Optical wavelet matched filter

Optical nonsubsampled contourlet transform

The nonsubsampled contourlet transform (NSCT) is a fully shift-invariant, multiscale, and multidirectional expansion implemented in optics using the Fourier transform of its filters. In this paper, we propose a novel optical NSCT filter design method and the corresponding post-processing method to avoid the use of holographic techniques. The novel optical NSCT filter has real and non-negative Fourier transforms. The input image is placed in the input plane of the VanderLugt 4f correlator, and these real and non-negative Fourier transform NSCT filters are placed in the frequency plane of the VanderLugt 4f correlator. Next, the NSCT result is captured by a CCD in the output plane of the VanderLugt 4f correlator, and its perfect reconstruction is theoretically possible, which is demonstrated by both simulation and optical experiment.

Implementing wavelet inverse-transform processor with surface acoustic wave device

The objective of this research was to investigate the implementation schemes of the wavelet inverse-transform processor using surface acoustic wave (SAW) device, the length function of defining the electrodes, and the possibility of solving the load resistance and the internal resistance for the wavelet inverse-transform processor using SAW device. In this paper, we investigate the implementation schemes of the wavelet inverse-transform processor using SAW device. In the implementation scheme that the input interdigital transducer (IDT) and output IDT stand in a line, because the electrode-overlap envelope of the input IDT is identical with the one of the output IDT (i.e. the two transducers are identical), the product of the input IDT's frequency response and the output IDT's frequency response can be implemented, so that the wavelet inverse-transform processor can be fabricated. X-112(0)Y LiTaO(3) is used as a substrate material to fabricate the wavelet inverse-transform processor. The size of the wavelet inverse-transform processor using this implementation scheme is small, so its cost is low. First, according to the envelope function of the wavelet function, the length function of the electrodes is defined, then, the lengths of the electrodes can be calculated from the length function of the electrodes, finally, the input IDT and output IDT can be designed according to the lengths and widths for the electrodes. In this paper, we also present the load resistance and the internal resistance as the two problems of the wavelet inverse-transform processor using SAW devices. The solutions to these problems are achieved in this study. When the amplifiers are subjected to the input end and output end for the wavelet inverse-transform processor, they can eliminate the influence of the load resistance and the internal resistance on the output voltage of the wavelet inverse-transform processor using SAW device.

Solution to the influence of the MSSW propagating velocity on the bandwidths of the single-scale wavelet-transform processor using MSSW device

The objective of this research was to investigate the possibility of solving the influence of the magnetostatic surface wave (MSSW) propagating velocity on the bandwidths of the single-scale wavelet transform processor using MSSW device. The motivation for this work was prompted by the processor that -3dB bandwidth varies as the propagating velocity of MSSW changes. In this paper, we present the influence of the magnetostatic surface wave (MSSW) propagating velocity on the bandwidths as the key problem of the single-scale wavelet transform processor using MSSW device. The solution to the problem is achieved in this study. we derived the function between the propagating velocity of MSSW and the -3dB bandwidth, so we know from the function that -3dB bandwidth of the single-scale wavelet transform processor using MSSW device varies as the propagating velocity of MSSW changes. Through adjusting the distance and orientation of the permanent magnet, we can implement the control of the MSSW propagating velocity, so that the influence of the MSSW propagating velocity on the bandwidths of the single-scale wavelet transform processor using MSSW device is solved.

A novel compensation method of insertion losses for wavelet inverse-transform processors using surface acoustic wave devices

The objective of this research was to investigate the possibility of compensating for the insertion losses of the wavelet inverse-transform processors using SAW devices. The motivation for this work was prompted by the processors which are of large insertion losses. In this paper, the insertion losses are the key problem of the wavelet inverse-transform processors using SAW devices. A novel compensation method of the insertion losses is achieved in this study. When the output ends of the wavelet inverse-transform processors are respectively connected to the amplifiers, their insertion losses can be compensated for. The bandwidths of the amplifiers and their adjustment method are also given in this paper.

Wavelet filter for improving detection performance of compression-based joint transform correlator

A new method for improving fingerprint detections by a compression-based joint transform correlator (JTC) via wavelet filter is proposed. The simulation results show that the proposed method has advantages over the conventional compression-based JTC in that detection performance can be maximized to be higher than a classical JTC by using a smaller file size for the compressed-reference images.

