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Multi Dimensional Dictionary Based Sparse Coding in ISAR Image Reconstruction

Mehrpooya, Ali | 2022

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 55753 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Nayebi, Mohammad Mahdi; Karbasi, Mohammad
  7. Abstract:
  8. By generalizing dictionary learning (DL) algorithms to Multidimensional (MD) mode and using them in applications where signals are inherently multidimensional, such as in three-dimensional (3D) Inverse Synthetic Aperture Radar (ISAR) imaging, it is possible to achieve much higher speed and less computational complexity. In this thesis, the formulation of the Multidimensional Dictionary Learning (MDDL) problem is expressed and six algorithms are proposed to solve it. The first one is based on the method of optimum directions (MOD) algorithm for 1D dictionary learning (1DDL), which uses alternating minimization and gradient projection approach. As the MDDL problem is non-convex, the second algorithm approximates the non-convex objective with a new jointly convex function and efficiently solves it. The third and fourth algorithms are generalizations of the 1DDL algorithm KSVD and SGK to the MD mode, respectively. In the fifth algorithm, we convert the MDDL problem into multiple 1DDL problems and solve each one using 1D methods. The sixth algorithm deals with the problem of DL on incomplete (masked) training data, and there we propose a MD algorithm that obtains with dictionary using masked training data. Then, using the proposed MDDL algorithms, we will present a restoration and denoising method for the tensors. As an application, we use this proposed method in the reconstruction and denoising of 3D ISAR images. The numerical experiments highlight that the proposed algorithms, in addition to reducing the computational complexity and the amount of required memory, also entail less training data for learning the dictionary, and enjoy higher convergence speed in comparison to their one-dimensional (1D) counterparts. Specifically, convergence speed of MD algorithms, depending on the size of the training data, is up to at least 10.7 times faster than the equivalent 1DDL algorithm. According to the simulation results, the SNR value achieved by the proposed algorithms is higher than the case where we use the 3D-IFFT for image reconstruction and the case of fixed dictionaries, by approximately 10 dB and 2 dB, respectively
  9. Keywords:
  10. Motion Compensation ; Compressive Sensing ; Interferometric Inverse Synthetic Aperture Radar (InISAR) ; Multidimensional Sparse Representation ; Range Doppler Profile ; Multidimensional Dictionary Learning

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