Partially sparse imaging of stationary indoor scenes

Abstract

In this paper, we exploit the notion of partial sparsity for scene reconstruction associated with through-the-wall radar imaging of stationary targets under reduced data volume. Partial sparsity implies that the scene being imaged consists of a sparse part and a dense part, with the support of the latter assumed to be known. For the problem at hand, sparsity is represented by a few stationary indoor targets, whereas the high scene density is defined by exterior and interior walls. Prior knowledge of wall positions and extent may be available either through building blueprints or from prior surveillance operations. The contributions of the exterior and interior walls are removed from the data through the use of projection matrices, which are determined from wall-and corner-specific dictionaries. The projected data, with enhanced sparsity, is then processed using l 1 norm reconstruction techniques. Numerical electromagnetic data is used to demonstrate the effectiveness of the proposed approach for imaging stationary indoor scenes using a reduced set of measurements.

Wall clutter mitigation and target detection using Discrete Prolate Spheroidal Sequences

“…We compare our wall mitigation method using a bandpass modulated DPSS basis to the one using a Fourier basis in [11] and the one based on a multiband modulated DPSS dictionary in [5]. The construction of the multiband modulated DPSS dictionary is the same as that used in [5], which includes choosing 5.5ns · ∆F as the bandwidth for the DPSS vectors.…”

“…Ignoring the wall reverberations, the wall return defined in (1) ], which was used in [11]. However, because of the wall reverberations, such a dictionary may not be able to represent the wall return well.…”

“…Let Φ m denote an N 1 × N (often random) sensing matrix which is used at the m-th antenna to further reduce the sensing cost. A sensing matrix Φ m widely used for target detection applications is generated by randomly selecting N 1 rows from the N × N identity matrix [4,5,11]. In this case, computing Φ m y m simply involves picking N 1 entries from y m .…”

“…The measurement y m received by m-th antenna is the sum of r In order to decrease the data size, CS techniques can be utilized to reduce the number of measurements [4,5,11]. Let Γ ⊂ [M ] denote the indices of the (randomly) selected antennas for collecting data, and assume M 1 := #(Γ) antennas are used.…”

“…To overcome this shortcoming, Ahmad et al [5] utilized a dictionary of multiband modulated Discrete Prolate Spheroidal Sequences (DPSS's) [9,10] to efficiently represent the wall return. In a recent paper [11], Ahmad et al cancelled the wall clutter directly in the compressive domain by applying an orthogonal projection matrix (which relates to a Fourier basis) to the measurement vectors. Danvenport et al [12] have provided theoretical results as well as experiments to support such a general framework of compressive signal processing.…”