Congratulations to our ESR 6 from MENELAOSᴺᵀ, Sanhita Guha, who successfully defended her PhD thesis on the topic of “Radar Band Fusion for improved Range Resolution using Compressed Sensing” on April 8, 2024 at the Fraunhofer FHR under the supervision of Prof. Ender Joachim and Dr.-Ing. Miguel Heredia Conde (Center for Sensor Systems -ZESS).
High range resolution radar imaging is possible only when a scene is detected using a wide band radar. In the past few years, remote sensing applications have multiplied and evolved rapidly, which has led to an increased demand for such high resolution imaging. As a result, the need for wider frequency bands has also increased. However, there has been an exponential rise in spectrum congestion, leading to a direct conflict with this wide band requirement. A large number of devices and applications need access to the frequency spectrum, which is a limited resource. Consequently, in many cases, only disjoint narrow frequency bands are available for imaging. Therefore, the goal is to now obtain the desired high resolution by making use of the available narrow bands.
Since this problem appears to be a specialized case of imaging with missing or limited measurements, it makes sense to examine past research clone in this area. lt is found that several efforts have been made to obtain high resolution images using a limited number of measurements, out of which Compressed Sensing (CS) based methods are quite popular. CS techniques exploit the underlying sparsity of a scene to efficiently solve an under-determined system of linear equations and provide a high-resolution scene estimate. Since radar scenes are inherently sparse, this is a logical approach. However, it is found that in most existing works, the limitation in the number of measurement arises due to randomly missing samples. The problem addressed here is slightly different. The disjoint narrow bands in the current situation give rise to continuous blocks of missing data, or, in other words, continuous gaps in the frequency band.
CS applied to such a ‘gapped-band’ problem has, to the author’s knowledge, not been explored in literature and this thesis aims to address this research gap. Specifically, two issues are addressed:
• Coherence: The coherence is a metric that determines the quality of the CS sensing matrix and a lower coherence value corresponds to a better scene estimate. For a higher range resolution, the scene estimation must be carried out on a finely spaced range grid, which leads to an increase in coherence. The presence of a continuous gap further aggravates this problem.
• Large computational load: High computational load is a popular challenge in using CS for practical radar applications. Specially for systems like Synthetic Aperture Radar (SAR), the volume of raw data generated per scene is large. The additional requirement of a higher resolution makes the SAR image reconstruction even more computationally expensive.
This thesis addresses the aforementioned problems via the following contributions. First, structured sensing matrices are formulated taking the ‘gapped-band’ into consideration. Then, two algorithms are proposed- the Subdivision Fusion (SF) algorithm, and the Approximated Observation (AO) algorithm. The SF algorithm addresses both the problems via a subdivision scheme based on the proposed structured sensing matrices. The subdivision step improves the coherence value, reduces the size of the CS problem and makes a parallel execution possible. The AO algorithm also addresses both issues by replacing the CS sensing matrix with matched filter based processors. Computationally heavy multiplications involving the sensing matrix are replaced by FFTs within a soft-thresholding CS algorithm loop. Both algorithms introduce new ideas and modifications to adapt existing CS methods to the gapped-band problem. In addition, the thesis presents an extension of the SF algorithm that deals with multi-path imaging for a ToF system, thereby showing that the proposed idea is flexible and may be adapted for different imaging systems.
The algorithms are tested on synthetic scenes as well as real world data and the results achieved show significant improvement in range resolution despite the coherence limitations imposed by the gapped band. lt is concluded that the proposed modifications to the CS sensing matrix improve the conditioning of the previously ill-posed CS problem and allow it to provide better scene estimates. Possible future directions involving practical applications of the proposed ideas are also discussed.
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