基于最大范數(shù)的低秩稀疏分解模型
doi: 10.11999/JEIT150468 cstr: 32379.14.JEIT150468
基金項目:
國家自然科學基金(61271294, 61472303)和中央高?；究蒲袠I(yè)務費專項資金(NSIY21)
Low-rank Sparse Decomposition Model Based on Max-norm
Funds:
The National Natural Science Foundation of China (61271294, 61472303)
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摘要: 為了更好地解決高維數(shù)據(jù)矩陣低秩稀疏分解問題，該文提出以Max-范數(shù)凸化秩函數(shù)的Max極小化模型，并給出該模型的相應算法。在對新模型計算復雜性分析的基礎上，該文進一步提出了Max約束模型，改進模型不僅在分解問題中效果良好，且相應的投影梯度算法具有更強的時效性。實驗結(jié)果表明，該文提出的兩組模型對于低秩稀疏分解問題均行之有效。
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關鍵詞:
- 圖像分解 /
- Max-范數(shù) /
- 投影梯度法
Abstract: In order to better solve the low-rank and sparse decomposition problem for high-dimensional data matrix, this paper puts forward a novel Max minimization model with Max-norm as the convex relaxation of the rank function, and provides the corresponding algorithm. Based on the complexity analysis on the novel model, an improved Max constraint model is further proposed, which not only has good performance in the decomposition problem but also can be solved with a fast projection gradient method. The experimental results show that the proposed two models are effective for low-rank sparse decomposition problem.-
Key words:
- Image decomposition /
- Max-norm /
- Projected Gradient Method (PGM)
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