---
datasets:
- danjacobellis/LSDIR_540
- danjacobellis/musdb_segments
---
# Wavelet Learned Lossy Compression
- [Project page and documentation](https://danjacobellis.net/walloc)
- [Paper: "Learned Compression for Compressed Learning"](https://danjacobellis.net/_static/walloc.pdf)
- [Additional code accompanying the paper](https://github.com/danjacobellis/lccl)
Comparison of WaLLoC with other autoencoder designs for RGB Images and stereo audio.
Example of forward and inverse WPT with $J=2$ levels. Each level applies filters $\text{L}_{\text{A}}$ and $\text{H}_{\text{A}}$ independently to each of the signal channels, followed by downsampling by two $(\downarrow 2)$. An inverse level consists of upsampling $(\uparrow 2)$ followed by $\text{L}_{\text{S}}$
and $\text{H}_{\text{S}}$, then summing the two channels. The full WPT $\tilde{\textbf{X}}$ of consists of $J$ levels.
WaLLoC’s encode-decode pipeline. The entropy bottleneck and entropy coding steps are only required to achieve high compression ratios for storage and transmission. For compressed-domain learning where dimensionality reduction is the primary goal, these steps can be skipped to reduce overhead and completely eliminate CPU-GPU transfers.
# Wavelet Learned Lossy Compression (WaLLoC)
WaLLoC sandwiches a convolutional autoencoder between time-frequency analysis and synthesis transforms using CDF 9/7 wavelet filters. The time-frequency transform increases the number of signal channels, but reduces the temporal or spatial resolution, resulting in lower GPU memory consumption and higher throughput. WaLLoC's training procedure is highly simplified compared to other $\beta$-VAEs, VQ-VAEs, and neural codecs, but still offers significant dimensionality reduction and compression. This makes it suitable for dataset storage and compressed-domain learning. It currently supports 1D and 2D signals, including mono, stereo, or multi-channel audio, and grayscale, RGB, or hyperspectral images.
## Installation
1. Follow the installation instructions for [torch](https://pytorch.org/get-started/locally/)
2. Install WaLLoC and other dependencies via pip
```pip install walloc PyWavelets pytorch-wavelets```
## Image compression
```python
import os
import torch
import json
import matplotlib.pyplot as plt
import numpy as np
from types import SimpleNamespace
from PIL import Image, ImageEnhance
from IPython.display import display
from torchvision.transforms import ToPILImage, PILToTensor
from walloc import walloc
from walloc.walloc import latent_to_pil, pil_to_latent
```
### Load the model from a pre-trained checkpoint
```wget https://hf.co/danjacobellis/walloc/resolve/main/RGB_16x.pth```
```wget https://hf.co/danjacobellis/walloc/resolve/main/RGB_16x.json```
```python
device = "cpu"
codec_config = SimpleNamespace(**json.load(open("RGB_16x.json")))
checkpoint = torch.load("RGB_16x.pth",map_location="cpu",weights_only=False)
codec = walloc.Codec2D(
channels = codec_config.channels,
J = codec_config.J,
Ne = codec_config.Ne,
Nd = codec_config.Nd,
latent_dim = codec_config.latent_dim,
latent_bits = codec_config.latent_bits,
lightweight_encode = codec_config.lightweight_encode
)
codec.load_state_dict(checkpoint['model_state_dict'])
codec = codec.to(device)
codec.eval();
```
### Load an example image
```wget "https://r0k.us/graphics/kodak/kodak/kodim05.png"```
```python
img = Image.open("kodim05.png")
img
```
### Full encoding and decoding pipeline with .forward()
* If `codec.eval()` is called, the latent is rounded to nearest integer.
* If `codec.train()` is called, uniform noise is added instead of rounding.
