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Research Interests: Mathematics, Computer Science, Convex Optimization, Numerical Analysis, Convergence, and 12 moreAlgorithm, Optimization, Optimization Problem, Generalization, Hyperspectral Imaging, Convex Programming, Numerical Analysis and Computational Mathematics, Signal to Noise Ratio, Augmented Lagrangian, Direct Method, Basis Pursuit, and model error
Research Interests: Mathematics, Computer Science, Image Processing, Compressed Sensing, Algorithm, and 11 moreImage Reconstruction, Deconvolution, Image Restoration, Efficient Algorithm for ECG Coding, Inverse Problem, Mathematical Optimization, Basis Pursuit, Fast Algorithm, Commercial Off-The-Shelf, Total Variation, and Iterative Reconstruction
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This paper describes an expectation-maximization(EM) algorithm for wavelet-based image restoration (deconvolution). The observed image is assumed to be a convolved (e.g., blurred) and noisy ver- sion of the original image. Regularization... more
This paper describes an expectation-maximization(EM) algorithm for wavelet-based image restoration (deconvolution). The observed image is assumed to be a convolved (e.g., blurred) and noisy ver- sion of the original image. Regularization is achieved by using a complexity penalty/prior in the wavelet domain, taking advantage of the well known sparsity of wavelet representations. The EM algorithm herein proposed combines the efficient image represen- tation offered by the discrete wavelet transform (DWT) with the diagonalization of the convolution operator in the discrete Fourier domain. The algorithm alternates between an FFT-based E-step and a DWT-based M-step, resulting in a very efficient iterative process requiring operations per iteration (where stands for the numper of pixels). The algorithm, which also esti- mates the noise variance, is called WAFER, standing for Wavelet and Fourier EM Restoration. The conditions for convergence of the proposed algorithm are also presented.
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Research Interests: Cognitive Science, Mathematics, Computer Science, Convex Optimization, Medicine, and 15 moreWavelet, Image Reconstruction, Image Restoration, Algorithm Design, Efficient Algorithm for ECG Coding, Inverse Problem, Mathematical Optimization, Electrical And Electronic Engineering, Approximation Method, Augmented Lagrangian, Constrained Optimization, Direct Method, Basis Pursuit, Fast Algorithm, and Total Variation
Research Interests: Cognitive Science, Mathematics, Computer Science, Image Processing, Signal Processing, and 15 moreCompressed Sensing, Convex Optimization, Inverse Problems, Medicine, Algorithm, Compressive Sensing, Image Reconstruction, Image Restoration, Inverse Problem, Convex Programming, Electrical And Electronic Engineering, Augmented Lagrangian, Constrained Optimization, Direct Method, and Fast Algorithm
Research Interests: Cognitive Science, Mathematics, Computer Science, Algorithms, Image Processing, and 15 moreConvex Optimization, Medicine, Algorithm, Optimization, Deconvolution, Image Restoration, Convex Analysis, Accuracy, Mathematical Optimization, Convex Programming, Image Enhancement, Electrical And Electronic Engineering, Augmented Lagrangian, Direct Method, and Existence and uniqueness
Research Interests: Cognitive Science, Mathematics, Computer Science, Computational Complexity, Medicine, and 15 moreAlgorithm, Wavelet, Image Representation, Image Restoration, Global Optimization, EM algorithm, Expectation Maximization, Convolution Operator, Discrete wavelet transform, Fast Fourier Transform, Electrical And Electronic Engineering, Frequency Domain, Bayesian Estimator, Low Complexity, and Maximum
Research Interests: Cognitive Science, Mathematics, Computer Science, Algorithms, Medicine, and 13 moreAlgorithm, Deconvolution, Image Restoration, Convex Analysis, Convergence Rate, Image Enhancement, Reproducibility of Results, Sensitivity and Specificity, Electrical And Electronic Engineering, Total Variation, Objective function, Rate of Convergence, and convex function
Research Interests: Cognitive Science, Mathematics, Computer Science, Algorithms, Enhancement, and 15 moreMedicine, Algorithm, Optimization Problem, Deconvolution, Image Restoration, Convolution Operator, Information Storage and Retrieval, Blind Deconvolution, Image Enhancement, Reproducibility of Results, High Dimensionality, Deblurring, Electrical And Electronic Engineering, Objective function, and Prior probability
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Research Interests: Mathematics, Computer Science, Biomedical Engineering, Image Processing, Signal Processing, and 15 moreModeling, Learning, Denoising, Deconvolution, Noise reduction, Image Restoration, Dictionaries, Robustness, Sparse representation, High resolution satelite image, Inspection, Gaussian noise, Spatial resolution, Electrical And Electronic Engineering, and Inpainting
In recent work, we proposed a distributed Picard iteration (DPI) that allows a set of agents, linked by a communication network, to find a fixed point of a locally contractive (LC) map that is the average of individual maps held by said... more
In recent work, we proposed a distributed Picard iteration (DPI) that allows a set of agents, linked by a communication network, to find a fixed point of a locally contractive (LC) map that is the average of individual maps held by said agents. In this work, we build upon the DPI and its local linear convergence (LLC) guarantees to make several contributions. We show that Sanger’s algorithm for principal component analysis (PCA) corresponds to the iteration of an LC map that can be written as the average of local maps, each map known to each agent holding a subset of the data. Similarly, we show that a variant of the expectation-maximization (EM) algorithm for parameter estimation from noisy and faulty measurements in a sensor network can be written as the iteration of an LC map that is the average of local maps, each available at just one node. Consequently, via the DPI, we derive two distributed algorithms – distributed EM and distributed PCA – whose LLC guarantees follow from tho...