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Face recognition on mobile devices, such as personal digital assistants and cell phones, is a big challenge owing to the limited computational resources available to run verifications on the devices themselves. One approach is to transmit the captured face images by use of the cell-phone connection and to run the verification on a remote station. However, owing to limitations in communication bandwidth, it may be necessary to transmit a compressed version of the image. We propose using the image compression standard JPEG2000, which is a wavelet-based compression engine used to compress the face images to low bit rates suitable for transmission over low-bandwidth communication channels. At the receiver end, the face images are reconstructed with a JPEG2000 decoder and are fed into the verification engine. We explore how advanced correlation filters, such as the minimum average correlation energy filter [Appl. Opt. 26, 3633 (1987)] and its variants, perform by using face images captured under different illumination conditions and encoded with different bit rates under the JPEG2000 wavelet-encoding standard. We evaluate the performance of these filters by using illumination variations from the Carnegie Mellon University's Pose, Illumination, and Expression (PIE) face database. We also demonstrate the tolerance of these filters to noisy versions of images with illumination variations.

We introduce wavelet packet correlation filter classifiers. Correlation filters are traditionally designed in the image domain by minimization of some criterion function of the image training set. Instead, we perform classification in wavelet spaces that have training set representations that provide better solutions to the optimization problem in the filter design. We propose a pruning algorithm to find these wavelet spaces by using a correlation energy cost function, and we describe a match score fusion algorithm for applying the filters trained across the packet tree. The proposed classification algorithm is suitable for any object-recognition task. We present results by implementing a biometric recognition system that uses the NIST 24 fingerprint database, and show that applying correlation filters in the wavelet domain results in considerable improvement of the standard correlation filter algorithm.

As storage density increases, the performance of volume holographic storage channels is degraded, because intersymbol interference and noise also increase. Equalization and detection methods must be employed to mitigate the effects of intersignal interference and noise. However, the output detector array in a holographic storage system detects the intensity of the incident light's wave front, leading to loss of sign information. This sign loss precludes the applicability of conventional equalization and detection schemes. We first address channel modeling under quadratic nonlinearity and develop an efficient model named the discrete magnitude-squared channel model. We next introduce an advanced equalization method called the iterative magnitude-squared decision feedback equalization (IMSDFE), which takes the channel nonlinearity into account. The performance of IMSDFE is quantified for optical-noise-dominated channels as well as for electronic-noise-dominated channels. Results indicate that IMSDFE is a good candidate for a high-density, high-intersignal-interference volume holographic storage channel.

Using biometrics for subject verification can significantly improve security over that of approaches based on passwords and personal identification numbers, both of which people tend to lose or forget. In biometric verification the system tries to match an input biometric (such as a fingerprint, face image, or iris image) to a stored biometric template. Thus correlation filter techniques are attractive candidates for the matching precision needed in biometric verification. In particular, advanced correlation filters, such as synthetic discriminant function filters, can offer very good matching performance in the presence of variability in these biometric images (e.g., facial expressions, illumination changes, etc.). We investigate the performance of advanced correlation filters for face, fingerprint, and iris biometric verification.

We introduce what is to our knowledge a new nonlinear shift-invariant classifier called the polynomial distance classifier correlation filter (PDCCF). The underlying theory extends the original linear distance classifier correlation filter [Appl. Opt. 35, 3127 (1996)] to include nonlinear functions of the input pattern. This new filter provides a framework (for combining different classification filters) that takes advantage of the individual filter strengths. In this new filter design, all filters are optimized jointly. We demonstrate the advantage of the new PDCCF method using simulated and real multi-class synthetic aperture radar images.

A new correlation filter formulation (that we refer to as the minimax distance transform correlation filter (MDTCF) is presented that minimizes the average squared distance from the filtered desired (or true-) class training images to a filtered reference image while maximizing the mean squared distance of the filtered undesired (or false-) class training images to this filtered reference image. This approach increases the separation between the false-class correlation outputs and the true-class correlation outputs. Classification can be performned using the squared distance of a filtered test image to the chosen filtered reference image. We show that the previously introduced distance classifier correlation filter (DCCF) is similar to a special case of MDTCF. We also examine the differences between the DCCF and the MDTCF, and show that MDTCF can offer increased discrimination performance. Also, MDTCF performance is evaluated on two different face databases.

