C. Richard Johnson

Exponential convergence of recursive least squares with exponential forgetting factor

This paper demonstrates that, provided the system input is persistently exciting, the recursive least squares estimation algorithm with exponential forgetting factor is exponentially convergent. Further, it is shown that the incorporation of the exponential forgetting factor is necessary to attain this convergence and that the persistence of excitation is virtually necessary. The result holds for stable finite-dimensional, linear, time-invariant systems but has its chief implications to the robustness of the parameter estimator when these conditions fail.

CMA fractionally spaced equalizers: Stationary points and stability under i.i.d. and temporally correlated sources

A common assumption in blind equalization schemes using the Constant Modulus Algorithm (CMA) is that the source sequence is an independent identically distributed (i.i.d.) sequence with equiprobabl ...

Efficient channel shortening equalizer design

Time-domain equalization is crucial in reducing channel state dimension in maximum likelihood sequence estimation and intercarrier and intersymbol interference in multicarrier systems. A time-domain equalizer (TEQ) placed in cascade with the channel produces an effective impulse response that is shorter than the channel impulse response. This paper analyzes two TEQ design methods amenable to cost-effective real-time implementation: minimum mean square error (MMSE) and maximum shortening SNR (MSSNR) methods. We reduce the complexity of computing the matrices in the MSSNR and MMSE designs by a factor of 140 and a factor of 16 (respectively) relative to existing approaches, without degrading performance. We prove that an infinite-length MSSNR TEQ with unit norm TEQ constraint is symmetric. A symmetric TEQ halves FIR implementation complexity, enables parallel training of the frequency-domain equalizer and TEQ, reduces TEQ training complexity by a factor of 4, and doubles the length of the TEQ that can be designed using fixed-point arithmetic, with only a small loss in bit rate. Simulations are presented for designs with a symmetric TEQ or target impulse response.

PURSUING AUTOMATED CLASSIFICATION OF HISTORIC PHOTOGRAPHIC PAPERS FROM RAKING LIGHT IMAGES

Abstract Surface texture is a critical feature in the manufacture, marketing, and use of photographic paper. Raking light reveals texture through a stark rendering of highlights and shadows. Though close-up raking light images effectively document surface features of photographic paper, the sheer number and diversity of textures used for historic papers prohibits efficient visual classification. This work provides evidence that automatic, computer-based classification of texture documented with raking light is feasible by demonstrating an encouraging degree of success sorting a set of 120 images made from samples of historic silver gelatin paper. Using this dataset, four university teams applied different image-processing strategies for automatic feature extraction and degree of similarity quantification. All four approaches successfully detected strong affinities and outliers built into the dataset. The creation and deployment of the algorithms was carried out by the teams without prior knowledge of the distributions of similarities and outliers. These results indicate that automatic classification of silver gelatin photographic paper based on close-up texture images is feasible and should be pursued. To encourage the development of other classification schemes, the 120-sample “training” dataset used in this work is available to other academic researchers at http://www.PaperTextureID.org.

Characterizing persistent excitation for the sign-sign equation error identifier☆

Abstract The sign-sign (SS) algorithm is a computationally efficient adaptive identifier, often used in signal processing tasks. It is obtained by introducing signum functions on both the regressor and the prediction error multiplicands in the update kernel of the well-known LMS algorithm. This paper gives a deterministic persistent excitation condition on the regressor sequence which guarantees SS convergence. It also gives conditions under which SS may diverge, and discusses how these persistent excitation conditions may be verified through a finite amount of computations.

SINR, power efficiency, and theoretical system capacity of parallel interference cancellation

This paper analytically derives exact expressions for the SINR of the two-stage linear parallel interference cancellation (LPIC) and two-stage hard-decision parallel interference cancellation (HPIC) multiuser detectors in a synchronous, nonorthogonal, binary, CDMA communication system with deterministic short spreading sequences. We consider approximations to the SINR expressions that are justified in typical operating scenarios to obtain a more intuitive understanding of the SINR performance of the HPIC detector. We consider the case where a specific SINR requirement is given for each user in the system and derive expressions for the set of transmit powers necessary to meet this requirement when two-stage LPIC or HPIC detection is used. We also derive expressions for a measure of the theoretical system capacity using LPIC and HPIC detection, defined as the maximum number of users possible in a system with finite available transmit power. Numerical results are presented that compare the HPIC and LPIC detectors to the hard-decision successive interference cancellation (SIC) detector and matched filter (MF) detector. Our results suggest that HPIC detection may offer the best SINR and power efficiency performance when the number of users in the system is low to moderate and that SIC detection may offer superior performance when the number of users in the system is large.

