基于Berlekamp-Justesen碼的壓縮感知確定性測(cè)量矩陣的構(gòu)造
doi: 10.11999/JEIT140875
基金項(xiàng)目:
國(guó)家973計(jì)劃項(xiàng)目(2012CB315803)，國(guó)家自然科學(xué)基金(61371078)和高等學(xué)校博士學(xué)科點(diǎn)專項(xiàng)科研基金(20130002110051)資助課題
Deterministic Constructions of Compressive Sensing Matrices Based on Berlekamp-Justesen Codes
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摘要: 確定性測(cè)量矩陣構(gòu)造是近期壓縮感知領(lǐng)域的一個(gè)重要研究問(wèn)題。該文基于Berlekamp-Justesen(B-J)碼，構(gòu)造了兩類確定性測(cè)量矩陣。首先，給出一類相關(guān)性漸近最優(yōu)的稀疏測(cè)量矩陣，從而保證其具有較好的限定等距性(RIP)。接著，構(gòu)造一類確定性復(fù)測(cè)量矩陣，這類矩陣可以通過(guò)刪除部分行列使其大小靈活變化。第1類矩陣具有很高的稀疏性，第2類則是基于循環(huán)矩陣，因此它們的存儲(chǔ)開銷較小，編碼和重構(gòu)復(fù)雜度也相對(duì)較低。仿真結(jié)果表明，這兩類矩陣常常有優(yōu)于或相當(dāng)于現(xiàn)有的隨機(jī)和確定性測(cè)量矩陣的重建性能。
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關(guān)鍵詞:
- 壓縮感知 /
- Berlekamp-Justesen碼 /
- 漸近最優(yōu) /
- 復(fù)測(cè)量矩陣 /
- 限定等距性
Abstract: Nowadays the deterministic construction of sensing matrices is a hot topic in compressed sensing. Two classes of deterministic sensing matrices based on the Berlekamp-Justesen (B-J) codes are proposed. Firstly, a class of sparse sensing matrices with near-optimal coherence is constructed. It satisfies the Restricted Isometry Property (RIP) well. Afterwards, a class of deterministic complex-valued matrices is proposed. The row and column numbers of these matrices are tunable through the row and column puncturing. Moreover, the first proposed matrices are high sparsity and the second matrices are able to obtain from the cyclic matrices, thus the storage costs of them are relatively low and both the sampling and recovery processes can be simpler. The simulation results demonstrate that the proposed matrices often perform comparably to, or even better than some random matrices and deterministic measurement matrices. -
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