Harold H. Szu

Fast simulated annealing

Abstract Simulated annealing is a stochastic strategy for searching the ground state. A fast simulated annealing (FSA) is a semi-local search and consists of occasional long jumps. The cooling schedule of the FSA algorithm is inversely linear in time which is fast compared with the classical simulated annealing (CSA) which is strictly a local search and requires the cooling schedule to be inversely proportional to the logarithmic function of time. A general D-dimensional Cauchy probability for generating the state is given. Proofs for both FSA and CSA are sketched. A double potential well is used to numerically illustrate both schemes.

Optical wavelet transform

The wavelet transform is implemented using an optical multichannel correlator with a bank of wavelet transform filters. This approach provides a shift-invariant wavelet transform with continuous translation and discrete dilation parameters. The wavelet transform filters can be in many cases simply optical transmittance masks. Experimental results show detection of the frequency transition of the input signal by the optical wavelet transform.

Nonconvex optimization by fast simulated annealing

Recent advances in the solution of nonconvex optimization problems use simulated annealing techniques that are considerably faster than exhaustive global search techniques. This letter presents a simulated annealing technique, which is t/log (t) times faster than conventional simulated annealing, and applies it to a multisensor location and tracking problem.

Wavelet transform as a bank of the matched filters

The wavelet transform is a powerful tool for the analysis of short transient signals. We detail the advantages of the wavelet transform over the Fourier transform and the windowed Fourier transform and consider the wavelet as a bank of the VanderLugt matched filters. This methodology is particularly useful in those cases in which the shape of the mother wavelet is approximately known a priori. A two-dimensional optical correlator with a bank of the wavelet filters is implemented to yield the time-frequency joint representation of the wavelet transform of one-dimensional signals.

Optical implementation of associative memory with controlled nonlinearity in the correlation domain

A mathematical model for incorporating controllable nonlinearity in the correlation domain of a conventional associative memory is described. Such a mechanism provides the flexibility of rapidly and arbitrarily changing the strengths of the stored states in an associative memory. Such a feature corresponds to shifting of attention in psychological terms. This attentive associative memory can be implemented optically. Results obtained with computer simulation and a design for a compact optical implementation are discussed.

Wavelet transforms and neural networks for compression and recognition

Abstract Robust recognition for image and speech processing needs data compression that preserves features. To accomplish this, we have utilized the discrete wavelet transforms and the continuous wavelet transforms (CWT) together with artificial neural networks (ANN) to achieve automatic pattern recognition. Our approach is motivated by the mathematical analog of the CWT to the human hearing and visual systems, e.g., the so-called Mexican hat and Gabor functions, Gaussian window, respectively. We develop an ANN method to construct an optimum mother wavelet that can organize sensor input data in the multiresolution format that seems to become essential for brainstyle computing. In one realization, the architecture of our ANN is similar to that of a radial basis function approach, except that each node is a wavelet having three learnable parameters: weight W ij , scale a, and shift b. The node is not a McCullouch-Pitts neuron but a “wave-on”. We still use a supervised learning conjugate gradient descent algorithm in these parameters to construct a “super-mother” wavelet from a superposition of a set of waveons-mother wavelets. Using these techniques, we can accomplish the signal-enhanced and feature-preserving compression, e.g., on the infrared images, that avoids the overtraining and overfitting that have plagued ANNs ability to generalize and abstract information.

Fast TSP algorithm based on binary neuron output and analog neuron input using the zero-diagonal interconnect matrix and necessary and sufficient constraints of the permutation matrix

Alleged difficulties of the original Hopfield and Tank (H-T) neural network model reported by G.V. Wilson and G.S. Pawley (1988) in attempting a scaled-up VLSI implementation of the traveling salesman problem (TSP) are clarified and repudiated. A simple refinement is presented that has sped up and eliminated the decaying dynamics compounded by the feeble and indecisive analog neurons having a self-decaying interconnect. In summary, the modified TSP version is based on binary neuronic output, analog neuronic input, a zero diagonal interconnect matrix, the necessary and sufficient constraint of a permutation matrix, Lagrangian multipliers a=b=c=1, and Eulers first-order integration with the step constant about 10/sup -4/. Programs, one written in True Basic running on a microcomputer (Macintosh Plus or Mac II) and the other written in C on a mainframe computer, are briefly mentioned.<<ETX>>

Optical wavelet matched filters for shift-invariant pattern recognition

We introduce optical wavelet matched filters that perform the wavelet transforms for edge enhancement and perform correlations between the wavelet coefficients for shift-invariant pattern recognition. These new bandpass matched filters show improved discrimination capability with respect to the conventional matched spatial filter and improved signal-to-noise ratio with respect to the phase-only matched filter.

A Maximum Entropy Approach to Unsupervised Mixed-Pixel Decomposition

Due to the wide existence of mixed pixels, the derivation of constituent components (endmembers) and their fractional proportions (abundances) at the subpixel scale has been given a lot of attention. The entire process is often referred to as mixed-pixel decomposition or spectral unmixing. Although various algorithms have been proposed to solve this problem, two potential issues still need to be further investigated. First, assuming the endmembers are known, the abundance estimation is commonly performed by employing a least-squares error criterion, which, however, makes the estimation sensitive to noise and outliers. Second, the mathematical intractability of the abundance non-negative constraint results in computationally expensive numerical approaches. In this paper, we propose an unsupervised decomposition method based on the classic maximum entropy principle, termed the gradient descent maximum entropy (GDME), aiming at robust and effective estimates. We address the importance of the maximum entropy principle for mixed-pixel decomposition from a geometric point of view and demonstrate that when the given data present strong noise or when the endmember signatures are close to each other, the proposed method has the potential of providing more accurate estimates than the popular least-squares methods (e.g., fully constrained least squares). We apply the proposed GDME to the subject of unmixing multispectral and hyperspectral data. The experimental results obtained from both simulated and real images show the effectiveness of the proposed method

Landsat Spectral Demixing a la Superresolution of Blind Matrix Inversion by Constraint MaxEnt Neural Nets

A single pixel of a Landsat image has seven channels receiving 0.1 to 10 microns of radiation from the ground within a 20 by 20 meter footprint. In principle, the pattern of seven values can be utilized to identify ground sources within the pixel footprint by using methodologies called spectral blind demixing of unknown sources when the reflectance matrix Wij for the ith object and the jth band is either partially or difficult to measure in the outer space.