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23
SURELET for Orthonormal WaveletDomain Video Denoising
"... Abstract—We propose an efficient orthonormal waveletdomain video denoising algorithm based on an appropriate integration of motion compensation into an adapted version of our recently devised Stein’s unbiased risk estimatorlinear expansion of thresholds (SURELET) approach. To take full advantage ..."
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Abstract—We propose an efficient orthonormal waveletdomain video denoising algorithm based on an appropriate integration of motion compensation into an adapted version of our recently devised Stein’s unbiased risk estimatorlinear expansion of thresholds (SURELET) approach. To take full advantage of the strong spatiotemporal correlations of neighboring frames, a global motion compensation followed by a selective blockmatching is first applied to adjacent frames, which increases their temporal correlations without distorting the interframe noise statistics. Then, a multiframe interscale wavelet thresholding is performed to denoise the current central frame. The simulations we made on standard grayscale video sequences for various noise levels demonstrate the efficiency of the proposed solution in reducing additive white Gaussian noise. Obtained at a lighter computational load, our results are even competitive with most stateoftheart redundant waveletbased techniques. By using a cyclespinning strategy, our algorithm is in fact able to outperform these methods. Index Terms—Blockmatching, Stein’s unbiased risk estimatorlinear expansion of thresholds (SURELET), video denoising, wavelet. I.
Sparse and Redundant Representation Modeling  What Next?
, 2012
"... Signal processing relies heavily on data models; these are mathematical constructions imposed on the data source that force a dimensionality reduction of some sort. The vast activity in signal processing during the past several decades is essentially driven by an evolution of these models and their ..."
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Signal processing relies heavily on data models; these are mathematical constructions imposed on the data source that force a dimensionality reduction of some sort. The vast activity in signal processing during the past several decades is essentially driven by an evolution of these models and their use in practice. In that respect, the past decade has been certainly the era of sparse and redundant representations, a popular and highly effective data model. This very appealing model led to a long series of intriguing theoretical and numerical questions, and to many innovative ideas that harness this model to real engineering problems. The new entries recently added to the IEEESPL EDICS reflect the popularity of this model and its impact on signal processing research and practice. Despite the huge success of this model so far, this field
Incremental Kernel Learning for Active Image Retrieval without Global Dictionaries
, 2011
"... In contentbased image retrieval context, a classic strategy consists in computing offline a dictionary of visual features. This visual dictionary is then used to provide a new representation of the data which should ease any task of classification or retrieval. This strategy, based on past researc ..."
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In contentbased image retrieval context, a classic strategy consists in computing offline a dictionary of visual features. This visual dictionary is then used to provide a new representation of the data which should ease any task of classification or retrieval. This strategy, based on past research works in text retrieval, is suitable for the context of batch learning, when a large training set can be built either by using a strong prior knowledge of data semantics (like for textual data) or with an expensive offline precomputation. Such an approach has major drawbacks in the context of interactive retrieval, where the user iteratively builds the training data set in a semisupervised approach by providing positive and negative annotations to the system in the relevance feedback loop. The training set is thus built for each retrieval session without any prior knowledge about the concepts of interest for this session. We propose a completely different approach to build the dictionary online from features extracted in relevant images. We design the corresponding kernel function, which is learnt during the retrieval session. For each new label, the kernel function is updated with a complexity linear with respect to the size of the database. We propose an efficient active learning strategy for the weakly supervised retrieval method developed in this paper. Moreover this framework allows the combination of features of different types. Experiments are carried out on standard databases, and show that a small dictionary can be dynamically extracted from the features with better performances than a global one.
1 Video Denoising, Deblocking and Enhancement Through Separable 4D Nonlocal Spatiotemporal Transforms
"... Abstract—We propose a powerful video filtering algorithm that exploits temporal and spatial redundancy characterizing natural video sequences. The algorithm implements the paradigm of nonlocal grouping and collaborative filtering, where a higherdimensional transformdomain representation of the obse ..."
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Abstract—We propose a powerful video filtering algorithm that exploits temporal and spatial redundancy characterizing natural video sequences. The algorithm implements the paradigm of nonlocal grouping and collaborative filtering, where a higherdimensional transformdomain representation of the observations is leveraged to enforce sparsity and thus regularize the data: 3D spatiotemporal volumes are constructed by tracking blocks along trajectories defined by the motion vectors. Mutually similar volumes are then grouped together by stacking them along an additional fourth dimension, thus producing a 4D structure, termed group, where different types of data correlation exist along the different dimensions: local correlation along the two dimensions of the blocks, temporal correlation along the motion trajectories, and nonlocal spatial correlation (i.e. selfsimilarity) along the fourth dimension of the group. Collaborative filtering is then realized by transforming each group through a decorrelating 4D separable transform and then by shrinkage and inverse transformation. In this way, the collaborative filtering provides estimates for each volume stacked in the group, which are then returned and adaptively aggregated to their original positions in the video. The proposed filtering procedure addresses several video processing applications, such as denoising, deblocking, and enhancement of both grayscale and color data. Experimental results prove the effectiveness of our method in terms of both subjective and objective visual quality, and shows that it outperforms the state of the art in video denoising. Index Terms—Video filtering, video denoising, video deblocking, video enhancement, nonlocal methods, adaptive transforms, motion estimation. I.
1 The Cramér–Rao Bound for Sparse Estimation
, 905
"... Abstract — The goal of this paper is to characterize the best achievable performance for the problem of estimating an unknown parameter having a sparse representation. Specifically, we consider the setting in which a sparsely representable deterministic parameter vector is to be estimated from measu ..."
