I thought so… thanks for detailed explanation and the suggestions. One more thing, if the subject is huge in size, (say a painting of 1.5 square meters) and it is required to be printed at 1:1 size using 360ppi as input to the printer (say Epson 9900), then the process should be 1. up-sampling to 360ppi, 2. sharpening, 3. print or should it be 1. Upsampling to 720 ppi 2. sharpening 3. Downsampling back to 360ppi and then, 4. print ? …Is there a benefit if one doesn't down-sample when the image size comes to less than 360ppi? Thanks.
First of all, it is not absolutely necessary to upsample/sharpen/downsample, it is just a method to allow very accurate sharpening. With the proper technique, and precautions, and experience, it is possible to directly sharpen at the final output size (that also means the use of blend-if sharpening layers to avoid clipping).
Second, when the original file already has a lot of pixels, upsampling it by a factor of e.g. 3x just for sharpening may cause issues due to file size, and the deconvolution sharpening will take a lot of processing time and system memory to complete.
Third, depending on the printing pipeline, and given the physical size of the output (and thus normal viewing distance), I think that upsampling to 360 PPI will probably be adequate and printing will be faster than at 720 PPI. Only if very close inspection needs to be possible without compromises, and the input file has enough detail to require little interpolation to reach output dimensions, then creating a 720 PPI output file can make a difference (because the printer interpolation is not very good, and doesn't allow to sharpen at the final output size). The 'finest detail' option must be activated in the Epson printer driver to actually print at 720 PPI.
When an output file has less than 360 PPI at the final output size, one can consider upsampling with an application like PhotoZoom Pro
(only for upsampling), because that actually adds edge detail at a higher resolution, but it depends on the original image contents. Other upsampling methods do not create additional resolution, but will allow to push sharpening a bit further at 720 PPI (because small artifacts will be rendered too small to notice). So once you have more than 360 PPI useful data, I would not downsample to 360 PPI, but upsample to 720 PPI and sharpen at that size and print with 'finest detail' activated.
Since output sharpening also needs to pre-compensate for contrast losses due to print media (ink diffusion, paper structure, limited media contrast, etc.) I'd seriously consider using Topaz Detail, because that not only offers deconvolution (deblur) but also micro-contrast controls. It also allows to boost the low contrast micro-detail in shadows more than in the highlights, which is especially useful for non-glossy output media or dim viewing conditions. But that all goes beyond the main subject of this thread.