Analysis dictionary learning using block coordinate descent framework with proximal operators

Li, Zhenni; Ding, Shuxue; Hayashi, Takafumi; Li, Yujie

doi:10.1016/j.neucom.2017.02.014

Cited by 7 publications

(2 citation statements)

References 23 publications

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“…Employing the proximal operator approach [37, 38], we can obtain the closed‐form solutions of

\mathbf {h}_{k}

, given as:

\begin{align} h_{kj}^*&=[\mathrm{P}_{g,\lambda }(\mathbf {d}_{k}+\mathbf {z}_{k})]_j\nonumber \\ &= {\left\lbrace \def\eqcellsep{&}\begin{array}{rl}[\mathbf {d}_{k}+\mathbf {z}_{k}]_j-\lambda \mathrm{sign}([\mathbf {d}_{k}+\mathbf {z}_{k}]_j), & [\mathbf {d}_{k}+\mathbf {z}_{k}]_j&gt;\alpha ; \\[7pt] 0, & \mathrm{otherwise}, \end{array} \right.} \end{align}

where

h_{kj}

is the j th element of

\mathbf {h}_k

.…”

Section: Mcp‐regularized Sparse Coding For Keyframe Extraction Using Dcamentioning

confidence: 99%

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A DCA‐based sparse coding for video summarization with MCP

Tan

et al. 2023

IET Image Processing

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Video summarization offers a summary version that conveys the primary information of a longer video. The main challenges of video summarization are related to keyframe extraction and saliency mapping. Thus, this work proposes a sparse coding model for keyframe extraction and saliency mapping applications. Specifically, the minimax concave penalty (MCP) is utilized as a sparse regularization scheme and the regularized non‐convex MCP problem is solved by decomposing MCP into two convex functions and the convex function's algorithm difference is relied on to solve the resulting sub‐problems. The experimental results demonstrate higher compressed keyframes and saliency maps than current state‐of‐the‐art algorithms. In particular, the model attains a lower summary length of 34% and 19% compared to sparse modeling representation selection (SMRS) and sparse modeling using the determinant sparsity measure (SC‐det), respectively. In addition, the developed scheme has a shorter computation time, requiring 82% and 33% less time than the ITTI and the dense and sparse reconstruction (DSR) methods.

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“…Employing the proximal operator approach [37, 38], we can obtain the closed‐form solutions of

\mathbf {h}_{k}

, given as:

\begin{align} h_{kj}^*&=[\mathrm{P}_{g,\lambda }(\mathbf {d}_{k}+\mathbf {z}_{k})]_j\nonumber \\ &= {\left\lbrace \def\eqcellsep{&}\begin{array}{rl}[\mathbf {d}_{k}+\mathbf {z}_{k}]_j-\lambda \mathrm{sign}([\mathbf {d}_{k}+\mathbf {z}_{k}]_j), & [\mathbf {d}_{k}+\mathbf {z}_{k}]_j&gt;\alpha ; \\[7pt] 0, & \mathrm{otherwise}, \end{array} \right.} \end{align}

where

h_{kj}

is the j th element of

\mathbf {h}_k

.…”

Section: Mcp‐regularized Sparse Coding For Keyframe Extraction Using Dcamentioning

confidence: 99%

“…where z k is the kth row of Z. Then, we compute h k by solving the following formulation: Employing the proximal operator approach [37,38], we can obtain the closed-form solutions of h k , given as:…”

Section: Proposed Keyframe Extraction Model Using Dcamentioning

confidence: 99%