• Title, Summary, Keyword: ${\ell}_1$ norm minimization

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Robust inversion of seismic data using ${\ell}^1/{\ell}^2$ norm IRLS method (${\ell}^1/{\ell}^2$ norm IRLS 방법을 사용한 강인한 탄성파자료역산)

  • Ji Jun
    • 한국지구물리탐사학회:학술대회논문집
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    • pp.227-232
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    • 2005
  • Least squares (${\ell}^2-norm$) solutions of seismic inversion tend to be very sensitive to data points with large errors. The ${\ell}^p-norm$ minimization for $1{\le}p<2$ gives more robust solutions, but usually with higher computational cost. Iteratively reweighted least squares (IRLS) gives efficient approximate solutions of these ${\ell}^p-norm$ problems. I propose a simple way to implement the IRLS method for a hybrid ${\ell}^1/{\ell}^2$ minimization problem that behaves as ${\ell}^2$ fit for small residual and ${\ell}^1$ fit for large residuals. Synthetic and a field-data examples demonstrates the improvement of the hybrid method over least squares when there are outliers in the data.

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Performance Analysis of Compressed Sensing Given Insufficient Random Measurements

  • Rateb, Ahmad M.;Syed-Yusof, Sharifah Kamilah
    • ETRI Journal
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    • v.35 no.2
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    • pp.200-206
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    • 2013
  • Most of the literature on compressed sensing has not paid enough attention to scenarios in which the number of acquired measurements is insufficient to satisfy minimal exact reconstruction requirements. In practice, encountering such scenarios is highly likely, either intentionally or unintentionally, that is, due to high sensing cost or to the lack of knowledge of signal properties. We analyze signal reconstruction performance in this setting. The main result is an expression of the reconstruction error as a function of the number of acquired measurements.

Patch based Semi-supervised Linear Regression for Face Recognition

  • Ding, Yuhua;Liu, Fan;Rui, Ting;Tang, Zhenmin
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.13 no.8
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    • pp.3962-3980
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    • 2019
  • To deal with single sample face recognition, this paper presents a patch based semi-supervised linear regression (PSLR) algorithm, which draws facial variation information from unlabeled samples. Each facial image is divided into overlapped patches, and a regression model with mapping matrix will be constructed on each patch. Then, we adjust these matrices by mapping unlabeled patches to $[1,1,{\cdots},1]^T$. The solutions of all the mapping matrices are integrated into an overall objective function, which uses ${\ell}_{2,1}$-norm minimization constraints to improve discrimination ability of mapping matrices and reduce the impact of noise. After mapping matrices are computed, we adopt majority-voting strategy to classify the probe samples. To further learn the discrimination information between probe samples and obtain more robust mapping matrices, we also propose a multistage PSLR (MPSLR) algorithm, which iteratively updates the training dataset by adding those reliably labeled probe samples into it. The effectiveness of our approaches is evaluated using three public facial databases. Experimental results prove that our approaches are robust to illumination, expression and occlusion.

Measurement Coding for Compressive Sensing of Color Images

  • Dinh, Khanh Quoc;Trinh, Chien Van;Nguyen, Viet Anh;Park, Younghyeon;Jeon, Byeungwoo
    • IEIE Transactions on Smart Processing and Computing
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    • v.3 no.1
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    • pp.10-18
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    • 2014
  • From the perspective of reducing the sampling cost of color images at high resolution, block-based compressive sensing (CS) has attracted considerable attention as a promising alternative to conventional Nyquist/Shannon sampling. On the other hand, for storing/transmitting applications, CS requires a very efficient way of representing the measurement data in terms of data volume. This paper addresses this problem by developing a measurement-coding method with the proposed customized Huffman coding. In addition, by noting the difference in visual importance between the luma and chroma channels, this paper proposes measurement coding in YCbCr space rather than in conventional RGB color space for better rate allocation. Furthermore, as the proper use of the image property in pursuing smoothness improves the CS recovery, this paper proposes the integration of a low pass filter to the CS recovery of color images, which is the block-based ${\ell}_{20}$-norm minimization. The proposed coding scheme shows considerable gain compared to conventional measurement coding.