Nonsparsity influence on the ISAR recovery from reduced data [Correspondence]

Error in the Reconstruction of Nonsparse Images

“…Signals that can be characterized by a small number of nonzero coefficients are referred to as sparse signals [1][2][3][4][5][6][7][8][9][10][11]. These signals can be reconstructed from a reduced set of measurements .…”

“…Signal sparsity in a transformation domain can be observed in a number of important applications. For example, ISAR images are commonly sparse in the two-dimensional Fourier transform domain, whereas digital images are well known for their good concentration in the domain of two-dimensional (2D) discrete cosine transform (DCT) [8,[21][22][23][24].…”

“…The reduced number of measurements may appear due to different causes. In the CS applications, it arises as a consequence of intentional sampling strategy, aiming to reduce the signal acquisition time, equipment load, and subject exposure to potentially dangerous radiation during the acquisition in biomedical applications, or, simply, there is a particular interest to reduce the amount of acquired samples while preserving the complete information (compression) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. In certain cases, physical unavailability can be a cause of a reduced number of measurements.…”

“…It means that besides the coefficients with significant values, carrying most of the signal energy, small valued coefficients may appear instead of zero-valued ones. As sparse recovery algorithms assume certain sparsity level, these coefficients will remain unreconstructed [8,24]. This leads to inevitable reconstruction errors.…”

“…However, if weak signal coefficients of a nonsparse signal remain unreconstructed, their contribution to the noise in the reconstructed coefficients remains. If a nonsparse signal is reconstructed with a reduced set of available samples, then the noise due to the missing samples in unreconstructed coefficients will be considered as an additive input noise in the reconstructed signal [8].…”