Application of well-localized Weyl-Heisenberg frames for radar images filtering based on correlation properties of decomposition coefficients

Improving the quality of information supplied by radar systems to solve the tasks of detection and classification of objects, as well as decision-making is an urgent direction of technical improvement, including for systems that form radar images. To combat the effects of interference and distortions of signals affecting the quality of the output information, various filtering methods are used, including the use of transformations that translate the signal into a different space. The Fourier transform is most often used for these purposes, but when analyzing non-stationary signals, one has to resort to additional techniques that reduce the energy and computational efficiency of the transformation, therefore, alternative transformations are considered, including those with good localization of the basis functions, for example, the Weyl–Heisenberg frame decomposition. Due to the redundancy of the frame, the question of creating a filtering algorithm that utilizes this property arises. The purpose of the research was to study the correlation properties of the Weyl–Heisenberg frame decomposition coefficients on the example of radar images; to develop an algorithm for filtering spatial noise and image distortions based on the studied properties; to obtain and describe the results of the algorithm. The local groups of the decomposition coefficients were allocated on account of frame localization structure that take place due to discrete frequency-time shifts of the initializing function in the basis of the frame construction procedure. A set of local groups was analyzed by constructing a covariation matrix. The total correlation parameter was introduced and used for covariation matrix thresholding, which takes place as the algorithm core operation. Afterwards the local groups set was processed by applying the mask based on the thresholding results. The correlation of objects in the original image with local groups of decomposition coefficients with certain values was revealed during the experiments through thresholding. The developed filtering algorithm can be used in processing radar images obtained from ground-based circular radars to minimize the influence of extraneous objects, as well as to build a terrain map of the controlled area. Though the structure of local groups and covariation matrix depends on the structure of the original image, method can be used with various images regarding object detection.