Wavelet-modified maximum average correlation height filter for rotation invariance that uses chirp encoding in a hybrid digital-optical correlator

We discuss and implement a wavelet-modified maximum average correlation height (MACH) filter for 0 degrees -360 degrees in-plane rotations in a hybrid digital-optical correlator. Use of a wavelet transform improves the performance of the MACH filter by reducing the number of filters that are required to identify a target rotated at any angle between 0 degrees and 360 degrees in-plane rotations and enhances the autocorrelation peak intensity significantly. The output of a hybrid digital-optical correlator contains two autocorrelation peaks and a strong dc. Using a chirp function with the wavelet-modified MACH filter, the correlation signals are focused in three different planes. Thus placing a peak-capturing CCD camera at a particular plane, only one autocorrelation peak is recorded, discarding the strong dc and other autocorrelation peaks. A signal-to-noise ratio has been calculated as a metric of goodness of the proposed wavelet-modified MACH filter.

Liquid crystal polarization-converting devices for edge and corner extractions of images using optical wavelet transforms

Optical properties of radially polarized light generated by liquid crystal (LC) polarization-converting devices with two LC molecular orientations (+/-180 degrees and +/-90 degrees twist modes) are measured and the applicability to optical wavelet transforms (WTs) are discussed. It is found that the radially polarized lights in both the +/-180 degrees and +/-90 degrees twist modes can be regarded as wavelets. Based on the principle of WT, feature extractions of a simple binary image are carried out by applying the LC polarization-converting device to a shadow-casting system. Unique feature extraction properties of the shadow-casting system using the LC polarization-converting device and a LC microlens array are discussed. It is experimentally confirmed that edge and corner features are successfully extracted using the LC polarization-converting device with +/-180 degrees and +/-90 degrees twist modes, respectively.

Optical security system for the protection of personal identification information

A new optical security system for the protection of personal identification information is proposed. First, authentication of the encrypted personal information is carried out by primary recognition of a personal identification number (PIN) with the proposed multiplexed minimum average correlation energy phase-encrypted (MMACE_p) filter. The MMACE_p filter, synthesized with phase-encrypted training images, can increase the discrimination capability and prevent the leak of personal identification information. After the PIN is recognized, speedy authentication of personal information can be achieved through one-to-one optical correlation by means of the optical wavelet filter. The possibility of information counterfeiting can be significantly decreased with the double-identification process. Simulation results demonstrate the effectiveness of the proposed technique.

Continuous-scale-invariant pattern recognition with adaptive-wavelet-matched filters

We designed and implemented a composite-wavelet-matched filter that is invariant to continuous-scale changes of the input and is useful for correlation-based pattern recognition of objects whose size is not known exactly. We optimize the adaptive wavelet to extract sparse image features and use the scale-space analysis to determine the wavelet scale for the scale invariance. Experimental results obtained by use of a programmable optical correlator with three liquid-crystal spatial light modulators are demonstrated.

Hologram reconstruction by use of optical wavelet transform

High-speed in-line holography is used to visualize the trajectories of glass fibers being drawn out in a turbulent flame. To improve the signal-to-noise ratio, the images are not observed by a conventional reconstruction setup, but the holographic plate is placed directly on the input plane of a wavelet-transform optical system. This processing system is based on a VanderLugt correlator with inclusion of an electrically addressed spatial light modulator. The shape of the matched filters is deduced by successive rotation and dilatation operations of wavelet functions in the Fourier domain. We estimate the three-dimensional location of a fiber element and its orientation by searching for the daughter wavelet that yields the maximum intensity on the output plane of the correlator, which also contains the reconstructed image. The results are compared with those obtained by conventional optical reconstruction. The signal-to-noise ratios of the images observed on the output plane are improved. Moreover, it is shown that the axis coordinate accuracy is improved to Dz = +/-50 microm, instead of +/-0.5 mm for holographic reconstruction.

Wavelet transform methods for object detection and recovery

We show that a biorthogonal spline wavelet closely approximates the prewhitening matched filter for detecting Gaussian objects in Markov noise. The filterbank implementation of the wavelet transform acts as a hierarchy of such detectors operating at discrete object scales. If the object to be detected is Gaussian and its scale happens to coincide with one of those computed by the wavelet transform, and if the background noise is truly Markov, then optimum detection is realized by thresholding the appropriate subband image. In reality, the Gaussian may be a rather coarse approximation of the object, and the background noise may deviate from the Markov assumption. In this case, we may view the wavelet decomposition as a means for computing an orthogonal feature set for input to a classifier. We use a supervised linear classifier applied to feature vectors comprised of samples taken from the subbands of an N-octave, undecimated wavelet transform. The resulting map of test statistic values indicates the presence and location of objects. The object itself is reconstructed by using the test statistic to emphasize wavelet subbands, followed by computing the inverse wavelet transform. We show two contrasting applications of the wavelets-based object recovery algorithm. For detecting microcalcifications in digitized mammograms, the object and noise models closely match the real image data, and the multiscale matched filter paradigm is highly appropriate. The second application, extracting ship outlines in noisy forward-looking infrared images, is presented as a case where good results are achieved despite the data models being less well matched to the assumptions of the algorithm.