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The Global Change Observation Mission 1st-Water (GCOM-W1) satellite, which was launched by the Japan Aerospace Exploration Agency in May 2012, contains an Advanced Microwave Scanning Radiometer-2 (AMSR2). The AMSR2 provides multifrequency measurements of microwave energy (brightness temperature) emitted by the Earth's surface and atmosphere. However, each frequency field of view (FOV) differs in size because of its hardware design. For the retrieval of more accurate geophysical parameters from multifrequency brightness temperatures, the brightness temperatures should be modified to be the same as measured in the same FOV. The Backus–Gilbert (BG) method is one of the antenna pattern matching techniques used for this modification. We applied the BG method to the AMSR2 data to define a new data set of modified brightness temperatures, a level 1R (L1R) product that is freely and widely available. We optimized the implementation of the BG method to obtain the L1R product, with smoothing factors dynamically determined for all modified brightness temperatures. This paper describes the implementation method, including the criterion used to determine the smoothing factors and presents a quality assessment of the L1R product. [ABSTRACT FROM PUBLISHER]