Image & Video Compression · Wavelets

Discrete Wavelet Transform

Step through a 2D Haar decomposition of the demo image: start with the original, split horizontally, decompose vertically, and refine the low-pass branch twice.

Multi-resolution Demo image (grayscale) Haar wavelet

How to read each panel

  • Left regions show low-pass content; right regions show detail bands.
  • After each split, the newest subband is highlighted in the top-left quadrant.
  • All bands are contrast-stretched so small details stay visible.

Decomposition steps

Original image

Reference demo frame (grayscale).

Original image

Click through the steps to see how the 2D Haar transform peels away horizontal, vertical, and nested low-pass information.

What’s happening?

1. Horizontal

Rows are filtered with h = [1, 1]/√2 and g = [1, -1]/√2, then downsampled. The left half is smooth (LL), the right half captures horizontal detail (HL).

2. Vertical

Both halves are filtered column-wise, producing four quadrants: LL, LH, HL, and HH. Darker regions highlight where energy concentrates.

3. Refine LL

The LL quadrant is decomposed horizontally into an even smoother LLL block and a gentle LLH detail band.

4. Refine again

LLL is finally split vertically, exposing the most compact low-pass core (LLLL) and a faint vertical detail (LLLH).

Tip: Use the stage buttons to follow the wavelet refinement order. Every subband is contrast-stretched so edges are easy to spot even in the smallest tiles.

Successive reconstruction

See how subbands add back detail

Drag the slider to reveal how each subband contributes to the demo frame. The newest band glows while completed bands stay shaded.

LL-2 reconstruction Step 1 · LL-2
LL-2
HL-2
LH-2
HH-2
LH-1
HL-1
HH-1

  • 1. LL-2

    Start from the coarsest approximation; it carries the broad luminance structure.

  • 2. LH-2

    Add vertical edges from the second-level low-pass band.

  • 3. HL-2

    Blend in horizontal edges at the same coarse scale.

  • 4. HH-2

    Introduce diagonal detail to complete the level-2 block.

  • 5. LH-1

    Layer in medium-scale vertical contrast from the next level up.

  • 6. HL-1

    Restore medium-scale horizontal contrast.

  • 7. HH-1

    Finish with diagonal detail to reach the full-resolution reconstruction order.