微波成像中的參數(shù)化稀疏表征模型

李剛 張顥 孟華東 劉一民 王希勤

摘 要：稀疏表征的任務是找到一個基信號矩陣，在雷達回波數(shù)據(jù)域和稀疏域之間構建一個線性映射。經典稀疏表征模型中，基信號矩陣是預先設定的，例如：傅里葉矩陣、小波矩陣等等，而且在稀疏求解過程中是固定不變的。然而，雷達目標往往存在非合作運動，這將給雷達回波帶來未知的距離徙動和頻率調制，導致傳統(tǒng)基矩陣無法實現(xiàn)非合作目標回波信號的稀疏表征。為解決這一難題，提出了參數(shù)化稀疏表征模型，構建了以目標特征狀態(tài)為參數(shù)的基信號矩陣，并實現(xiàn)了目標運動狀態(tài)估計與稀疏恢復的聯(lián)合求解。仿真和實測雷達數(shù)據(jù)實驗表明，參數(shù)化稀疏表征模型能夠有效地提高雷達圖像質量。

關鍵詞：壓縮感知 雷達成像 稀疏表征 字典學習

Abstract：The goal of sparse representation is to find a dictionary matrix that maps radar signals onto a sparse domain.In traditional models of sparse representation，the dictionary is pre-designed and fixed during the solution process.The popular dictionaries include Fourier and Wavelet matrices.However，the non-cooperative motion of the target causes unknown range migration and frequency modulation. Therefore，traditional dictionaries cannot ensure the sparse representation of the echo from a non-cooperative target.To solve this problem，we propose parametric sparse representation model，create the dictionary related to target motion status parameters，and simultaneously achieve the sparse representation and the parameter estimation.Simulations and experiments on real radar data show that parametric sparse representation is helpful to improve the quality of radar images.

Key Words：Compressed sensing；Radar imaging；Sparse representation；Dictionary learning

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