Correlation filters have traditionally been designed without much attention given to the issue of the training images within a class or the relative spatial position between classes. We examine the impact of training-set registration on correlation-filter performance and develop techniques for centering the training images from a class that result in improved performance. We also show that it is beneficial to adjust the spatial position of the classes relative to one another. Although the proposed techniques are relevant for many types of correlation filter, we limit our discussion to algorithms for the maximum average correlation height filter and the distance classifier correlation filter.

When target densities of volume holographic data storage systems are increased, the systems experience increased interference from adjacent pixels and noise. Here we present a method for designing and applying linear minimum mean-squared-error (LMMSE) equalization to improve the bit error rates (BER's) and hence the storage densities achievable. Numerical results with five defocused data pages indicate that a significant improvement in the BER is possible with LMMSE equalization.

We present two different channel models (the magnitude model and the intensity model) for a pixel-matched volume holographic data storage system that employs the 4-focal-length architecture. First, a framework to describe the channel models is developed. We evaluate the linearity of the channel models by comparing data values obtained from diffraction-limited interference with data values predicted by the channel models. The models are evaluated for linearity and equalization gain under different storage and read-back conditions, such as fill factors, apertures, and contrast ratios. Bit error rate results obtained by use of linear equalization methods in conjunction with the channel models developed are also presented. Our results suggest that the magnitude model leads to better performance when the fill factors are small, whereas the intensity model appears to be more appropriate for the high-fill-factor cases. The magnitude model, when suitable, appears to provide a storage density improvement of as great as 65%, whereas the intensity model seems capable of providing as much as 15% density gain through deconvolution. The optimum aperture for storage seems to be close to the Nyquist aperture.

We describe a correlation-based distance-classifier scheme for the recognition and the classification of multiple classes. The underlying theory uses shift-invariant filters to compute distances between the input image and ideal references under an optimum transformation. The original distance-classifier correlation filter was developed for a two-class problem. We introduce a distance-classifier correlation filter that simultaneously considers multiple classes, and we show that the earlier two-class formulation is a special case of the classifier presented. Initial results are presented to demonstrate the discrimination- and distortion-tolerance capabilities of the proposed filter.

The circular-harmonic-function correlation filter originally proposed by Hsu and Arsenault [Appl. Opt. 21, 4016 (1982)] for in-plane rotation invariance uses only one harmonic, which results in poor discrimination capability of the filter. Various methods to use multiple harmonics were explored previously by different researchers. We present a new method to combine multiple circular harmonics into a single filter that can provide the desired correlation response to in-plane rotation while minimizing the correlation-plane energy. Since multiple harmonics are included, the filter can discriminate well, and since correlation-plane energy is minimized, correlation peaks tend to be sharp. Since the designer can specify the desired in-plane rotation response, a variety of filter behaviors (including complete invariance to input rotations) can be obtained. Underlying theory is discussed, and simulation results are presented.

A mathematical analysis of the distortion tolerance in correlation filters is presented. A good measure for distortion performance is shown to be a generalization of the minimum average correlation energy criterion. To optimize the filter's performance, we remove the usual hard constraints on the outputs in the synthetic discriminant function formulation. The resulting filters exhibit superior distortion tolerance while retaining the attractive features of their predecessors such as the minimum average correlation energy filter and the minimum variance synthetic discriminant function filter. The proposed theory also unifies several existing approaches and examines the relationship between different formulations. The proposed filter design algorithm requires only simple statistical parameters and the inversion of diagonal matrices, which makes it attractive from a computational standpoint. Several properties of these filters are discussed with illustrative examples.

A tutorial survey is presented of the many composite filter designs proposed for distortion-invariant optical pattern recognition. Remarks are made throughout regarding areas for further investigation.

Expressions are derived for real filters that have a maximum correlation signal to noise ratio. Both continuous and discrete cases are treated and shown to have similar forms. The signal can be complex, and the case of a real signal is considered and related to previous results.

Very efficient suboptimal algorithms for the design of phase-only filters and binary phase-only filters are presented. A reduction of 2- to 3-orders of magnitude in computer time is obtained over previous algorithms. The loss in signal-to-noise ratio is negligible (<0.001 dB).

Several performance criteria are described to enable a fair comparison among the various correlation filter designs: signal-to-noise ratio, peak sharpness, peak location, light efficiency, discriminability, and distortion invariance. The trade-offs resulting between some of these criteria are illustrated with the help of a new family of filters called fractional power filters (FPFs). The classical matched filter, phase-only filter (POF), and inverse filter are special cases of FPFs. Using examples, we show that the POF appears to provide a good compromise between noise tolerance and peak sharpness.

