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