Algebraic Signal Processing Theory: Cooley-Tukey Type Algorithms for Polynomial Transforms Based on Induction

A polynomial transform is the multiplication of an input vector x\in\C^n by a matrix \PT_{b,\alpha}\in\C^{n\times n}, whose $(k,\ell)$-th element is defined as $p_\ell(\alpha_k)$ for polynomials p_\ell(x)\in\C[x] from a list $b=\{p_0(x),\dots,p_{n-1}(x)\}$ and sample points \alpha_k\in\C from a list $\alpha=\{\alpha_0,\dots,\alpha_{n-1}\}$. Such transforms find applications in the areas of signal processing, data compression, and function interpolation. Important examples include the discrete Fourier and cosine transforms. In this paper we introduce a novel technique to derive fast algorithms for polynomial transforms. The technique uses the relationship between polynomial transforms and the representation theory of polynomial algebras. Specifically, we derive algorithms by decomposing the regular modules of these algebras as a stepwise induction. As an application, we derive novel $O(n\log{n})$ general-radix algorithms for the discrete Fourier transform and the discrete cosine transform of type 4.Comment: 19 pages. Submitted to SIAM Journal on Matrix Analysis and Application

Robust hyperspectral image classification with rejection fields

In this paper we present a novel method for robust hyperspectral image classification using context and rejection. Hyperspectral image classification is generally an ill-posed image problem where pixels may belong to unknown classes, and obtaining representative and complete training sets is costly. Furthermore, the need for high classification accuracies is frequently greater than the need to classify the entire image. We approach this problem with a robust classification method that combines classification with context with classification with rejection. A rejection field that will guide the rejection is derived from the classification with contextual information obtained by using the SegSALSA algorithm. We validate our method in real hyperspectral data and show that the performance gains obtained from the rejection fields are equivalent to an increase the dimension of the training sets.Comment: This paper was submitted to IEEE WHISPERS 2015: 7th Workshop on Hyperspectral Image and Signal Processing: Evolution on Remote Sensing. 5 pages, 1 figure, 2 table

Towards a Culturally Grounded Typology of Magical Realism

Among the recent publications which seek to offer yet another re-definition of magical realism, Christopher Warnes' study Magical Realism and the Postcolonial Novel: Between Faith and Irreverence accomplishes a double feat: while bringing into dialogue the development of both the term 'magical realism' and the mode itself, Warnes develops two paradigms representing two major structural and functional tendencies in magical realism. One is based on an attitude of faith towards the cultural values represented by the supernatural in the texts, the other is characterized by an irreverent stance towards both the real and the supernatural. Applied to some of the key works of magical realism by Borges, Carpentier, Asturias, García Márquez, Rushdie, and Okri, the two paradigms produce acute readings of the cultural and political functions of the deployment of the mode in each individual work. The result is not a redefinition of magical realism, but a thought provoking re-contextualization which offers a typology capable of spanning the varieties of the mode

Assessment of a gas-solid vortex reactor for SO2/NOx adsorption from flue gas

The feasibility of performing the SO2/NOx adsorption process in a gas-solid vortex reactor (GSVR) is examined and compared with the more traditional riser technology. The multiphase reacting flow is modeled using the Eulerian-Eulerian two-fluid model. Models of nonreacting flows were validated using data from a bench-scale experimental setup. The GSVR has the potential to significantly improved heat/mass transfer between phases, as compared to more conventional fluidization technologies. Process intensification opportunities are investigated. The model predicts continuous removal efficiencies greater than 99% for SO2 and approximately 80% for NOx. The gas-solid slip velocity and convective mass transfer coefficient for the riser were 0.2-0.5 and 0.06-0.12 m/s, respectively, whereas the values for the GSVR were 6-7 and 1.0-1.1 m/s, respectively. This order of magnitude increase in the external mass transfer coefficient highlights the potential intensification opportunities provided by the GSVR

Guaranteeing Convergence of Iterative Skewed Voting Algorithms for Image Segmentation

In this paper we provide rigorous proof for the convergence of an iterative voting-based image segmentation algorithm called Active Masks. Active Masks (AM) was proposed to solve the challenging task of delineating punctate patterns of cells from fluorescence microscope images. Each iteration of AM consists of a linear convolution composed with a nonlinear thresholding; what makes this process special in our case is the presence of additive terms whose role is to "skew" the voting when prior information is available. In real-world implementation, the AM algorithm always converges to a fixed point. We study the behavior of AM rigorously and present a proof of this convergence. The key idea is to formulate AM as a generalized (parallel) majority cellular automaton, adapting proof techniques from discrete dynamical systems