Quantum holography for image recognition

Gabor wavelet is considered the best mathematical descriptor for receptive fields in the striate cortex. As a basis function, it is suitable to sparsely represent natural scenes due to its property in maximizing information. It is argued that Gabor-like receptive fields emerged by the sparseness-enforcing or infomax method, with sparseness-enforcing being more biologically plausible. This paper incorporates Gabor over-complete representation into Quantum Holography for image recognition tasks. Correlations are performed using sampled result from all frequencies as well as the optimum frequency. Correlation is also performed using only those points of least activity, which shows improvements in recognition. Analysis on the use of conjugation in reconstruction is provided. The authors also suggest improvements through iterative methods for reconstruction. DOI: 10.4018/jnmc.2010010104 International Journal of Nanotechnology and Molecular Computation, 2(1), 44-61, January-March 2010 45 Copyright © 2010, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. condition, enabling reconstruction of highresolution images from the wavelets. This, of course, is a lot more convenient than finding biorthogonal function which is quite difficult (Bastiaan, 1980). According to (Grossman, 1989), this overcompleteness provides a robust representation that is able to be stored by low precision neurons through redundancy. Besides, it provides a good medium for tasks like image segmentation. (Daugman, 1988; Lee, 1996) Normal images are generally highly self-correlated due to internal morphological consistency, which should be utilized and exploited in image recognition (Daugman, 1988). Field (1993) shows that wavelet is the most suitable descriptor for natural images, which is relatively sparse compared to total spectral or spatial domain representation. Under the general cases, Gabor wavelet function can extract maximum information from an input image (Okajima, 1998). As shown by (Linsker, 1988), 1993, the RF of neurons employ an information-theoretic method by maximizing mutual information. He showed that mutualinformation maximization is related to Hebbian learning rule for neural network connectivity (Linsker, 1988). Gabor-like receptive fields can emerge by sparseness-enforcing (Olshausen & Field, 1996, 1997) or by an Infomax method (Bell & Sejnowski, 1995, 1997). Both methods produce Gabor-like outputs as statistically independent scene-components. (Peruš, 2001a, 2005) have argued that the Olshausen-Field method is more biologically plausible than Bell-Sejnowski approach. According to (Pribram, 1991), there is a triple convolution for preliminary visual pathway from retina to lateral geniculate nucleus (LGN) to the striate cortex (V1), with the 1st and 2nd convoluted with a Difference-of-Gaussian function and the 3rd with the Gabor wavelet. Since this paper focuses on the Gabor transform in image recognition, the 1st and 2nd stage of the visual pathway with not be touched upon. Images are convoluted with the Gabor-like receptive field which is then conveyed to V1 hyper-column that is overcomplete where every point of the column is selective to a particular orientation and ocular dominance (Hubel & Wiesel, 1962). According to (Pribram, 1991), the spectral image in V1 is inversed to the spatial topologically correct image into V2. Either spatial or spectral representation can be processed by Hebbian-like association for image recognition and other tasks. For this paper, we report on our motivation to use Gabor wavelet for image recognition using Quantum associative network as well as the processes involved in transformation and reconstruction. It also serves as a preliminary for research work on exploiting the information maximization of Gabor wavelet. A brief description of quantum associative network is given in section 2. In section 3, we talk about the applicability of wavelet for natural scenes and defining the Gabor wavelet family we will be concentrating on. Section 4 is about the reconstruction processes. Analysis on the method of reconstruction we applied will be performed, as well as methods of improvements for image reconstruction through iterative method. Recognition tests for different poses and different persons are given in section 5 using all frequency and optimum frequency sampling and also sampling with points of least activity to maximize orthogonality. Quantum associative Memory A quantum implementable model has been proposed by (Peruš, 2001ab, 2004ab, 2005) for associative memory for image recognition. For the associative model, an n by m image (n m N ́ = ) is represented as a vector