1,765 research outputs found
A proximal iteration for deconvolving Poisson noisy images using sparse representations
We propose an image deconvolution algorithm when the data is contaminated by
Poisson noise. The image to restore is assumed to be sparsely represented in a
dictionary of waveforms such as the wavelet or curvelet transforms. Our key
contributions are: First, we handle the Poisson noise properly by using the
Anscombe variance stabilizing transform leading to a {\it non-linear}
degradation equation with additive Gaussian noise. Second, the deconvolution
problem is formulated as the minimization of a convex functional with a
data-fidelity term reflecting the noise properties, and a non-smooth
sparsity-promoting penalties over the image representation coefficients (e.g.
-norm). Third, a fast iterative backward-forward splitting algorithm is
proposed to solve the minimization problem. We derive existence and uniqueness
conditions of the solution, and establish convergence of the iterative
algorithm. Finally, a GCV-based model selection procedure is proposed to
objectively select the regularization parameter. Experimental results are
carried out to show the striking benefits gained from taking into account the
Poisson statistics of the noise. These results also suggest that using
sparse-domain regularization may be tractable in many deconvolution
applications with Poisson noise such as astronomy and microscopy
Self-organized learning in multi-layer networks
We present a framework for the self-organized formation of high level learning by a statistical preprocessing of features. The paper focuses first on the formation of the features in the context of layers of feature processing units as a kind of resource-restricted associative multiresolution learning We clame that such an architecture must reach maturity by basic statistical proportions, optimizing the information processing capabilities of each layer. The final symbolic output is learned by pure association of features of different levels and kind of sensorial input. Finally, we also show that common error-correction learning for motor skills can be accomplished also by non-specific associative learning. Keywords: feedforward network layers, maximal information gain, restricted Hebbian learning, cellular neural nets, evolutionary associative learnin
Modeling of evolving textures using granulometries
This chapter describes a statistical approach to classification of dynamic texture images, called parallel evolution functions (PEFs). Traditional classification methods predict texture class membership using comparisons with a finite set of predefined texture classes and identify the closest class. However, where texture images arise from a dynamic texture evolving over time, estimation of a time state in a continuous evolutionary process is required instead. The PEF approach does this using regression modeling techniques to predict time state. It is a flexible approach which may be based on any suitable image features. Many textures are well suited to a morphological analysis and the PEF approach uses image texture features derived from a granulometric analysis of the image. The method is illustrated using both simulated images of Boolean processes and real images of corrosion. The PEF approach has particular advantages for training sets containing limited numbers of observations, which is the case in many real world industrial inspection scenarios and for which other methods can fail or perform badly. [41] G.W. Horgan, Mathematical morphology for analysing soil structure from images, European Journal of Soil Science, vol. 49, pp. 161ā173, 1998. [42] G.W. Horgan, C.A. Reid and C.A. Glasbey, Biological image processing and enhancement, Image Processing and Analysis, A Practical Approach, R. Baldock and J. Graham, eds., Oxford University Press, Oxford, UK, pp. 37ā67, 2000. [43] B.B. Hubbard, The World According to Wavelets: The Story of a Mathematical Technique in the Making, A.K. Peters Ltd., Wellesley, MA, 1995. [44] H. Iversen and T. Lonnestad. An evaluation of stochastic models for analysis and synthesis of gray-scale texture, Pattern Recognition Letters, vol. 15, pp. 575ā585, 1994. [45] A.K. Jain and F. Farrokhnia, Unsupervised texture segmentation using Gabor filters, Pattern