Image deconvolution using tree-structured Bayesian group sparse modeling

Zhang, Ganchi; Roberts, T.; Kingsbury, Nick

doi:10.1109/icip.2014.7025920

Cited by 3 publications

(5 citation statements)

References 15 publications

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“…To encourage the persistence of large/small coefficients across scales, where ŵ is a P × 1 vector that forms groups of wavelet coefficients in the non-overlapping space, and the sparse transformation matrix D indicates the presence or absence of correspondence between the overlapping and non-overlapping spaces. Unlike [30], in this paper we construct the D matrix to be a Parseval tight frame such that D T D = I. A simple example of this non-overlapping redundant transformation is shown in Fig.…”

Section: Extension For Tree-structured Modelingmentioning

confidence: 98%

“…To achieve the goal of a fully overlapped group sparse solution, it is possible to incorporate the VBMM model with a wavelet tree structure as shown in [30]. Recent works have demonstrated that modeling wavelet parent-children relationships can be viewed as overlapping group regularization [29,43].…”

Section: Extension For Tree-structured Modelingmentioning

confidence: 99%

“…In addition, the VBMM method has also shown good potential with group-sparse modeling. In [30], we incorporate the VBMM method with a wavelet tree structure based on overlapped groups, which leads to an improved solution compared with unstructured coefficient-sparse modeling.…”

Section: Introductionmentioning

confidence: 99%

“…Different from [26] and [30], we also include the results of image superresolution and MRI image reconstruction. The proposed method can handle very large data sets with a good performance and low computation cost.…”

Section: Introductionmentioning

confidence: 99%

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Variational Bayesian image restoration with group-sparse modeling of wavelet coefficients

Zhang

Kingsbury

2015

Digital Signal Processing

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a r t i c l e i n f o a b s t r a c tArticle history: Available online xxxx Keywords: Image restoration Wavelet group-sparse modeling Variational Bayesian inference Majorization minimization Dual-tree complex waveletsIn this work, we present a recent wavelet-based image restoration framework based on a group-sparse Gaussian scale mixture model. A hierarchical Bayesian estimation is derived using a combination of variational Bayesian inference and a subband-adaptive majorization-minimization method that simplifies computation of the posterior distribution. We show that both of these iterative methods can converge together without needing nested loops, and thus good solutions can be found rapidly in the nonconvex search space. We also integrate our method, variational Bayesian with majorization minimization (VBMM), with tree-structured modeling of the wavelet coefficients. This extension achieves significant gains in performance over the coefficient-sparse version of the algorithm. The experimental results demonstrate that the proposed method and its tree-structured extensions are effective for various imaging applications such as image deconvolution, image superresolution and compressive sensing magnetic resonance imaging (MRI) reconstruction, and that they outperform more conventional sparsityinducing methods based on the l 1 -norm.

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Section: Extension For Tree-structured Modelingmentioning

confidence: 98%

Section: Extension For Tree-structured Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Variational Bayesian image restoration with group-sparse modeling of wavelet coefficients

Zhang

Kingsbury

2015

Digital Signal Processing

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“…Hierarchical sparsity was first studied in [44], [45], [46] and later incorporated into a unimodal dictionary learning framework in [47]. Later, Bayesian hierarchical sparse signal recovery techniques were developed, which form the basis for the following derivation [48], [49].…”

Section: B Hierarchical Sparsitymentioning

confidence: 99%

Multimodal Sparse Bayesian Dictionary Learning

Fedorov,

Rao

2018

Preprint

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This paper addresses the problem of learning dictionaries for multimodal datasets, i.e. datasets collected from multiple data sources. We present an algorithm called multimodal sparse Bayesian dictionary learning (MSBDL). MSBDL leverages information from all available data modalities through a joint sparsity constraint. The underlying framework offers a considerable amount of flexibility to practitioners and addresses many of the shortcomings of existing multimodal dictionary learning approaches. In particular, the procedure includes the automatic tuning of hyperparameters and is unique in that it allows the dictionaries for each data modality to have different cardinality, a significant feature in cases when the dimensionality of data differs across modalities. MSBDL is scalable and can be used in supervised learning settings. Theoretical results relating to the convergence of MSBDL are presented and the numerical results provide evidence of the superior performance of MSBDL on synthetic and real datasets compared to existing methods.

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