Abstract
Iterative hard thresholding (IHT) is a beneficial tool for the recovery of sparse vectors in compressed sensing. In this study, we propose a high-accuracy distributed iterative hard thresholding algorithm (HDIHT) with explicit consideration given to the case in which noise is generated. The results of our theoretical analysis show that it is possible to cancel the noise in the HDIHT compared to the IHT. The performance of the HDIHT in the case including noise was equivalent to the classic IHT in the noise-free case. A numerical experiment is also included, and the results are in accordance with the theoretical analysis.
Highlights
Many natural signals and images can have concise representations when represented on a convenient basis
We consider a noisy environment where the samples are polluted by random noise. This setting is common in the compressed sensing literature, where x = y +
The noise is regarded as a vector, whereas in this study, we consider it as a random variable. By treating it as a random variable, theoretical analysis can show that the noise can be canceled using a distributed approach, and an expectation estimation can be conducted using not just a worst case estimation in the classical analysis of classical Iterative hard thresholding (IHT)
Summary
Many natural signals and images can have concise representations when represented on a convenient basis. The distributed approach has garnered research interest because of its divide-and-conquer strategy, which reduces the difficulty of managing a substantial amount of data This approach works in three steps: partitioning data into disjoint subsets according to the number of machines, applying the same algorithm to each machine with the corresponding subset of data, and obtaining the global output using an averaging method from the individual outputs of each machine [10]. We consider a noisy environment where the samples are polluted by random noise This setting is common in the compressed sensing literature, where x = y +. The noise is regarded as a vector, whereas in this study, we consider it as a random variable By treating it as a random variable, theoretical analysis can show that the noise can be canceled using a distributed approach, and an expectation estimation can be conducted using not just a worst case estimation in the classical analysis of classical IHT.
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