An MM-Based Algorithm for ℓ1-Regularized Least-Squares Estimation with an Application to Ground Penetrating Radar Image Reconstruction

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
Mandoye NdoyeDavid Greene

Abstract

A penalized least-squares estimation method known as least absolute shrinkage and selection operator (LASSO) and ℓ1-regularized least-squares estimation has been found to perform well in a number of applications, such as machine learning and neuroimaging. In this manuscript, we use the majorizeminimize method to develop an algorithm for minimizing the LASSO objective function, which is the sum of a linear leastsquares objective function plus an ℓ1 penalty term. The proposed algorithm, which we call the LASSO estimation via majorizationminimization (LMM) algorithm, is straightforward to implement, parallelizable, and guaranteed to produce LASSO objective function values that monotonically decrease. Additionally, we formulate an extension of the LMM algorithm for reconstructing ground penetrating radar (GPR) images that is much faster than the standard LMM algorithm and utilizes significantly less memory. Thus, the GPR specific LMM (GPR-LMM) algorithm is able to accommodate the "big data" associated with GPR imaging. We compare our proposed algorithms to state-of-the-art ℓ1-regularized LS algorithms using a time and space complexity analysis. The GPR-LMM greatly outperforms the competing algorithms in terms of the performance met...Continue Reading

References

Feb 1, 1962·Journal of the Optical Society of America·J B KELLER
Feb 6, 2008·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·M Cetin, W C Karl
Jan 29, 2009·Academic Medicine : Journal of the Association of American Medical Colleges·Viet Nguyen
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May 15, 2009·Computational Statistics & Data Analysis·Jan de Leeuw, Kenneth Lange

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