Comparison of l1-Minimization and Iteratively Reweighted least Squares-l p-Minimization for Image Reconstruction from Compressive Sensing

Este trabalho apresenta um método de compressão de sinais da rede elétrica baseado na técnica de Compressive Sensing combinada com uma abordagem dissociativa. Para isso, utilizam-se os algoritmos Iteratively Reweighted Least-Squares e o Conjugate Gradient. O primeiro adequado para a reconstrução de sinais unidimensionais, enquanto que o segundo é adequado para a reconstrução do sinal em um formato bidimensional. Os resultados demonstram a preservação do sinal após a reconstrução (SNR > 40 dB), além da redução da complexidade computacional, a partir da dissociação do sinal segundo seu comportamento: regime permanente ou disturbio.

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IMAGE RECONSTRUCTION BASED ON COMPRESSIVE SAMPLING USING IRLS AND OMP ALGORITHM

Jurnal Teknologi ◽

10.11113/jt.v78.8327 ◽

2016 ◽

Vol 78 (5) ◽

Author(s):

Indrarini Dyah Irawati ◽

Andriyan B. Suksmono

Keyword(s):

Image Reconstruction ◽

Compressive Sensing ◽

Wavelet Transformation ◽

Matching Pursuit ◽

Sampling Rate ◽

Iteratively Reweighted Least Squares ◽

High Quality ◽

High Quality Image ◽

Quality Image ◽

Test Result

We proposed compressive sensing to reduce the sampling rate of the image and improve the accuracy of image reconstruction. Compressive sensing requires that the representation of the image is sparse on a certain basis. We use wavelet transformation to provide sparsity matrix basis. Meanwhile, to get a projection matrix using a random orthonormal process. The algorithm used to reconstruct the image is orthogonal matching pursuit (OMP) and Iteratively Reweighted Least Squares (IRLS). The test result indicates that a high quality image is obtained along with the number of coefficients M. IRLS has a good performance on PSNR than OMP while OMP takes the least time for reconstruction.

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A Shrinkage Factor-based Iteratively Reweighted Least Squares Shrinkage Algorithm for Image Reconstruction

ISME 2016 - Information Science and Management Engineering IV ◽

10.5220/0006449202890293 ◽

2016 ◽

Author(s):

Jian Zhao ◽

Chao Zhang ◽

Tingting Lu ◽

Weiwen Su ◽

Jian Jia ◽

...

Keyword(s):

Image Reconstruction ◽

Least Squares ◽

Iteratively Reweighted Least Squares ◽

Shrinkage Factor

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A convex program for mixed linear regression with a recovery guarantee for well-separated data

Information and Inference A Journal of the IMA ◽

10.1093/imaiai/iax018 ◽

2018 ◽

Vol 7 (3) ◽

pp. 563-579

Author(s):

Paul Hand ◽

Babhru Joshi

Keyword(s):

Linear Regression ◽

Least Squares ◽

Regression Coefficient ◽

Synthetic Data ◽

Second Order ◽

Convex Program ◽

Iteratively Reweighted Least Squares ◽

L1 Minimization ◽

Second Order Cone ◽

Estimate Regression Coefficient

Abstract We introduce a convex approach for mixed linear regression over d features. This approach is a second-order cone program, based on L1 minimization, which assigns an estimate regression coefficient in $\mathbb {R}^{d}$ for each data point. These estimates can then be clustered using, for example, k-means. For problems with two or more mixture classes, we prove that the convex program exactly recovers all of the mixture components in the noiseless setting under technical conditions that include a well-separation assumption on the data. Under these assumptions, recovery is possible if each class has at least d-independent measurements. We also explore an iteratively reweighted least squares implementation of this method on real and synthetic data.

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