Regularization in radio tomographic imaging

Ramakrishnan Sundaram; Richard Martin; Christopher Anderson

doi:10.1117/12.2012167

28 May 2013 Regularization in radio tomographic imaging

Ramakrishnan Sundaram, Richard Martin, Christopher Anderson

Proceedings Volume 8753, Wireless Sensing, Localization, and Processing VIII; 87530O (2013) https://doi.org/10.1117/12.2012167
Event: SPIE Defense, Security, and Sensing, 2013, Baltimore, Maryland, United States

Abstract

This paper demonstrates methods to select and apply regularization to the linear least-squares model formulation of the radio tomographic imaging (RTI) problem. Typically, the RTI inverse problem of image reconstruction is ill-conditioned due to the extremely small singular values of the weight matrix which relates the link signal strengths to the voxel locations of the obstruction. Regularization is included to offset the non-invertible nature of the weight matrix by adding a regularization term such as the matrix approximation of derivatives in each dimension based on the difference operator. This operation yields a smooth least-squares solution for the measured data by suppressing the high energy or noise terms in the derivative of the image. Traditionally, a scalar weighting factor of the regularization matrix is identified by trial and error (adhoc) to yield the best fit of the solution to the data without either excessive smoothing or ringing oscillations at the boundaries of the obstruction. This paper proposes new scalar and vector regularization methods that are automatically computed based on the weight matrix. Evidence of the effectiveness of these methods compared to the preset scalar regularization method is presented for stationary and moving obstructions in an RTI wireless sensor network. The variation of the mean square reconstruction error as a function of the scalar regularization is calculated for known obstructions in the network. The vector regularization procedure based on selective updates to the singular values of the weight matrix attains the lowest mean square error.

Citation Download Citation

Ramakrishnan Sundaram, Richard Martin, and Christopher Anderson "Regularization in radio tomographic imaging", Proc. SPIE 8753, Wireless Sensing, Localization, and Processing VIII, 87530O (28 May 2013); https://doi.org/10.1117/12.2012167

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