2.1. Upsampling

• 2.1.1. "Fourier Zero Padding"
  • 2.1.1.1. Sinus cardinal interpolation
  • 2.1.1.2. Simple example
  • 2.1.1.3. Summary
• 2.1.2. Tile processing of the large image
  • 2.1.2.1. The implicit edges discontinuities and their associated artifacts
  • 2.1.2.2. The possible solutions
    • 2.1.2.2.1. Margin the original data
    • 2.1.2.2.2. Mirroring the original data
    • 2.1.2.2.3. The periodic + smooth decomposition
  • 2.1.2.3. Conclusion : Sirius uses the p+s decomposition
• 2.1.3. The discontinuous signals
  • 2.1.3.1. Illustrating the issue
  • 2.1.3.2. The windowing solution
• 2.1.4. User kernel interpolator
  • 2.1.4.1. One can give Sirius his own low-pass filter
  • 2.1.4.2. The Sirius Filter must lie on the spatial domain
  • 2.1.4.3. The Sirius Filter must be sampled like the upsampled (targeted) signal
  • 2.1.4.4. The Sirius Filter is odd and a GDAL supported image format
  • 2.1.4.5. Sirius auto-shifts the Filter before its FT is computed
  • 2.1.4.6. Sirius can normalize the Filter
  • 2.1.4.7. When Sirius uses a Filter to upsample, the spectrum is periodized instead of zero padded
• 2.1.5. Convolution near the data edges
  • 2.1.5.1. The real edges
  • 2.1.5.2. The virtual edges
  • 2.1.5.3. What Sirius proposes
• 2.1.6. Float upsampling factor