By generalising 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 apert...
详细信息
By generalising 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 study, the formulation of the multidimensional dictionary learning (mdDL) problem is expressed and two 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 minimisation 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. As an application, we use the proposed methods to restore and denoise the ISAR image. 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 12 and 4 dB, respectively.
Generalisation of one-dimensional dictionary learning (1DDL) algorithms to Multidimensional (md) mode and its utilisation in md data applications, increases the speed and reduces the computational complexity. An examp...
详细信息
Generalisation of one-dimensional dictionary learning (1DDL) algorithms to Multidimensional (md) mode and its utilisation in md data applications, increases the speed and reduces the computational complexity. An example of such an application is 3D inverse synthetic aperture radar (ISAR) image reconstruction and noise reduction. In this study, in addition to md mode generalisation, the formulation structure of the multidimensional dictionary learning (mdDL) problem is discussed followed by two novel algorithms to solve it. The first one is based on the K-singular value decomposition algorithm for 1DDL, which uses alternating minimisation and singular value decomposition. The second algorithm is the extension of the sequential generalisation of K-means 1DDL algorithm to the md mode. Moreover, the md tensor denoising method based on the mdDL algorithm (mdDL-ALG) is proposed. As an application, the proposed method is used to denoise the 3D ISAR image. The numerical simulations reveal that the proposed methods, in addition to reducing the memory consumption and the computational complexity, also enjoy higher convergence rate in comparison to 1D algorithms. Specifically, convergence speed of md algorithms, depending on the training data size, is up to at least 10 times faster than the equivalent 1D counterparts. As revealed through the simulations, the amount of signal to noise ratio recovered by the proposed methods is almost 2 dB higher than the case using a pre-designed dictionary for denoising. Moreover, it outperforms about 10 dB over the case with the conventional 3D-IFFT method for image construction.
暂无评论