We introduce the notion of optimal phase-only filters (OPOFs) that yield improved signal to noise ratios (SNRs). We illustrate the improvement in SNR resulting from the use of OPOFs with the help of several analytical examples and simulation results.

The power spectral density estimate obtained by an acoustooptic (AO) system is analyzed. We find that the variance of the estimate depends on the ratio T(2)/T(1), where T(1) is the aperture of the AO cell and T(2) is the integration time of the detector.

The performance of distortion-invariant correlation filters in the presence of background clutter is addressed. Background images are modeled as Markov noise processes, and a synthesis procedure for the optimal filter is described. It is shown that spatially filtering the training set images eliminates the need for the inversion of large noise covariance matrices, thus leading to a computationally efficient filter realization. The effect of errors (in the estimation of clutter correlation coefficient) on filter performance is theoretically analyzed, and a bound on the relative degradation of the SNR due to such errors is presented.

A new 2-D acoustooptic processor that estimates the angular as well as spectral distributions of jammers in the far field of an adaptive phased array radar is described. The operating modes of the system are discussed together with the estimation accuracy achieved. Experimental results are presented to illustrate the operation of the processor, and different acoustooptic cell operating modes are discussed.

Correlations of binarized data and gray-scale data in the presence of additive noise are compared using two performance criteria (mean ratio and peak-to-sidelobe ratio). General expressions are provided to evaluate these performance measures as a function of input data length, bandwidth, and signal-to-noise ratio. We find that binarized correlators outperform gray-scale correlators when the input SNR(i) exceeds a threshold level that depends on input bandwidth and sequence length.

The synthesis of a new category of spatial filters that produces sharp output correlation peaks with controlled peak values is considered. The sharp nature of the correlation peak is the major feature emphasized, since it facilitates target detection. Since these filters minimize the average correlation plane energy as the first step in filter synthesis, we refer to them as minimum average correlation energy filters. Experimental laboratory results from optical implementation of the filters are also presented and discussed.

Three power methods to compute the eigenvalues and eigenvectors of a matrix on an iterative optical processor (IOP) are analyzed. Each is appropriate for a different eigenvalue and eigenvector application. When implementation on an IOP and the processing speed are considered, the second method is found to be preferable to others recently described.

The signal model used and the output SNR(0) measure chosen are shown to affect the performance of an acoustooptic time-integrating correlator. Nonuniform acoustic fields are also shown to affect the results, but these error sources can be overcome with a new hybrid time- and space-integrating acoustooptic matched filter correlator that we describe and for which initial simulation data are provided.

An optical image plane correlator is described which computes the ambiguity function for passive, wideband, complex, and basebanded signals. Quadrature input modulation, single-sideband filtering, and a modified image plane correlator requiring no moving parts are used to achieve the required complex correlations. The scenario, theory, and design are provided together with experimental verification on LFM and Barkercoded waveforms as well as synthetic data.

The bias and variance of the delay estimation from a time integrating acoustooptic correlator are considered. A parabolic interpolation of the sampled correlation output is included. General expressions for the bias and variance are derived that include the effect of finite detector element area. Quantitative data are provided for the case of an exponential autocorrelation signal model as functions of various system, signal, and noise parameters. These results show that the estimate is biased. They also provide guidelines on the delay estimation variance obtainable from a given system and on the design of a system to achieve a desired estimation accuracy.

It is shown that proper selection of constraint phases in minimum variance synthetic discriminant functions can further reduce the output variance due to input noise. It is demonstrated with the help of examples that this reduction in variance can range from being negligible to being significant. The exact amount of reduction depends on the constraint magnitudes, training images, and the noise covariance matrix.

An efficient algorithm for designing a ternary valued filter yielding the highest signal to noise ratio (SNR) is utlined. Numerical evaluations using the image of a tank indicate that using such a filter can provide an improvement in SNR of ~5 dB over the conventional binary phase-only filter (BPOF). This is superior to the 1-dB improvement obtained for that image by varying the threshold line angle (TLA) in filter binarization. Simulation results are presented. They agree with the numerically computed SNRs.

Simple expressions are derived for the loss in signal-tonoise ratio when a real filter is used instead of a complex filter in an optical correlator.