The path-integral analysis of an associative memory model storing an infinite number of finite limit cycles

It is shown that an exact solution of the transient dynamics of an associative memory model storing an infinite number of limit cycles with l finite steps by means of the path-integral analysis. Assuming the Maxwell construction ansatz, we have succeeded in deriving the stationary state equations of the order parameters from the macroscopic recursive equations with respect to the finite-step sequence processing model which has retarded self-interactions. We have also derived the stationary state equations by means of the signal-to-noise analysis (SCSNA). The signal-to-noise analysis must assume that crosstalk noise of an input to spins obeys a Gaussian distribution. On the other hand, the path-integral method does not require such a Gaussian approximation of crosstalk noise. We have found that both the signal-to-noise analysis and the path-integral analysis give the completely same result with respect to the stationary state in the case where the dynamics is deterministic, when we assume the Maxwell construction ansatz. We have shown the dependence of storage capacity (alpha_c) on the number of patterns per one limit cycle (l). Storage capacity monotonously increases with the number of steps, and converges to alpha_c=0.269 at l ~= 10. The original properties of the finite-step sequence processing model appear as long as the number of steps of the limit cycle has order l=O(1).Comment: 24 pages, 3 figure

Image restoration using HOS and the Radon transform

The authors propose the use of higher-order statistics (HOS) to study the problem of image restoration. They consider images degraded by linear or zero phase blurring point spread functions (PSF) and additive Gaussian noise. The complexity associated with the combination of two-dimensional signal processing and higher-order statistics is reduced by means of the Radon transform. The projection at each angle is an one-dimensional signal that can be processed by any existing 1-D higher-order statistics-based method. They apply two methods that have proven to attain good one-dimensional signal reconstruction, especially in the presence of noise. After the ideal projections have been estimated, the inverse Radon transform gives the restored image. Simulation results are provided.Peer ReviewedPostprint (published version

Adaptive digital signal processing Java teaching tool

This publication presents a JAVA program for teaching the rudiments of adaptive digital signal processing (DSP) algorithms and techniques. Adaptive DSP is on of the most important areas of signal processsing, and provides the core algorithmic means to implement applications ranging from mobile telephone speech coding, to noise cancellation, to communication channel equalization. Over the last 30 years adaptive digital signal processing has progressed from being a strictly graduate level advanced class in signal processing theory to a topic that is part of the core curriculum for many undergraduate signal processing classes. The JAVA applet presented in this publication has been devised for students to use in combination with lecture notes and/or one of the recognised textbooks such that they can quickly and conveniently simulate algorithms such as the LMS (least mean squares), RLS (recursive least squares) and so on in a variety of applications without requiring to write programs or scripts or using any special purpose software. By the very nature of the JAVA code therefore, the applet can be run from any browser, even over a low bandwidth modem connection

Minimization of multi-penalty functionals by alternating iterative thresholding and optimal parameter choices

Inspired by several recent developments in regularization theory, optimization, and signal processing, we present and analyze a numerical approach to multi-penalty regularization in spaces of sparsely represented functions. The sparsity prior is motivated by the largely expected geometrical/structured features of high-dimensional data, which may not be well-represented in the framework of typically more isotropic Hilbert spaces. In this paper, we are particularly interested in regularizers which are able to correctly model and separate the multiple components of additively mixed signals. This situation is rather common as pure signals may be corrupted by additive noise. To this end, we consider a regularization functional composed by a data-fidelity term, where signal and noise are additively mixed, a non-smooth and non-convex sparsity promoting term, and a penalty term to model the noise. We propose and analyze the convergence of an iterative alternating algorithm based on simple iterative thresholding steps to perform the minimization of the functional. By means of this algorithm, we explore the effect of choosing different regularization parameters and penalization norms in terms of the quality of recovering the pure signal and separating it from additive noise. For a given fixed noise level numerical experiments confirm a significant improvement in performance compared to standard one-parameter regularization methods. By using high-dimensional data analysis methods such as Principal Component Analysis, we are able to show the correct geometrical clustering of regularized solutions around the expected solution. Eventually, for the compressive sensing problems considered in our experiments we provide a guideline for a choice of regularization norms and parameters.Comment: 32 page

Time course and robustness of ERP object and face differences

Conflicting results have been reported about the earliest “true” ERP differences related to face processing, with the bulk of the literature focusing on the signal in the first 200 ms after stimulus onset. Part of the discrepancy might be explained by uncontrolled low-level differences between images used to assess the timing of face processing. In the present experiment, we used a set of faces, houses, and noise textures with identical amplitude spectra to equate energy in each spatial frequency band. The timing of face processing was evaluated using face–house and face–noise contrasts, as well as upright-inverted stimulus contrasts. ERP differences were evaluated systematically at all electrodes, across subjects, and in each subject individually, using trimmed means and bootstrap tests. Different strategies were employed to assess the robustness of ERP differential activities in individual subjects and group comparisons. We report results showing that the most conspicuous and reliable effects were systematically observed in the N170 latency range, starting at about 130–150 ms after stimulus onset

Networks for image acquisition, processing and display

The human visual system comprises layers of networks which sample, process, and code images. Understanding these networks is a valuable means of understanding human vision and of designing autonomous vision systems based on network processing. Ames Research Center has an ongoing program to develop computational models of such networks. The models predict human performance in detection of targets and in discrimination of displayed information. In addition, the models are artificial vision systems sharing properties with biological vision that has been tuned by evolution for high performance. Properties include variable density sampling, noise immunity, multi-resolution coding, and fault-tolerance. The research stresses analysis of noise in visual networks, including sampling, photon, and processing unit noises. Specific accomplishments include: models of sampling array growth with variable density and irregularity comparable to that of the retinal cone mosaic; noise models of networks with signal-dependent and independent noise; models of network connection development for preserving spatial registration and interpolation; multi-resolution encoding models based on hexagonal arrays (HOP transform); and mathematical procedures for simplifying analysis of large networks