Michal Aharon

Bio: Michal Aharon is an academic researcher from Yahoo!. The author has contributed to research in topics: Sparse approximation & Collaborative filtering. The author has an hindex of 16, co-authored 46 publications receiving 14632 citations. Previous affiliations of Michal Aharon include Hewlett-Packard & Verizon Communications.

$rm K$ -SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation

Abstract: In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signal-atoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and include compression, regularization in inverse problems, feature extraction, and more. Recent activity in this field has concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. Designing dictionaries to better fit the above model can be done by either selecting one from a prespecified set of linear transforms or adapting the dictionary to a set of training signals. Both of these techniques have been considered, but this topic is largely still open. In this paper we propose a novel algorithm for adapting dictionaries in order to achieve sparse signal representations. Given a set of training signals, we seek the dictionary that leads to the best representation for each member in this set, under strict sparsity constraints. We present a new method-the K-SVD algorithm-generalizing the K-means clustering process. K-SVD is an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data. The update of the dictionary columns is combined with an update of the sparse representations, thereby accelerating convergence. The K-SVD algorithm is flexible and can work with any pursuit method (e.g., basis pursuit, FOCUSS, or matching pursuit). We analyze this algorithm and demonstrate its results both on synthetic tests and in applications on real image data

Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries

Abstract: We address the image denoising problem, where zero-mean white and homogeneous Gaussian additive noise is to be removed from a given image. The approach taken is based on sparse and redundant representations over trained dictionaries. Using the K-SVD algorithm, we obtain a dictionary that describes the image content effectively. Two training options are considered: using the corrupted image itself, or training on a corpus of high-quality image database. Since the K-SVD is limited in handling small image patches, we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image. We show how such Bayesian treatment leads to a simple and effective denoising algorithm. This leads to a state-of-the-art denoising performance, equivalent and sometimes surpassing recently published leading alternative denoising methods

Image Denoising Via Learned Dictionaries and Sparse representation

Abstract: We address the image denoising problem, where zeromean white and homogeneous Gaussian additive noise should be removed from a given image. The approach taken is based on sparse and redundant representations over a trained dictionary. The proposed algorithm denoises the image, while simultaneously trainining a dictionary on its (corrupted) content using the K-SVD algorithm. As the dictionary training algorithm is limited in handling small image patches, we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image. We show how such Bayesian treatment leads to a simple and effective denoising algorithm, with state-of-the-art performance, equivalent and sometimes surpassing recently published leading alternative denoising methods.

On the uniqueness of overcomplete dictionaries, and a practical way to retrieve them

Abstract: A full-rank under-determined linear system of equations Ax = b has in general infinitely many possible solutions. In recent years there is a growing interest in the sparsest solution of this equation—the one with the fewest non-zero entries, measured by ∥ x ∥ 0 . Such solutions find applications in signal and image processing, where the topic is typically referred to as “sparse representation”. Considering the columns of A as atoms of a dictionary, it is assumed that a given signal b is a linear composition of few such atoms. Recent work established that if the desired solution x is sparse enough, uniqueness of such a result is guaranteed. Also, pursuit algorithms, approximation solvers for the above problem, are guaranteed to succeed in finding this solution. Armed with these recent results, the problem can be reversed, and formed as an implied matrix factorization problem: Given a set of vectors { b i }, known to emerge from such sparse constructions, Ax i = b i , with sufficiently sparse representations x i , we seek the matrix A . In this paper we present both theoretical and algorithmic studies of this problem. We establish the uniqueness of the dictionary A , depending on the quantity and nature of the set { b i }, and the sparsity of { x i }. We also describe a recently developed algorithm, the K-SVD, that practically find the matrix A , in a manner similar to the K-Means algorithm. Finally, we demonstrate this algorithm on several stylized applications in image processing.

Sparse and Redundant Modeling of Image Content Using an Image-Signature-Dictionary

Abstract: Modeling signals by sparse and redundant representations has been drawing considerable attention in recent years. Coupled with the ability to train the dictionary using signal examples, these techniques have been shown to lead to state-of-the-art results in a series of recent applications. In this paper we propose a novel structure of such a model for representing image content. The new dictionary is itself a small image, such that every patch in it (in varying location and size) is a possible atom in the representation. We refer to this as the image-signature-dictionary (ISD) and show how it can be trained from image examples. This structure extends the well-known image and video epitomes, as introduced by Jojic, Frey, and Kannan [in Proceedings of the IEEE International Conference on Computer Vision, 2003, pp. 34-41] and Cheung, Frey, and Jojic [in Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2005, pp. 42-49], by replacing a probabilistic averaging of patches with their sparse representations. The ISD enjoys several important features, such as shift and scale flexibilities, and smaller memory and computational requirements, compared to the classical dictionary approach. As a demonstration of these benefits, we present high-quality image denoising results based on this new model.

Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering

Abstract: We propose a novel image denoising strategy based on an enhanced sparse representation in transform domain. The enhancement of the sparsity is achieved by grouping similar 2D image fragments (e.g., blocks) into 3D data arrays which we call "groups." Collaborative Altering is a special procedure developed to deal with these 3D groups. We realize it using the three successive steps: 3D transformation of a group, shrinkage of the transform spectrum, and inverse 3D transformation. The result is a 3D estimate that consists of the jointly filtered grouped image blocks. By attenuating the noise, the collaborative filtering reveals even the finest details shared by grouped blocks and, at the same time, it preserves the essential unique features of each individual block. The filtered blocks are then returned to their original positions. Because these blocks are overlapping, for each pixel, we obtain many different estimates which need to be combined. Aggregation is a particular averaging procedure which is exploited to take advantage of this redundancy. A significant improvement is obtained by a specially developed collaborative Wiener filtering. An algorithm based on this novel denoising strategy and its efficient implementation are presented in full detail; an extension to color-image denoising is also developed. The experimental results demonstrate that this computationally scalable algorithm achieves state-of-the-art denoising performance in terms of both peak signal-to-noise ratio and subjective visual quality.

Extracting and composing robust features with denoising autoencoders

Abstract: Previous work has shown that the difficulties in learning deep generative or discriminative models can be overcome by an initial unsupervised learning step that maps inputs to useful intermediate representations. We introduce and motivate a new training principle for unsupervised learning of a representation based on the idea of making the learned representations robust to partial corruption of the input pattern. This approach can be used to train autoencoders, and these denoising autoencoders can be stacked to initialize deep architectures. The algorithm can be motivated from a manifold learning and information theoretic perspective or from a generative model perspective. Comparative experiments clearly show the surprising advantage of corrupting the input of autoencoders on a pattern classification benchmark suite.

Image Super-Resolution Using Deep Convolutional Networks

Abstract: We propose a deep learning method for single image super-resolution (SR). Our method directly learns an end-to-end mapping between the low/high-resolution images. The mapping is represented as a deep convolutional neural network (CNN) that takes the low-resolution image as the input and outputs the high-resolution one. We further show that traditional sparse-coding-based SR methods can also be viewed as a deep convolutional network. But unlike traditional methods that handle each component separately, our method jointly optimizes all layers. Our deep CNN has a lightweight structure, yet demonstrates state-of-the-art restoration quality, and achieves fast speed for practical on-line usage. We explore different network structures and parameter settings to achieve trade-offs between performance and speed. Moreover, we extend our network to cope with three color channels simultaneously, and show better overall reconstruction quality.

Beyond a Gaussian Denoiser: Residual Learning of Deep CNN for Image Denoising

Abstract: The discriminative model learning for image denoising has been recently attracting considerable attentions due to its favorable denoising performance. In this paper, we take one step forward by investigating the construction of feed-forward denoising convolutional neural networks (DnCNNs) to embrace the progress in very deep architecture, learning algorithm, and regularization method into image denoising. Specifically, residual learning and batch normalization are utilized to speed up the training process as well as boost the denoising performance. Different from the existing discriminative denoising models which usually train a specific model for additive white Gaussian noise at a certain noise level, our DnCNN model is able to handle Gaussian denoising with unknown noise level (i.e., blind Gaussian denoising). With the residual learning strategy, DnCNN implicitly removes the latent clean image in the hidden layers. This property motivates us to train a single DnCNN model to tackle with several general image denoising tasks, such as Gaussian denoising, single image super-resolution, and JPEG image deblocking. Our extensive experiments demonstrate that our DnCNN model can not only exhibit high effectiveness in several general image denoising tasks, but also be efficiently implemented by benefiting from GPU computing.

Image Denoising Via Sparse and Redundant Representations Over Learned Dictionaries

Abstract: We address the image denoising problem, where zero-mean white and homogeneous Gaussian additive noise is to be removed from a given image. The approach taken is based on sparse and redundant representations over trained dictionaries. Using the K-SVD algorithm, we obtain a dictionary that describes the image content effectively. Two training options are considered: using the corrupted image itself, or training on a corpus of high-quality image database. Since the K-SVD is limited in handling small image patches, we extend its deployment to arbitrary image sizes by defining a global image prior that forces sparsity over patches in every location in the image. We show how such Bayesian treatment leads to a simple and effective denoising algorithm. This leads to a state-of-the-art denoising performance, equivalent and sometimes surpassing recently published leading alternative denoising methods