Inverse Projection Representation and Category Contribution Rate for Robust Tumor Recognition

Sparse representation based classification (SRC) methods have achieved remarkable results. SRC, however, still suffer from requiring enough training samples, insufficient use of test samples and instability of representation. In this paper, a stable inverse projection representation based classification (IPRC) is presented to tackle these problems by effectively using test samples. An IPR is firstly proposed and its feasibility and stability are analyzed. A classification criterion named category contribution rate is constructed to match the IPR and complete classification. Moreover, a statistical measure is introduced to quantify the stability of representation-based classification methods. Based on the IPRC technique, a robust tumor recognition framework is presented by interpreting microarray gene expression data, where a two-stage hybrid gene selection method is introduced to select informative genes. Finally, the functional analysis of candidate's pathogenicity-related genes is given. Extensive experiments on six public tumor microarray gene expression datasets demonstrate the proposed technique is competitive with state-of-the-art methods.Comment: 14 pages, 19 figures, 10 table

Perception of Motion and Architectural Form: Computational Relationships between Optical Flow and Perspective

Perceptual geometry refers to the interdisciplinary research whose objectives focuses on study of geometry from the perspective of visual perception, and in turn, applies such geometric findings to the ecological study of vision. Perceptual geometry attempts to answer fundamental questions in perception of form and representation of space through synthesis of cognitive and biological theories of visual perception with geometric theories of the physical world. Perception of form, space and motion are among fundamental problems in vision science. In cognitive and computational models of human perception, the theories for modeling motion are treated separately from models for perception of form.Comment: 10 pages, 13 figures, submitted and accepted in DoCEIS'2012 Conference: http://www.uninova.pt/doceis/doceis12/home/home.ph

Semi-blind Sparse Image Reconstruction with Application to MRFM

We propose a solution to the image deconvolution problem where the convolution kernel or point spread function (PSF) is assumed to be only partially known. Small perturbations generated from the model are exploited to produce a few principal components explaining the PSF uncertainty in a high dimensional space. Unlike recent developments on blind deconvolution of natural images, we assume the image is sparse in the pixel basis, a natural sparsity arising in magnetic resonance force microscopy (MRFM). Our approach adopts a Bayesian Metropolis-within-Gibbs sampling framework. The performance of our Bayesian semi-blind algorithm for sparse images is superior to previously proposed semi-blind algorithms such as the alternating minimization (AM) algorithm and blind algorithms developed for natural images. We illustrate our myopic algorithm on real MRFM tobacco virus data.Comment: This work has been submitted to the IEEE Trans. Image Processing for possible publicatio

Bayesian orthogonal component analysis for sparse representation

This paper addresses the problem of identifying a lower dimensional space where observed data can be sparsely represented. This under-complete dictionary learning task can be formulated as a blind separation problem of sparse sources linearly mixed with an unknown orthogonal mixing matrix. This issue is formulated in a Bayesian framework. First, the unknown sparse sources are modeled as Bernoulli-Gaussian processes. To promote sparsity, a weighted mixture of an atom at zero and a Gaussian distribution is proposed as prior distribution for the unobserved sources. A non-informative prior distribution defined on an appropriate Stiefel manifold is elected for the mixing matrix. The Bayesian inference on the unknown parameters is conducted using a Markov chain Monte Carlo (MCMC) method. A partially collapsed Gibbs sampler is designed to generate samples asymptotically distributed according to the joint posterior distribution of the unknown model parameters and hyperparameters. These samples are then used to approximate the joint maximum a posteriori estimator of the sources and mixing matrix. Simulations conducted on synthetic data are reported to illustrate the performance of the method for recovering sparse representations. An application to sparse coding on under-complete dictionary is finally investigated.Comment: Revised version. Accepted to IEEE Trans. Signal Processin

Multivariate statistical analysis for damage and delamination in composite structures

The article is devoted to the analysis of the vibration response of composite laminates .Our aim is to develop a method for analysis of the vibration response of structures made of composites which will also be used to develop a vibration-based health monitoring procedure for such structures. Composite materials and composite laminates in particular, exhibit complex dynamic behaviour which on most occasions cannot be modelled linearly. Delamination introduces additional nonlinearities in the vibration behaviour of the structure as a result of the interrupted contact between the layers or the opening and closing of the delamination. Thus conventional linear structural dynamics methods like modal analysis cannot be applied. In this study, the vibration response signals are recorded from damaged and non-damaged (healthy) laminated composite beams. The frequency domain signals are subjected to a special type of Principal Component Analysis, known as Multichannel Singular Spectrum Analysis (MSSA). This type of analysis is known to uncover oscillation patterns and was suggested in the investigation in place of modal analysis. The idea is to establish a new feature based state-space for the vibration response signal. The response of the healthy structure is used as a baseline to which all the responses are compared. MSSA decomposes the signal into new components which are lineal combinations of the original frequency series components. The first several components are responsible for most of the variance of the original signal. The new space is with a much smaller dimension as compared to the original data and creates new variables which can be used as damage features. The results demonstrate strong potential for using MSSA for the purpose of structural health monitoring