshold function that changes as a function of the spatial frequency. The output correlation term of the binary-encoded filter is equivalent to the output correlation term of the gray-scale nonlinear matched filter.

Binary representation of nonlinear correlators

We describe binary encoding of both gray scale nonlinear joint transform correlators and gray scale nonlinear matched filters. For the nonlinear joint transform correlator, the joint power spectrum transformed by various degrees of nonlinearity is represented in a binary format using a multiple level threshold function. For the nonlinear matched filter, the matched filter function transformed by a general type of nonlinearity, is represented in a binary format using a variable threshold function.

Experiments on nonlinearly transformed matched filters

Experiments on nonlinearly transformed matched filters for optical correlation are provided. Experimental results for the images tested indicate that nonlinear matched filters produce good correlation perlormance in terms of correlation peak intensity, signal-to-noise ratio, and peak-to-sidelobe ratio. The sensitivity of the <i>k</i>'th law nonlinearly transformed filter to rotational changes of the input signal is investigated. It is shown that for the images presented here, up to a certain degree of input signal rotation, a highly nonlinearly transformed matched filter may produce a larger peak-to-sidelobe ratio than a conventional matched filter.

Generalization of the linear matched filter concept to nonlinear matched filters

A nonlinear matched filter based image correlator is investigated. The linear matched filter is expressed as a bandpass function containing the amplitude and phase of the Fourier transform of the reference signal. The bandpass filter function is then applied to a kth law nonlinear device to produce the nonlinear matched filter function. Analytical expressions for the nonlinear matched filter are provided. The effects of the nonlinear transfer characteristics on the correlation signals at the output plane are investigated. The correlation signals are determined in terms of the nonlinear characteristics used to transform the filter. We show that the nonlinear filter results in a sum of infinite harmonic terms. Each harmonic term is envelope modulated due to the nonlinear characteristics of the device, and phase modulated by m times the phase modulation of the linear filter function. The correct phase information of the filter is recovered for the first-order harmonic of the series. The envelope of each harmonic term is proportional to the kth power of the Fourier transform magnitude of the reference signal. We show that various types of filter such as the continuous phase-only filters can be produced simply by varying the severity of the nonlinearity. Nonlinear filters provide higher correlation peak intensity and a better defined correlation spot.

Comparison on nonlinear joint transform correlator and nonlinear matched filter based correlator

We compare the performance of the nonlinear joint transform correlator, the nonlinearly transformed filter based correlator and the conventional linear correlator. The pattern recognition systems will be compared in the areas of correlation peak, peak to sidelobe ratio and the correlation width. We show that compared to the linear correlator, both types of nonlinear correlators produce better correlation performance.

Nonlinear matched filtering II

Symmetric nonlinear matched filters (SNMFs) involve the transformation of the signal spectrum and the filter transfer function through pointwise nonlinearities before they are multiplied in the transform domain. The resulting system is analogous to a multistage neural network. The experimental and theoretical results discussed indicate that SNMFs hold considerable potential to achieve a high power of discrimination and resolution and large SNR. The statistical analysis of a particular SNMF in the two-class problem indicates that the performance coefficient of the SNMF is about four times larger than the performance coefficient of the classical matched filter. In terms of resolving closeby signals, there seems to be no limit to the achievable resolution. However, artifacts should be carefully monitored.

Nonlinear matched filter based optical correlation

A nonlinear matched filter based optical correlation is presented. The nonlinear filter is produced by applying a nonlinear transformation to the linear matched filter.

Nonlinear matched filtering

A new class of nonlinear matched filters is discussed. These filters involve the transformation of the signal spectrum and the filter transfer function through a nonlinearity before they are multiplied in the transform domain. The resulting filter structures can be considered to be analogous to three-layer neural nets. They have better performance in terms of signal discrimination and lack of false correlation signals and artifacts than previously known filters. The matched filters are further subdivided into two major classes according to whether the filtering is based on a discrete Fourier transform (DFT) or a real discrete Fourier transform (RDFT). The DFT and the RDFT are approximations to the complex and real Fourier transforms, respectively. The RDFT-based filtering gives better performance in terms of signal discrimination and lack of false correlation signals and artifacts than the DFT-based filtering.