分塊的有序范德蒙矩陣作為壓縮感知測量矩陣的研究
doi: 10.11999/JEIT140860
基金項目:
國家自然科學基金(61073079),中央高?;究蒲袠I(yè)務(wù)費專項基金(2013JBZ003),高等學校博士點基金(20120009110008)和教育部新世紀優(yōu)秀人才支持計劃(NCET-12-0768)資助課題
Research on the Blocked Ordered Vandermonde Matrix Used as Measurement Matrix for Compressed Sensing
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摘要: 測量矩陣是壓縮感知(Compressed Sensing, CS)的重要組成部分,確定性的測量矩陣易于硬件實現(xiàn),但是重構(gòu)信號的精度一般不如隨機矩陣。針對這一缺點,該文提出并構(gòu)造了一種新的確定性測量矩陣,稱作分塊的有序范德蒙矩陣。范德蒙矩陣具有線性不相關(guān)的性質(zhì),在此基礎(chǔ)上加上分塊操作和對元素進行有序排列得到的分塊的有序范德蒙矩陣,實現(xiàn)了時域中的非均勻采樣,特別適合于維數(shù)較大的自然圖像信號。仿真實驗表明,對于圖像信號該矩陣具有遠高于高斯矩陣的重構(gòu)精度,可以作為實際中的測量矩陣使用。
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關(guān)鍵詞:
- 壓縮感知 /
- 測量矩陣 /
- 線性不相關(guān) /
- 非均勻采樣 /
- 范德蒙矩陣
Abstract: The measurement matrix is an important part of Compressed Sensing (CS). Although the deterministic matrix is easy to implement by the hardware, it performs not so well as a random matrix in the signal reconstruction. To solve this problem, a new deterministic measurement matrix which is called as the blocked ordered Vandermonde matrix is proposed. The blocked ordered Vandermonde matrix is constructed on the basis of the Vandermonde matrix, whose the vectors are linearly independent. Then the block operation is taken and its elements are sorted. The proposed new measurement matrix realizes the non-uniform sampling in the time domain and is specifically suitable for the natural images whose the dimension is usually high. The simulation results show that the proposed matrix is much superior to the Gaussian matrix in the image construction, and can be used in practice. -
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