# Error Bounds for Compressed Sensing Algorithms With Group Sparsity

Ranjan, Shashank (2016) Error Bounds for Compressed Sensing Algorithms With Group Sparsity. Masters thesis, Indian Institute of Technology Hyderabad.

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## Abstract

In compressed sensing, to recover a sparse signal or nearly sparse signal from noisy measurements, most popular method is `1-norm minimization [1]. The signals in this context are actually some vectors in Rn. For conventionally sparse signal, latest approch to derive upper bound for the `2; `1- norm of error between estimated signal and original signal is shown in [2] and [3]. For \group sparse" signals, upper bound for the norm of error is given in [4]. In the present work, we focused on group sparse signals, and presented a unified approach to eatablish upper bound on the norm of error. For group sparse signal recovery, we also introduced a new bound on RIC constant which is diiferent from the one proposed in [4]. A key technical tool, which represents a vector in polytope set by convex combination of sparse vectors is discussed in [2]. We modified this key technical tool for group sparse signals to establish the above discussed unified approach.

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IITH Creators:
IITH CreatorsORCiD
Item Type: Thesis (Masters)
Uncontrolled Keywords: Not available, TD620
Subjects: Others > Electricity
Divisions: Department of Electrical Engineering
Depositing User: Team Library
Date Deposited: 17 Aug 2016 10:40