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Optimality in the Design of Overcomplete Decompositions
"... We lay a philosophical framework for the design of overcomplete multidimensional signal decompositions based on the union of two or more orthonormal bases. By combining orthonormal bases in this way, tight (energy preserving) frames are automatically produced. The advantage of an overcomplete (tight ..."
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We lay a philosophical framework for the design of overcomplete multidimensional signal decompositions based on the union of two or more orthonormal bases. By combining orthonormal bases in this way, tight (energy preserving) frames are automatically produced. The advantage of an overcomplete
Weighted Averaging for Denoising with Overcomplete Dictionaries
"... We consider the scenario where additive, independent and identically distributed (i.i.d) noise in an image is removed using an overcomplete set of linear transforms and thresholding. Rather than the standard approach where one obtains the denoised signal by ad hoc averaging of the denoised estimates ..."
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Cited by 18 (3 self)
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We consider the scenario where additive, independent and identically distributed (i.i.d) noise in an image is removed using an overcomplete set of linear transforms and thresholding. Rather than the standard approach where one obtains the denoised signal by ad hoc averaging of the denoised
Unsupervised Learning of Overcomplete Face Descriptors
"... The current stateoftheart indicates that a very discriminative unsupervised face representation can be constructed by encoding overlapping multiscale face image patches at facial landmarks. If fixed as such, there are even suggestions (albeit subtle) that the underlying features may no longer ..."
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have as much meaning. In spite of the effectiveness of this strategy, we argue that one may still afford to improve especially at the feature level. In this paper, we investigate the role of overcompleteness in features for building unsupervised face representations. In our approach, we first learn
Overcomplete Systems of Wavelet and Related Local Bases for Adaptive Signal Representation and Estimation
"... this paper we will discuss the usefulness of overcomplete systems of basis functions, such as wavelets or localized sine and cosine functions, for the adaptive parsimonious representation and estimation of statistical signals which show an inhomogeneous behaviour over time. Typical examples can be f ..."
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on "locally stationary wavelet processes" by Nason et al (1998). Common to both is on one hand the inherent redundancy of the used overcomplete system which is the key to adaptation. On the other hand, to allow for rigorous modeling and statistical estimation, a control of this redundancy
Overcomplete source separation using laplacian mixture models
 IEEE Signal Processing Letters
, 2004
"... In this letter, the authors explore the use of Laplacian Mixture Models (LMMs) to address the overcomplete Blind Source Separation problem in the case that the source signals are very sparse. A twosensor setup was used to separate an instantaneous mixture of sources. A hard and a soft decision sche ..."
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Cited by 10 (2 self)
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In this letter, the authors explore the use of Laplacian Mixture Models (LMMs) to address the overcomplete Blind Source Separation problem in the case that the source signals are very sparse. A twosensor setup was used to separate an instantaneous mixture of sources. A hard and a soft decision
An Information Maximization Approach to Overcomplete and Recurrent Representations
 In Advances in Neural Information Processing Systems
, 2002
"... The principle of maximizing mutual information is applied to learning overcomplete and recurrent representations. The underlying model consists of a network of input units driving a larger number of output units with recurrent interactions. In the limit of zero noise, the network is deterministic ..."
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Cited by 9 (2 self)
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The principle of maximizing mutual information is applied to learning overcomplete and recurrent representations. The underlying model consists of a network of input units driving a larger number of output units with recurrent interactions. In the limit of zero noise, the network
Sparse Representations of Images Using Overcomplete Complex Wavelets
 2005 IEEE/SP 13th Workshop on Statistical Signal Processing
, 2005
"... This paper describes an algorithm developed for generating sparse representations of images in a quick and efficient way using an overcomplete subband representation. Here we demonstrate the algorithm applied to Kingsbury's popular Dual Tree Complex Wavelet Transform. ..."
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Cited by 6 (1 self)
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This paper describes an algorithm developed for generating sparse representations of images in a quick and efficient way using an overcomplete subband representation. Here we demonstrate the algorithm applied to Kingsbury's popular Dual Tree Complex Wavelet Transform.
Pointwise shapeadaptive DCT as an overcomplete denoising tool
 PROC. 2005 INT. TICSP WORKSHOP SPECTRAL METH. MULTIRATE SIGNAL PROCESS., SMMSP 2005
, 2005
"... A novel approach to imagedenoising based on the shapeadaptive DCT (SADCT) is presented. The anisotropic LPAICI technique is used in order to deÞne the shape of the transform’s support in a pointwise adaptive manner. It means that for each point in the image an adaptive estimation neighborhood is ..."
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Cited by 5 (5 self)
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is found. For each one of these neighborhoods a SADCT is performed. The thresholded SADCT coefÞcients are used to reconstruct a local estimate of the signal within the adaptiveshape region. Since regions corresponding to different points are in general overlapping (and thus generate an overcomplete
Robust perceptual coding of overcomplete frame expansions
 Proc. of SPIE
, 2001
"... The cortex transform provides a meaningful representation of images in terms of the responses of cortical cells. It is based on experimental results from human vision research. The multiple orientations obtained in the expansion are of interest for image analysis applications. In image coders, quant ..."
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Cited by 1 (0 self)
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, quantization can exploit to a large extent psychovisual properties. This transform belongs to a group of overcomplete transforms. This property has not benefited their use in coding applications. However, the inherent redundancy of overcomplete representations can be exploited to increase the robustness
Results 1  10
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