The "Alpha-Sources" blog notes that inflation in Japan and the United States are measured with different methodologies, with the U.S. applying to a much higher extent "hedonic adjustment" and substitution adjustments. As the anonymous blogger and the authors of the study he(?) quotes thinks the U.S. methodology is the correct, they argue that this means that price deflation in Japan have been even higher than previously thought, which also means that real growth have been higher. I would be more inclined to think the Japanese methodology is better and that inflation in the U.S. has been higher and real growth lower.
But regardless of whether Japanese deflation or U.S. inflation have been underestimated, two things are clear: First, relative inflation in the U.S. has clearly been higher and relative growth lower compared to Japan. Second, this implies that the real depreciation of the yen has been even more dramatic than I reported before and that the case for believing that the yen is extremely undervalued is even stronger