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The  l  1 -norm regularization has attracted attention for image reconstruction in computed tomography. The  l  0 -norm of the gradients of an image provides a measure of the sparsity of gradients of the image. In this paper, we present a new combined  l  1 -norm and  l  0 -norm regularization model for image reconstruction from limited projection data in computed tomography. We also propose an algorithm in the algebraic framework to solve the optimization effectively using the nonmonotone alternating direction algorithm with hard thresholding method. Numerical experiments indicate that this new algorithm makes much improvement by involving  l  0 -norm regularization.

international journal of biomedical imaging

An Algorithm of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:msub><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:math>-Norm and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:msub><mml:mrow><mml:mi>l</mml:mi></mml:mrow><mml:mrow><mml:mn>0</mml:mn></mml:mrow></mml:msub></mml:math>-Norm Regularization Algorithm for CT Image Reconstruction from Limited Projection

An Algorithm of l1-Norm and l0-Norm Regularization Algorithm for CT Image Reconstruction from Limited Projection