3D Haar Wavelet Transform Calculator

Description

This 3D Haar Wavelet Transform Calculator computes approximation and detail coefficients for a 3D signal, visualizing results for tensor analysis.

Input 3D Signal (e.g., [[[1,2],[3,4]],[[5,6],[7,8]]]):

For a 3D signal s[i,j,k] with even dimensions N×M×P, the 3D Haar wavelet transform computes coefficients over three dimensions:

Approximation: a[i,j,k] = (s[2i,2j,2k] + s[2i,2j,2k+1] + s[2i,2j+1,2k] + s[2i,2j+1,2k+1] + s[2i+1,2j,2k] + s[2i+1,2j,2k+1] + s[2i+1,2j+1,2k] + s[2i+1,2j+1,2k+1]) / √8
Detail coefficients (7 types, e.g., HLL): d_HLL[i,j,k] = (s[2i,2j,2k] - s[2i,2j,2k+1] + s[2i,2j+1,2k] - s[2i,2j+1,2k+1] + s[2i+1,2j,2k] - s[2i+1,2j,2k+1] + s[2i+1,2j+1,2k] - s[2i+1,2j+1,2k+1]) / √8

Where i = 0, ..., N/2-1, j = 0, ..., M/2-1, k = 0, ..., P/2-1, and √8 ensures orthogonality.

Example 1: Input: [[[1,2],[3,4]],[[5,6],[7,8]]]
Solution: Approximation: [[[4.5962]]], Detail (HLL): [[[-1.4142]]] (other details omitted for brevity)
Example 2: Input: [[[0,0],[1,1]],[[2,2],[3,3]]]
Solution: Approximation: [[[1.4142]]], Detail (HLL): [[[0]]]
Example 3: Input: [[[2,2],[2,2]],[[2,2],[2,2]]]
Solution: Approximation: [[[2.8284]]], Detail (HLL): [[[0]]]
Example 4: Input: [[[1,-1],[2,-2]],[[3,-3],[4,-4]]]
Solution: Approximation: [[[0]]], Detail (HLL): [[[2.8284]]]
Example 5: Input: [[[5,3],[7,1]],[[2,4],[6,8]]]
Solution: Approximation: [[[4.5962]]], Detail (HLL): [[[0]]]