Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

The search for efficient image denoising methods is still a valid challenge at the crossing of functional analysis and statistics In spite of the sophistication of the recently proposed methods, m

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A Review of Image Denoising Algorithms, with a New One

A reproducible evaluation of ANTs similarity metric performance in brain image registration.

Techniques from sparse signal representation are beginning to see significant impact in computer vision, often on nontraditional applications where the goal is not just to obtain a compact high-fidelity representation of the observed signal, but also to extract semantic information. The choice of dictionary plays a key role in bridging this gap: unconventional dictionaries consisting of, or learned from, the training samples themselves provide the key to obtaining state-of-the-art results and to attaching semantic meaning to sparse signal representations. Understanding the good performance of such unconventional dictionaries in turn demands new algorithmic and analytical techniques. This review paper highlights a few representative examples of how the interaction between sparse signal representation and computer vision can enrich both fields, and raises a number of open questions for further study.

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Sparse Representation for Computer Vision and Pattern Recognition

We propose in this paper to unify two different approaches to image restoration: On the one hand, learning a basis set (dictionary) adapted to sparse signal descriptions has proven to be very effective in image reconstruction and classification tasks. On the other hand, explicitly exploiting the self-similarities of natural images has led to the successful non-local means approach to image restoration. We propose simultaneous sparse coding as a framework for combining these two approaches in a natural manner. This is achieved by jointly decomposing groups of similar signals on subsets of the learned dictionary. Experimental results in image denoising and demosaicking tasks with synthetic and real noise show that the proposed method outperforms the state of the art, making it possible to effectively restore raw images from digital cameras at a reasonable speed and memory cost.

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Non-local sparse models for image restoration

Image restoration is an important and widely studied problem in computer vision and image processing. Various image filtering strategies have been effective, but invariably make strong assumptions about the properties of the signal and/or degradation. Hence, these methods lack the generality to be easily applied to new applications or diverse image collections. This paper describes a novel unsupervised, information-theoretic, adaptive filter (UINTA) that improves the predictability of pixel intensities from their neighborhoods by decreasing their joint entropy. In this way, UINTA automatically discovers the statistical properties of the signal and can thereby restore a wide spectrum of images. The paper describes the formulation to minimize the joint entropy measure and presents several important practical considerations in estimating neighborhood statistics. It presents a series of results on both real and synthetic data along with comparisons with state-of-the-art techniques, including novel applications to medical image processing.

/pdf/unsupervised-information-theoretic-adaptive-image-filtering-44v82u1xjw.pdf

Unsupervised, information-theoretic, adaptive image filtering for image restoration

The restoration of images is an important and widely studied problem in computer vision and image processing. Various image filtering strategies have been effective, but invariably make strong assumptions about the properties of the signal and/or degradation. Therefore, these methods typically lack the generality to be easily applied to new applications or diverse image collections. This paper describes a novel unsupervised, information-theoretic, adaptive filter (UINTA) that improves the predictability of pixel intensities from their neighborhoods by decreasing the joint entropy between them. Thus UINTA automatically discovers the statistical properties of the signal and can thereby restore a wide spectrum of images and applications. This paper describes the formulation required to minimize the joint entropy measure, presents several important practical considerations in estimating image-region statistics, and then presents results on both real and synthetic data.

/pdf/higher-order-image-statistics-for-unsupervised-information-2cou4h8yo6.pdf

Higher-order image statistics for unsupervised, information-theoretic, adaptive, image filtering

Dynamic contrast-enhanced (DCE) MRI is a powerful technique to probe an area of interest in the body. Here a temporally constrained reconstruction (TCR) technique that requires less k-space data over time to obtain good-quality reconstructed images is proposed. This approach can be used to improve the spatial or temporal resolution, or increase the coverage of the object of interest. The method jointly reconstructs the space-time data iteratively with a temporal constraint in order to resolve aliasing. The method was implemented and its feasibility tested on DCE myocardial perfusion data with little or no motion. The results obtained from sparse k-space data using the TCR method were compared with results obtained with a sliding-window (SW) method and from full data using the standard inverse Fourier transform (IFT) reconstruction. Acceleration factors of 5 (R = 5) were achieved without a significant loss in image quality. Mean improvements of 28 +/- 4% in the signal-to-noise ratio (SNR) and 14 +/- 4% in the contrast-to-noise ratio (CNR) were observed in the images reconstructed using the TCR method on sparse data (R = 5) compared to the standard IFT reconstructions from full data for the perfusion datasets. The method has the potential to improve dynamic myocardial perfusion imaging and also to reconstruct other sparse dynamic MR acquisitions.

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Temporally constrained reconstruction of dynamic cardiac perfusion MRI.

https://www.sci.utah.edu/~tolga/pubs/Awate_MRI_Segmentation.pdf

Adaptive Markov modeling for mutual-information-based, unsupervised MRI brain-tissue classification.

This paper presents a novel method for Bayesian denoising of magnetic resonance (MR) images that bootstraps itself by inferring the prior, i.e., the uncorrupted-image statistics, from the corrupted input data and the knowledge of the Rician noise model. The proposed method relies on principles from empirical Bayes (EB) estimation. It models the prior in a nonparametric Markov random field (MRF) framework and estimates this prior by optimizing an information-theoretic metric using the expectation-maximization algorithm. The generality and power of nonparametric modeling, coupled with the EB approach for prior estimation, avoids imposing ill-fitting prior models for denoising. The results demonstrate that, unlike typical denoising methods, the proposed method preserves most of the important features in brain MR images. Furthermore, this paper presents a novel Bayesian-inference algorithm on MRFs, namely iterated conditional entropy reduction (ICER). This paper also extends the application of the proposed method for denoising diffusion-weighted MR images. Validation results and quantitative comparisons with the state of the art in MR-image denoising clearly depict the advantages of the proposed method.

Suyash P. Awate

Papers

Unsupervised, information-theoretic, adaptive image filtering for image restoration

Higher-order image statistics for unsupervised, information-theoretic, adaptive, image filtering

Temporally constrained reconstruction of dynamic cardiac perfusion MRI.

Adaptive Markov modeling for mutual-information-based, unsupervised MRI brain-tissue classification.

Feature-Preserving MRI Denoising: A Nonparametric Empirical Bayes Approach