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Abstract — The goal of this paper is to characterize the best achievable performance for the problem of estimating an unknown parameter having a sparse representation. Specifically, we consider the setting in which a sparsely representable deterministic parameter vector is to be estimated from measurements corrupted by Gaussian noise, and derive a lower bound on the meansquared error (MSE) achievable in this setting. To this end, an appropriate definition of bias in the sparse setting is developed, and the constrained Cramér–Rao bound (CRB) is obtained. This bound is shown to equal the CRB of an estimator with knowledge of the support set, for almost all feasible parameter values. Consequently, in the unbiased case, our bound is identical to the MSE of the oracle estimator. Combined with the fact that the CRB is achieved at high signaltonoise ratios by the maximum likelihood technique, our result provides a new interpretation for the common practice of using the oracle estimator as a gold standard against which practical approaches are compared.
Color Demosaicking by Local Directional Interpolation and Nonlocal Adaptive Thresholding
"... Single sensor digital color cameras capture only one of the three primary colors at each pixel and a process called color demosaicking (CDM) is used to reconstruct the full color images. Most CDM algorithms assume the existence of high local spectral redundancy in estimating the missing color sample ..."
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Single sensor digital color cameras capture only one of the three primary colors at each pixel and a process called color demosaicking (CDM) is used to reconstruct the full color images. Most CDM algorithms assume the existence of high local spectral redundancy in estimating the missing color samples. However, for images with sharp color transitions and high color saturation, such an assumption may be invalid and visually unpleasant CDM errors will occur. In this paper we exploit the image nonlocal redundancy to improve the local color reproduction result. First, multiple local directional estimates of a missing color sample are computed and fused according to local gradients. Then nonlocal pixels similar to the estimated pixel are searched to enhance the local estimate. An adaptive thresholding method rather than the commonly used nonlocal means filtering is proposed to improve the local estimate. This allows the final reconstruction to be performed at the structural level as opposed to the pixel level. Experimental results demonstrate that the proposed local directional interpolation and nonlocal adaptive thresholding (LDINAT) method outperforms many stateoftheart CDM methods in reconstructing the edges and reducing color interpolation artifacts, leading to higher visual quality of reproduced color images.
The IterationTuned Dictionary for Sparse Representations
"... Abstract—We introduce a new dictionary structure for sparse representations better adapted to pursuit algorithms used in practical scenarios. The new structure, which we call an IterationTuned Dictionary (ITD), consists of a set of dictionaries each associated to a single iteration index of a pursu ..."
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Abstract—We introduce a new dictionary structure for sparse representations better adapted to pursuit algorithms used in practical scenarios. The new structure, which we call an IterationTuned Dictionary (ITD), consists of a set of dictionaries each associated to a single iteration index of a pursuit algorithm. In this work we first adapt pursuit decompositions to the case of ITD structures and then introduce a training algorithm used to construct ITDs. The training algorithm consists of applying a Kmeans to the (i − 1)th residuals of the training set to thus produce the ith dictionary of the ITD structure. In the results section we compare our algorithm against the stateoftheart dictionary training scheme and show that our method produces sparse representations yielding better signal approximations for the same sparsity level. I.
1 Blind compressive sensing dynamic MRI
"... We propose a novel blind compressive sensing (BCS) frame work to recover dynamic magnetic resonance images from undersampled measurements. This scheme models the dynamic signal as a sparse linear combination of temporal basis functions, chosen from a large dictionary. In contrast to classical compre ..."
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We propose a novel blind compressive sensing (BCS) frame work to recover dynamic magnetic resonance images from undersampled measurements. This scheme models the dynamic signal as a sparse linear combination of temporal basis functions, chosen from a large dictionary. In contrast to classical compressed sensing, the BCS scheme simultaneously estimates the dictionary and the sparse coefficients from the undersampled measurements. Apart from the sparsity of the coefficients, the key difference of the BCS scheme with current low rank methods is the nonorthogonal nature of the dictionary basis functions. Since the number of degrees of freedom of the BCS model is smaller than that of the lowrank methods, it provides improved reconstructions at high acceleration rates. We formulate the reconstruction as a constrained optimization problem; the objective function is the linear combination of a data consistency term and sparsity promoting ℓ1 prior of the coefficients. The Frobenius norm dictionary constraint is used to avoid scale ambiguity. We introduce a simple and efficient majorizeminimize algorithm, which decouples the original criterion into three simpler sub problems. An alternating minimization strategy is used, where we cycle through the minimization of three simpler problems. This algorithm is seen to be considerably faster than approaches that alternates between sparse coding and dictionary estimation, as well as the extension of KSVD dictionary learning scheme. The use of the ℓ1 penalty and Frobenius norm dictionary constraint enables the attenuation of insignificant basis functions compared to the ℓ0 norm and column norm constraint assumed in most dictionary learning algorithms; this is especially important since the number of basis
Efficient Implementation of the KSVD Algorithm and the BatchOMP Method
"... The KSVD algorithm is a highly effective method of training overcomplete dictionaries for sparse signal representation. In this report we discuss an efficient implementation of this algorithm, which both accelerates it and reduces its memory consumption. The two basic components of our implementati ..."
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The KSVD algorithm is a highly effective method of training overcomplete dictionaries for sparse signal representation. In this report we discuss an efficient implementation of this algorithm, which both accelerates it and reduces its memory consumption. The two basic components of our implementation are the replacement of the exact SVD computation with a much quicker approximation, and the use of the BatchOMP method for performing the sparsecoding operations. BatchOMP, which we also present in this report, is an implementation of the Orthogonal Matching Pursuit (OMP) algorithm which is specifically optimized for sparsecoding large sets of signals over the same dictionary. The BatchOMP implementation is useful for a variety of sparsitybased techniques which involve coding large numbers of signals. In the report, we discuss the BatchOMP and KSVD implementations and analyze their complexities. The report is accompanied by MatlabⓇ toolboxes which implement these techniques, and can be downloaded at