scholarly journals 2D Normalized Iterative Hard Thresholding Algorithm for Fast Compressive Radar Imaging

2017 ◽  
Vol 9 (6) ◽  
pp. 619 ◽  
Author(s):  
Gongxin Li ◽  
Jia Yang ◽  
Wenguang Yang ◽  
Yuechao Wang ◽  
Wenxue Wang ◽  
...  





2019 ◽  
Vol 55 (17) ◽  
pp. 957-959 ◽  
Author(s):  
Xiaobo Zhang ◽  
Wenbo Xu ◽  
Jiaru Lin ◽  
Yifei Dang




2019 ◽  
Vol 18 (01) ◽  
pp. 25-48 ◽  
Author(s):  
Simon Foucart ◽  
Rémi Gribonval ◽  
Laurent Jacques ◽  
Holger Rauhut

We investigate the problem of recovering jointly [Formula: see text]-rank and [Formula: see text]-bisparse matrices from as few linear measurements as possible, considering arbitrary measurements as well as rank-one measurements. In both cases, we show that [Formula: see text] measurements make the recovery possible in theory, meaning via a nonpractical algorithm. In case of arbitrary measurements, we investigate the possibility of achieving practical recovery via an iterative-hard-thresholding algorithm when [Formula: see text] for some exponent [Formula: see text]. We show that this is feasible for [Formula: see text], and that the proposed analysis cannot cover the case [Formula: see text]. The precise value of the optimal exponent [Formula: see text] is the object of a question, raised but unresolved in this paper, about head projections for the jointly low-rank and bisparse structure. Some related questions are partially answered in passing. For rank-one measurements, we suggest on arcane grounds an iterative-hard-thresholding algorithm modified to exploit the nonstandard restricted isometry property obeyed by this type of measurements.





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