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Hard thresholding pursuit (HTP) is a recently proposed iterative sparserecovery algorithm which is a result of combination of a support selection stepfrom iterated hard thresholding (IHT) and an estimation step from theorthogonal matching pursuit (OMP). HTP has been seen to enjoy improved recoveryguarantee along with enhanced speed of convergence. Much of the success of HTPcan be attributed to its improved support selection capability due to thesupport selection step from IHT. In this paper, we propose a generalized HTPalgorithm, called regularized HTP (RHTP), where the support selection step ofHTP is replaced by a IHT-type support selection where the cost function isreplaced by a regularized cost function, while the estimation step continues touse the least squares function. With decomposable regularizer, satisfyingcertain regularity conditions, the RHTP algorithm is shown to produce asequence dynamically equivalent to a sequence evolving according to a HTP-likeevolution, where the identification stage has a gradient premultiplied with atime-varying diagonal matrix. RHTP is also proven, both theoretically, andnumerically, to enjoy faster convergence vis-a-vis HTP with both noiseless andnoisy measurement vectors.

Modified Hard Thresholding Pursuit with Regularization Assisted Support Identification