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Abstract - IMDSP10 |
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IMDSP10.1 |
Affine Equivariance in Multichannel OS-filtering V. Koivunen (Tampere University of Technology, Finland); S. Luukkonen, H. Oja (University of Oulu, Finland) Nonlinear multichannel filters have successfully been applied to biomedical signals, multichannel images as well as processing of vector fields. In multichannel signals, component variances and correlations among components may be unequal and time-varying. Such changes can be expressed as an affine transformation of the input signal. In this paper, we investigate how the performance and statistical properties of multichannel filters stemming from order statistics (OS) change under affine transformations. An affine equivariant multichannel filter is introduced and the use of affine equivariant performance metric replacing the Mean Square Error is proposed. Advantages of affine equivariance are demonstrated in simulation, and filtering examples using real data are given. |
| IMDSP10.2 |
Grid Filters for Local Nonlinear Image Restoration T. Veldhuizen, M. Jernigan (University of Waterloo, Canada) We describe a new approach to local nonlinear image restoration, based on approximating functions using a regular grid of points in a many-dimensional space. Symmetry reductions and compression of the sparse grid make it feasible to work with eight-dimensional grids as large as 14^8. Unlike polynomials and neural networks whose filtering complexity per pixel is linear in the number of filter coefficients, grid filters have O(1) complexity per pixel. Grid filters require only a single presentation of the training samples, are numerically stable, leave unusual image features unchanged, and are a superset of order statistic filters. Results are presented for blurring and additive noise. |
| IMDSP10.3 |
Denoising by Extracting Fractional Order Singularities H. Shekarforoush (University of Maryland, USA); J. Zerubia, M. Berthod (INRIA, France) In this paper we will introduce a method of isolating and extracting certain class of local singular behaviours of signals/images which in turn will lead to a method of point-wise noise estimation and suppression. The underlying motivation is to decompose functions directly in terms of components which would naturally represent different orders of regular or singular behaviours defined by the local Holder exponents. We have shown that such a decomposition can lead to a factorization of the spectrum of the singular portion of the signal in terms of the spectrum of the original signal and that of a denoising filter. |
| IMDSP10.4 |
Perception Based Adaptive Image Restoration S. Perry, L. Guan (University of Sydney, Australia) This paper presents an image restoration technique which uses a cost function based on a novel image error measure. The cost function presented here takes into account local statistical information of the image when performing restoration. It is shown that the technique compares favourably with other techniques, especially when applied to color images. |
| IMDSP10.5 |
On Estimating the Quality of Noisy Images Z. Zhang, R. Blum (Lehigh University, USA) Some new techniques are proposed for estimating the quality of a noisy image of a natural scene. Analytical justifications are given which explain why these techniques work. Experimental results are provided which indicate that the techniques work well in practice. These techniques need only the images to be evaluated and do not use detailed information about the formation of the image. The focus is on the case where the image is only corrupted by additive Gaussian noise, which is independent from pixel to pixel, but some cases with blurring are also considered. These results should be useful in the process of fusing several images to obtain a higher quality image. Quality measures of this type are needed for fusion, but they have not received much attention to date. In this research, a mixture model is used in conjugation with the expectation-maximization (EM) algorithm to model edge images. This approach yields an accurate representation which should also be useful in other image processing research. |
| IMDSP10.6 |
Adaptive Fuzzy Morphological Filtering of Images J. Oh, L. Chaparro (University of Pittsburgh, USA) In this paper we introduce a neural network implementation of fuzzy mathematical morphology operators and apply it to image denoising. Using a supervised training method and differentiable equivalent representations for the fuzzy morphological operators, we derive efficient adaptation algorithms to optimize the structuring elements. We can then design fuzzy morphological filters for processing multi-level or binary images. The convergence behavior of basic structuring elements for the opening filter and different signals, and its significance for other structuring elements of different shape is discussed. To illustrate the performance of the fuzzy opening filter we consider the removal of impulse noise in multi-level and binary images. |
| IMDSP10.7 |
Hierarchical Bayesian Restoration from Partially Known Blur V. Mesarovic (Crystal Semiconductor Corporation, USA); N. Galatsanos (Illinois Institute. of Technology, USA); R. Molina (University of Granada, Spain); A. Katsaggelos (Northwestern University, USA) A number of restoration filters have been proposed for the restoration problem from partially-known blurs. We derived the regularized constrained total least-squares (RCTLS) filter for this problem and we showed that it has a number of advantages over previous filters for this problem. However, the problem of estimating the parameters that define this filter has not been addressed yet. In this paper we propose a two-step algorithm based on the hierarchical Bayesian approach to simultaneously restore the image and estimate the parameters of the RCTLS restoration filter. The algorithm is derived in the DFT domain; thus, it is very efficient even for very large images. The algorithm is demonstrated in numerical experiments. |
| IMDSP10.8 |
Bayesian Estimation in an Image Restoration Problem in X-Ray Fiber Diffraction. S. Baskaran, R. Millane (Purdue University, USA) The restoration of an incomplete image from a known part and experimental data in the form of the Fourier amplitude squared sums is formulated as a Bayesian estimation problem. This problem is motivated by the structure completion problem in x-ray fiber diffraction analysis. An appropriate prior of uniformly distributed impulses is used. The Bayesian MMSE and MAP estimates are obtained. Simulations are used to compare the performance of the estimates as a function of image and data reduction. The results show that the MMSE estimate significantly outperforms the other estimates. The restored images exhibit some bias towards the known part of the image. This can be partly reduced by an unbiasing procedure. |
| IMDSP10.9 |
A Natural Pixel Decomposition for Tomographic Imaging of the Ionosphere J. Semeter (Max Planck Insitute, Germany); F. Kamalabadi (Boston University, USA) We apply a natural pixel (NP) decomposition to the problem of computerized ionospheric tomography (CIT). For tomography from very few angles, the NP approach provides some distinct advantages over standard basis expansions. The NP solution requires no prior assumption and as such embeds into the solution the natural spatial resolution supported by the data. For the uniquely constrained CIT geometry, however, NP estimated fields will contain significant negative values. We propose a method of improving the NP estimates by enforcing positivity through an entropy regularization algorithm. These techniques are demonstrated in an example. |
| IMDSP10.10 |
A Block-Iterative Quadratic Signal Recovery Algorithm P. Combettes (City University of New York, USA) We propose a block-iterative parallel decomposition method to solve quadratic signal recovery problems under convex constraints. The idea of the method is to disintegrate the original multi-constraint problem into a sequence of simple quadratic minimizations over the intersection of two half-spaces constructed by linearizing blocks of constraints. The implementation of the algorithm is quite flexible thanks to its block-parallel structure. In addition, a wide range of complex constraints can be incorporated since the algorithm does not require exact constraint enforcement at each step but merely approximate enforcement via linearization. An application to deconvolution is demonstrated. |
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