In mirrored aperture synthesis (MAS), the existing brightness temperature image reconstruction methods include inverse cosine transform and impulse matrix reconstruction methods. However, the quality of the MAS brightness temperature images reconstructed by the existing methods is still poor and needs to be improved. This article proposes a method of MAS brightness temperature image reconstruction with deep convolutional neural network (CNN). The network includes two fully connected (FC) layers, multiple convolutional layers, and deconvolutional layers, which realize the image reconstruction for MAS. This method uses deep CNN to learn the MAS image reconstruction mapping and system errors, so as to improve the performance of the brightness temperature image reconstruction. Both simulation and experimental results verify that the performance of the proposed MAS-CNN method is better than the existing MAS image reconstruction methods.

The arrangement of the antenna array of the mirrored aperture synthesis (MAS) determines the transformation matrix for solving the cosine visibilities. When the transformation matrix is rank deficient, the solved cosine visibilities will introduce the rank-deficient error. For the two-dimensional (2-D) mirrored aperture synthesis (2-D MAS), the existing literature has discussed the relationship between the arrangement of the antenna array and the rank-deficient error but has not proposed an array that can achieve a full rank transformation matrix, which is called the rank-full array (RFA). Based on a new method for calculating the rank of the transformation matrix (RTM) and the literature on one-dimensional (1-D) RFAs, this letter proves that 2-D RFA cannot be obtained when the reflectors are all metal, and by introducing a reflector made of a magnetic conductor, 2-D RFA can be obtained. Besides, this letter obtained the existence conditions for 2-D RFA. Based on those conditions, two methods are proposed to obtain 2-D RFAs.

In two-dimensional mirrored aperture synthesis (2-D MAS), the rank of the transformation matrix can affect the accuracy of the solved cosine visibilities; therefore, it has an impact on the accuracy of the reconstructed brightness temperature image. In this article, the influence of the rank deficient on the accuracy of the reconstructed brightness temperature image of 2-D MAS is discussed. An analysis of the rank-deficient error is performed by computing its impact on the radiometric accuracy for a reference scene. Two correction methods based on multiple measurements are proposed to correct the rank-deficient error. The simulations and experiments are carried out to demonstrate the effectiveness of the proposed methods.

Mirrored aperture synthesis (MAS) has been proposed as a novel interferometry to achieve higher spatial resolution in passive microwave remote sensing. The phase and amplitude errors for MAS are a crucial problem that has yet to be analyzed. In this letter, a model for the phase and amplitude errors is established. A correction method based on an external source is proposed to correct the phase and amplitude errors. An analysis of the position of the external source is performed by computing its impact on the radiometric accuracy of a reference scene. The imaginary parts of the cross correlations for MAS are analyzed for the first time. Simulations and experiments are carried out to demonstrate the effectiveness of the correction method.

In 2-D mirrored aperture synthesis (2-D MAS), the array configuration determines the rank of the transformation matrix, which can affect the accuracy of the solved cosine visibilities. Ultimately, errors in solved cosine visibilities degrade the quality of reconstructed brightness temperature images. In this letter, the maximum rank of the transformation matrix is analyzed and proven by mathematical induction. An array optimization model of 2-D MAS based on the ``maximum-rank'' criterion is established, and optimal arrays are presented. Finally, the simulations and experiments are carried out to demonstrate the effectiveness of the optimization model.