Recognition, vol. 24(12), pp. 1167ā1186, 1991. [46] T. Jossang and F. Feder, The fractal characterization of rough surfaces, Physica Scripta, vol. T44, pp. 9ā14, 1992. [47] A.K. Katsaggelos and T. Chun-Jen, Iterative image restoration, Handbook of Image and Video Processing, A. Bovik, ed., Academic Press, London, pp. 208ā209, 2000. [48] M. KĀØoppen, C.H. Nowack and G. RĀØosel, Pareto-morphology for color image processing, Proceedings of SCIA99, 11th Scandinavian Conference on Image Analysis 1, Kangerlussuaq, Greenland, pp. 195ā202, 1999. [49] S. Krishnamachari and R. Chellappa, Multiresolution Gauss-Markov random field models for texture segmentation, IEEE Transactions on Image Processing, vol. 6(2), pp. 251ā267, 1997. [50] T. Kurita and N. Otsu, Texture classification by higher order local autocorrelation features, Proceedings of ACCV93, Asian Conference on Computer Vision, Osaka, pp. 175ā178, 1993. [51] S.T. Kyvelidis, L. Lykouropoulos and N. Kouloumbi, Digital system for detecting, classifying, and fast retrieving corrosion generated defects, Journal of Coatings Technology, vol. 73(915), pp. 67ā73, 2001. [52] Y. Liu, T. Zhao and J. Zhang, Learning multispectral texture features for cervical cancer detection, Proceedings of 2002 IEEE International Symposium on Biomedical Imaging: Macro to Nano, pp. 169ā172, 2002. [53] G. McGunnigle and M.J. Chantler, Modeling deposition of surface texture, Electronics Letters, vol. 37(12), pp. 749ā750, 2001. [54] J. McKenzie, S. Marshall, A.J. Gray and E.R. Dougherty, Morphological texture analysis using the texture evolution function, International Journal of Pattern Recognition and Artificial Intelligence, vol. 17(2), pp. 167ā185, 2003. [55] J. McKenzie, Classification of dynamically evolving textures using evolution functions, Ph.D. Thesis, University of Strathclyde, UK, 2004. [56] S.G. Mallat, Multiresolution approximations and wavelet orthonormal bases of L2(R), Transactions of the American Mathematical Society, vol. 315, pp. 69ā87, 1989. [57] S.G. Mallat, A theory for multiresolution signal decomposition: the wavelet representation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, pp. 674ā693, 1989. [58] B.S. Manjunath and W.Y. Ma, Texture features for browsing and retrieval of image data, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 18, pp. 837ā842, 1996. [59] B.S. Manjunath, G.M. Haley and W.Y. Ma, Multiband techniques for texture classification and segmentation, Handbook of Image and Video Processing, A. Bovik, ed., Academic Press, London, pp. 367ā381, 2000. [60] G. Matheron, Random Sets and Integral Geometry, Wiley Series in Probability and Mathematical Statistics, John Wiley and Sons, New York, 1975
Multiscale Computation with Interpolating Wavelets
Multiresolution analyses based upon interpolets, interpolating scaling
functions introduced by Deslauriers and Dubuc, are particularly well-suited to
physical applications because they allow exact recovery of the multiresolution
representation of a function from its sample values on a finite set of points
in space. We present a detailed study of the application of wavelet concepts to
physical problems expressed in such bases. The manuscript describes algorithms
for the associated transforms which, for properly constructed grids of variable
resolution, compute correctly without having to introduce extra grid points. We
demonstrate that for the application of local homogeneous operators in such
bases, the non-standard multiply of Beylkin, Coifman and Rokhlin also proceeds
exactly for inhomogeneous grids of appropriate form. To obtain less stringent
conditions on the grids, we generalize the non-standard multiply so that
communication may proceed between non-adjacent levels. The manuscript concludes
with timing comparisons against naive algorithms and an illustration of the
scale-independence of the convergence rate of the conjugate gradient solution
of Poisson's equation using a simple preconditioning, suggesting that this
approach leads to an O(n) solution of this equation.Comment: 33 pages, figures available at
http://laisla.mit.edu/muchomas/Papers/nonstand-figs.ps . Updated: (1) figures
file (figs.ps) now appear with the posting on the server; (2) references got
lost in the last submissio
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