1D Cellular Automata for Pulse Width Modulated Compressive Sampling CMOS Image Sensors

Compressive sensing (CS) is an alternative to the Shannon limit when the signal to be acquired is known to be sparse or compressible in some domain. Since compressed samples are non-hierarchical packages of information, this acquisition technique can be employed to overcome channel losses and restricted data rates. The quality of the compressed samples that a sensor can deliver is affected by the measurement matrix used to collect them. Measurement matrices usually employed in CS image sensors are recursive random-like binary matrices obtained using pseudo-random number generators (PRNG). In this paper we analyse the performance of these PRNGs in order to understand how their non-idealities affect the quality of the compressed samples. We present the architecture of a CMOS image sensor that uses class-III elementary cellular automata (ECA) and pixel pulse width modulation (PWM) to generate onchip a measurement matrix and high the quality compressed samples.Ministerio de Economía y Competitividad TEC2015-66878-C3-1-RJunta de Andalucía TIC 2338-2013Office of Naval Research N000141410355CONACYT (Mexico) MZO-2017-29106

Compressive Imaging Using RIP-Compliant CMOS Imager Architecture and Landweber Reconstruction

In this paper, we present a new image sensor architecture for fast and accurate compressive sensing (CS) of natural images. Measurement matrices usually employed in CS CMOS image sensors are recursive pseudo-random binary matrices. We have proved that the restricted isometry property of these matrices is limited by a low sparsity constant. The quality of these matrices is also affected by the non-idealities of pseudo-random number generators (PRNG). To overcome these limitations, we propose a hardware-friendly pseudo-random ternary measurement matrix generated on-chip by means of class III elementary cellular automata (ECA). These ECA present a chaotic behavior that emulates random CS measurement matrices better than other PRNG. We have combined this new architecture with a block-based CS smoothed-projected Landweber reconstruction algorithm. By means of single value decomposition, we have adapted this algorithm to perform fast and precise reconstruction while operating with binary and ternary matrices. Simulations are provided to qualify the approach.Ministerio de Economía y Competitividad TEC2015-66878-C3-1-RJunta de Andalucía TIC 2338-2013Office of Naval Research (USA) N000141410355European Union H2020 76586

Local Causal States and Discrete Coherent Structures

Coherent structures form spontaneously in nonlinear spatiotemporal systems and are found at all spatial scales in natural phenomena from laboratory hydrodynamic flows and chemical reactions to ocean, atmosphere, and planetary climate dynamics. Phenomenologically, they appear as key components that organize the macroscopic behaviors in such systems. Despite a century of effort, they have eluded rigorous analysis and empirical prediction, with progress being made only recently. As a step in this, we present a formal theory of coherent structures in fully-discrete dynamical field theories. It builds on the notion of structure introduced by computational mechanics, generalizing it to a local spatiotemporal setting. The analysis' main tool employs the \localstates, which are used to uncover a system's hidden spatiotemporal symmetries and which identify coherent structures as spatially-localized deviations from those symmetries. The approach is behavior-driven in the sense that it does not rely on directly analyzing spatiotemporal equations of motion, rather it considers only the spatiotemporal fields a system generates. As such, it offers an unsupervised approach to discover and describe coherent structures. We illustrate the approach by analyzing coherent structures generated by elementary cellular automata, comparing the results with an earlier, dynamic-invariant-set approach that decomposes fields into domains, particles, and particle interactions.Comment: 27 pages, 10 figures; http://csc.ucdavis.edu/~cmg/compmech/pubs/dcs.ht

Slime mould computes planar shapes

Computing a polygon defining a set of planar points is a classical problem of modern computational geometry. In laboratory experiments we demonstrate that a concave hull, a connected alpha-shape without holes, of a finite planar set is approximated by slime mould Physarum polycephalum. We represent planar points with sources of long-distance attractants and short-distance repellents and inoculate a piece of plasmodium outside the data set. The plasmodium moves towards the data and envelops it by pronounced protoplasmic tubes

A new class of multiscale lattice cell (MLC) models for spatio-temporal evolutionary image representation

Spatio-temporal evolutionary (STE) images are a class of complex dynamical systems that evolve over both space and time. With increased interest in the investigation of nonlinear complex phenomena, especially spatio-temporal behaviour governed by evolutionary laws that are dependent on both spatial and temporal dimensions, there has been an increased need to investigate model identification methods for this class of complex systems. Compared with pure temporal processes, the identification of spatio-temporal models from observed images is much more difficult and quite challenging. Starting with an assumption that there is no apriori information about the true model but only observed data are available, this study introduces a new class of multiscale lattice cell (MLC) models to represent the rules of the associated spatio-temporal evolutionary system. An application to a chemical reaction exhibiting a spatio-temporal evolutionary behaviour, is investigated to demonstrate the new modelling framework

Massively parallel computing on an organic molecular layer

Current computers operate at enormous speeds of ~10^13 bits/s, but their principle of sequential logic operation has remained unchanged since the 1950s. Though our brain is much slower on a per-neuron base (~10^3 firings/s), it is capable of remarkable decision-making based on the collective operations of millions of neurons at a time in ever-evolving neural circuitry. Here we use molecular switches to build an assembly where each molecule communicates-like neurons-with many neighbors simultaneously. The assembly's ability to reconfigure itself spontaneously for a new problem allows us to realize conventional computing constructs like logic gates and Voronoi decompositions, as well as to reproduce two natural phenomena: heat diffusion and the mutation of normal cells to cancer cells. This is a shift from the current static computing paradigm of serial bit-processing to a regime in which a large number of bits are processed in parallel in dynamically changing hardware.Comment: 25 pages, 6 figure

Automatic Filters for the Detection of Coherent Structure in Spatiotemporal Systems

Most current methods for identifying coherent structures in spatially-extended systems rely on prior information about the form which those structures take. Here we present two new approaches to automatically filter the changing configurations of spatial dynamical systems and extract coherent structures. One, local sensitivity filtering, is a modification of the local Lyapunov exponent approach suitable to cellular automata and other discrete spatial systems. The other, local statistical complexity filtering, calculates the amount of information needed for optimal prediction of the system's behavior in the vicinity of a given point. By examining the changing spatiotemporal distributions of these quantities, we can find the coherent structures in a variety of pattern-forming cellular automata, without needing to guess or postulate the form of that structure. We apply both filters to elementary and cyclical cellular automata (ECA and CCA) and find that they readily identify particles, domains and other more complicated structures. We compare the results from ECA with earlier ones based upon the theory of formal languages, and the results from CCA with a more traditional approach based on an order parameter and free energy. While sensitivity and statistical complexity are equally adept at uncovering structure, they are based on different system properties (dynamical and probabilistic, respectively), and provide complementary information.Comment: 16 pages, 21 figures. Figures considerably compressed to fit arxiv requirements; write first author for higher-resolution version