Blind adaptive decision feedback equalization: A class of channels resulting in ill‐convergence from a zero initialization

This paper addresses the ill-convergence of blind adaptive decision feedback equalizers using the decision-directed algorithm under a zero initialization. In particular, the paper identifies analytically a class of channels for which the adaptive equalizer parameters converge to an undesired minimum where incorrect decision estimates can be made under zero noise. This misbehaviour occurs despite the existence of a DFE parameter setting that perfectly equalizes the channel.

Locally robust identification of linear systems containing unknown gain elements with application to adapted IIR lattice models

Abstract We consider the identification of stable linear systems whose unknown parameters may be interpreted as feedback gains. By using the output error between the true system and a model of it containing adjustable parameters, we develop a recursive algorithm for estimating the unknown parameters. We describe a persistency of excitation condition on the system input which guarantees a robust, local convergence property for the algorithm. We then apply our results to the identification of the parameters of a tapped lattice model of a linear, infinite-impulse response (IIR) plant. Considering the identification of a lattice, rather than a direct form, model of a linear system is attractive due to (i) the simplicity of its crucial stability check and maintenance procedure for the adapted IIR parametrization and (ii) the numerical insensitivity properties of the lattice structure. Reproducible simulation evidence is presented that supports our results.

Canvas Matches in Vermeer: A Case Study in the Computer Analysis of Fabric Supports

Old master paintings were executed on various types of support, most commonly on wood panel or canvas, but also on copper and other metal sheets, and much more rarely on slabs of stone, such as slate, alabaster, or marble. The type of wood (usually oak in northern Europe and poplar in Italy) and, when possible, dendrochronology can help determine the approximate period of a painting’s execution, country of origin, and, in some cases, authorship. The weave of a canvas (its pattern or fineness) may bear on the same questions or be otherwise revealing, for instance, by suggesting that two paintings were intended as a pair.1 For the past several years two of the present study’s authors, C. Richard Johnson Jr. and Don H. Johnson, have developed computer algorithms that allow an analysis of canvas weaves that is more precise than traditional methods.2 They have digitally mapped canvases used by European artists ranging in date from the 1450s (Dieric Bouts’s tüchlein paintings, in London, Los Angeles, and Pasadena) to Vincent van Gogh’s pictures of 1888 – 90 (187 canvases from that period alone).3 The results so far have been variously revealing for those artists and for Velázquez, Vermeer, Monet, Renoir, Gauguin, and Matisse.4 In the case of Johannes Vermeer (1632 – 1675), twentynine of his canvases have been digitally mapped to date, out of the thirty-six paintings by him (two of which are on wood) that are generally accepted by scholars.5 As discussed below, three canvas weave matches were found, with three different implications: a question of authenticity; another concerning chronology; and the hypothesis that two pictures were intended by the artist as a pair. Most Dutch painters, including Vermeer, used linen canvases of a “plain” or “tabby” weave: the threads go under and over each other one at a time, forming the simplest crisscross pattern. Until very recently, distinguishing one canvas from another was largely limited to making thread counts. The standard method of thread counting uses a radiograph (X-ray image) of a particular canvas support, the lead-bearing priming of which makes the individual threads visible.6 Threads per centimeter in both directions are counted with a pointer under magnification, with fractions estimated by eye. Several samples are taken on each canvas, perhaps four or as many as fifteen (their locations are virtually impossible to specify using this manual method). The samples on one canvas are then averaged, and the support may be said to consist of an average of about 12.5 x 17.2 threads per centimeter or a similar (by digital standards) approximation. In our survey of twenty-nine canvases used by Vermeer, four of them present a very close correlation of thread counts in both the warp and the weft direction. Here are the average thread counts per centimeter (with height before width), as calculated automatically by computer:

Matching canvas weave patterns from processing x-ray images of master paintings

Thread counting algorithms seek to determine from x-ray images the vertical and horizontal thread counts (frequencies) of the canvas weave comprising a paintings support. Our spectral-based algorithm employs a variant of short-time Fourier analysis to the image domain that reveals isolated peaks at the proper vertical and horizontal frequencies. Paintings made on canvas sections cut from the same canvas roll have been hypothesized to have similar, distinctive weave characteristics, allowing art historians to more accurately date paintings. Spatial variation of weave frequency measurements across a painting were cross-correlated using a new measure to determine possible common weave patterns between pairs of x-rays. By analyzing a database of x-rays made from 180 paintings by van Gogh, our algorithms confirmed situations where paintings were known to have been made on canvases cut from the same roll and found new ones.