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Compressive sensing reconstruction algorithm using L1-norm minimization via L2-norm minimization
Usman K.a,b, Gunawan H.a, Suksmono A.B.a
a School of Electrical and Informatics Engineering, Institut Teknologi Bandung, Bandung, 40132, Indonesia
b Faculty of Electrical Engineering, Telkom University, Jawa Barat, Indonesia
[vc_row][vc_column][vc_row_inner][vc_column_inner][vc_separator css=”.vc_custom_1624529070653{padding-top: 30px !important;padding-bottom: 30px !important;}”][/vc_column_inner][/vc_row_inner][vc_row_inner layout=”boxed”][vc_column_inner width=”3/4″ css=”.vc_custom_1624695412187{border-right-width: 1px !important;border-right-color: #dddddd !important;border-right-style: solid !important;border-radius: 1px !important;}”][vc_empty_space][megatron_heading title=”Abstract” size=”size-sm” text_align=”text-left”][vc_column_text]© 2018, School of Electrical Engineering and Informatics. All rights reserved.At the moment, there are two main methods of solving the compressive sensing (CS) reconstruction problem which are the convex optimization and the greedy algorithm. Convex optimization has good reconstruction stability but very slow in computation. Greedy algorithm, on the other hand, is very fast but less stable. A fast and stable CS reconstruction algorithm is necessary for a better provision of CS in practical application. In this paper we proposed a CS reconstruction algorithm using L1-norm minimization via L2-norm minimization. This method is based on geometrical interpretation of L1-norm minimization of the reconstruction problem and the fact that the Euclidean distance between L1-norm and L2-norm solution lie closely. In other word, if L2-norm solution is found, then direction to the L1-norm solution is on the shortest path connecting them. This approach offers a simpler computation. Computer simulation showed that proposed algorithm has better stability than the greedy algorithm and faster computation than the convex optimization. The proposed algorithm thus provides an alternative solution for CS reconstruction problem when a balance between speed and stability is required.[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Author keywords” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Indexed keywords” size=”size-sm” text_align=”text-left”][vc_column_text]Compressive sampling,Convex optimization,Greedy algorithm,L1-norm,L2-norm,Sparse reconstruction[/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”Funding details” size=”size-sm” text_align=”text-left”][vc_column_text][/vc_column_text][vc_empty_space][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][vc_empty_space][megatron_heading title=”DOI” size=”size-sm” text_align=”text-left”][vc_column_text]https://doi.org/10.15676/ijeei.2018.10.1.3[/vc_column_text][/vc_column_inner][vc_column_inner width=”1/4″][vc_column_text]Widget Plumx[/vc_column_text][/vc_column_inner][/vc_row_inner][/vc_column][/vc_row][vc_row][vc_column][vc_separator css=”.vc_custom_1624528584150{padding-top: 25px !important;padding-bottom: 25px !important;}”][/vc_column][/vc_row]