Reflector Image Restoration Using the Compressive Sensing Method from the Echo Signals Measured by an Antenna Array
Abstract
To obtain a reflector image from the echo signals measured by an antenna array, the combined synthetic aperture focusing technique (C-SAFT) method is used. To do so, it is necessary to record the echo signals р for all emitter-receiver pairs of antenna array elements (the dual scanning mode). That is, for an antenna array containing 32 elements, 1024 echo signals should be measured. For restoring the image of reflectors without loss of quality for the number of data рCS fewer than the original set of echo signals р, it is proposed to use the method of compressed measurements or recognition with compression, commonly known as the compressive sensing (CS) method. In addition to reducing the amount of data, the CS method improves the image quality due to increasing its resolution. There are several implementations of this algorithm, the application of which depends on the signal parameters, such as noise and sparsity of the image being restored. For comparison purposes, the reflector images were restored from a part of echo signals using the nonlinear method of maximal entropy (ME). The reflector images restored from the incomplete set of echo signals obtained in numerical and model experiments according to the C-SAFT, ME, and CS methods are presented. In the numerical experiment, the use of the CS method made it possible to resolve, by means of an eight-element array with a 2-mm pitch, 12 point reflectors with reflection coefficients equal to 0.1, 0.5, and 1.0 at a distance of about 12 mm from the antenna array that were located at the corners of three squares with a side of 1 mm (1.18 of the wavelength). The images of the point reflectors took one pixel with the size 0.1×0.1 mm with retaining the specified values of the reflection coefficient ε. Compared with the image obtained using the C-SAFT method, the resolution has been improved by more a factor of 5. Moreover, the amount of data рCS was reduced by 88 times compared with its original value р. In the model experiment, the use of the CS method made it possible to restore the image of reflectors with the amount of data 13 times smaller than its original value р. The CS image was found to be of better quality than the C-SAFT image and commensurable with the ME image. The longitudinal and frontal resolutions of the CS- and ME images have increased by more than a factor of 3 compared with the C-SAFT image.
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Для цитирования: Базулин Е.Г., Соколов Д.М. Восстановление изображения отражателей методом распознавания со сжатием по эхосигналам, измеренным антенной решеткой // Вестник МЭИ. 2018. № 6. С. 128—135. DOI: 10.24160/1993-6982-2018-6-128-135.
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For citation: Bazulin E.G., Sokolov D.M. Reflector Image Restoration Using the Compressive Sensing Method from the Echo Signals Measured by an Antenna Array. MPEI Vestnik. 2018;6:128—135. (in Russian). DOI: 10.24160/1993-6982-2018-6-128-135.