```python
with torch.no_grad():
codec.eval()
x = PILToTensor()(img).to(torch.float)
x = (x/255 - 0.5).unsqueeze(0).to(device)
x_hat, _, _ = codec(x)
ToPILImage()(x_hat[0]+0.5)
```
### Accessing latents
```python
with torch.no_grad():
X = codec.wavelet_analysis(x,J=codec.J)
z = codec.encoder[0:2](X)
z_hat = codec.encoder[2](z)
X_hat = codec.decoder(z_hat)
x_rec = codec.wavelet_synthesis(X_hat,J=codec.J)
print(f"dimensionality reduction: {x.numel()/z.numel()}×")
```
dimensionality reduction: 16.0×
```python
plt.figure(figsize=(5,3),dpi=150)
plt.hist(
z.flatten().numpy(),
range=(-25,25),
bins=151,
density=True,
);
plt.title("Histogram of latents")
plt.xlim([-25,25]);
```
# Lossless compression of latents
```python
def scale_for_display(img, n_bits):
scale_factor = (2**8 - 1) / (2**n_bits - 1)
lut = [int(i * scale_factor) for i in range(2**n_bits)]
channels = img.split()
scaled_channels = [ch.point(lut * 2**(8-n_bits)) for ch in channels]
return Image.merge(img.mode, scaled_channels)
```
### Single channel PNG (L)
```python
z_padded = torch.nn.functional.pad(z_hat, (0, 0, 0, 0, 0, 4))
z_pil = latent_to_pil(z_padded,codec.latent_bits,1)
display(scale_for_display(z_pil[0], codec.latent_bits))
z_pil[0].save('latent.png')
png = [Image.open("latent.png")]
z_rec = pil_to_latent(png,16,codec.latent_bits,1)
assert(z_rec.equal(z_padded))
print("compression_ratio: ", x.numel()/os.path.getsize("latent.png"))
```
compression_ratio: 26.729991842653856
### Three channel WebP (RGB)
```python
z_pil = latent_to_pil(z_hat,codec.latent_bits,3)
display(scale_for_display(z_pil[0], codec.latent_bits))
z_pil[0].save('latent.webp',lossless=True)
webp = [Image.open("latent.webp")]
z_rec = pil_to_latent(webp,12,codec.latent_bits,3)
assert(z_rec.equal(z_hat))
print("compression_ratio: ", x.numel()/os.path.getsize("latent.webp"))
```
compression_ratio: 28.811254396248536
### Four channel TIF (CMYK)
```python
z_padded = torch.nn.functional.pad(z_hat, (0, 0, 0, 0, 0, 4))
z_pil = latent_to_pil(z_padded,codec.latent_bits,4)
display(scale_for_display(z_pil[0], codec.latent_bits))
z_pil[0].save('latent.tif',compression="tiff_adobe_deflate")
tif = [Image.open("latent.tif")]
z_rec = pil_to_latent(tif,16,codec.latent_bits,4)
assert(z_rec.equal(z_padded))
print("compression_ratio: ", x.numel()/os.path.getsize("latent.tif"))
```
compression_ratio: 21.04034530731638
# Audio Compression
```python
import io
import os
import torch
import torchaudio
import json
import matplotlib.pyplot as plt
from types import SimpleNamespace
from PIL import Image
from datasets import load_dataset
from einops import rearrange
from IPython.display import Audio
from walloc import walloc
```
### Load the model from a pre-trained checkpoint
```wget https://hf.co/danjacobellis/walloc/resolve/main/stereo_5x.pth```
```wget https://hf.co/danjacobellis/walloc/resolve/main/stereo_5x.json```
```python
codec_config = SimpleNamespace(**json.load(open("stereo_5x.json")))
checkpoint = torch.load("stereo_5x.pth",map_location="cpu",weights_only=False)
codec = walloc.Codec1D(
channels = codec_config.channels,
J = codec_config.J,
Ne = codec_config.Ne,
Nd = codec_config.Nd,
latent_dim = codec_config.latent_dim,
latent_bits = codec_config.latent_bits,
lightweight_encode = codec_config.lightweight_encode,
post_filter = codec_config.post_filter
)
codec.load_state_dict(checkpoint['model_state_dict'])
codec.eval();
```
/home/dan/g/lib/python3.12/site-packages/torch/nn/utils/weight_norm.py:143: FutureWarning: `torch.nn.utils.weight_norm` is deprecated in favor of `torch.nn.utils.parametrizations.weight_norm`.
WeightNorm.apply(module, name, dim)
### Load example audio track
```python
MUSDB = load_dataset("danjacobellis/musdb_segments_val",split='validation')
audio_buff = io.BytesIO(MUSDB[40]['audio_mix']['bytes'])
x, fs = torchaudio.load(audio_buff,normalize=False)
x = x.to(torch.float)
x = x - x.mean()
max_abs = x.abs().max()
x = x / (max_abs + 1e-8)
x = x/2
```
```python
Audio(x[:,:2**20],rate=44100)
```
### Full encoding and decoding pipeline with .forward()
* If `codec.eval()` is called, the latent is rounded to nearest integer.
* If `codec.train()` is called, uniform noise is added instead of rounding.
```python
with torch.no_grad():
codec.eval()
x_hat, _, _ = codec(x.unsqueeze(0))
```
```python
Audio(x_hat[0,:,:2**20],rate=44100)
```
### Accessing latents
```python
with torch.no_grad():
X = codec.wavelet_analysis(x.unsqueeze(0),J=codec.J)
z = codec.encoder[0:2](X)
z_hat = codec.encoder[2](z)
X_hat = codec.decoder(z_hat)
x_rec = codec.wavelet_synthesis(X_hat,J=codec.J)
print(f"dimensionality reduction: {x.numel()/z.numel():.4g}×")
```
dimensionality reduction: 4.74×
```python
plt.figure(figsize=(5,3),dpi=150)
plt.hist(
z.flatten().numpy(),
range=(-25,25),
bins=151,
density=True,
);
plt.title("Histogram of latents")
plt.xlim([-25,25]);
```
# Lossless compression of latents
```python
def pad(audio, p=2**16):
B,C,L = audio.shape
padding_size = (p - (L % p)) % p
if padding_size > 0:
audio = torch.nn.functional.pad(audio, (0, padding_size), mode='constant', value=0)
return audio
with torch.no_grad():
L = x.shape[-1]
x_padded = pad(x.unsqueeze(0), 2**16)
X = codec.wavelet_analysis(x_padded,codec.J)
z = codec.encoder(X)
ℓ = z.shape[-1]
z = pad(z,128)
z = rearrange(z, 'b c (w h) -> b c w h', h=128).to("cpu")
webp = walloc.latent_to_pil(z,codec.latent_bits,3)[0]
buff = io.BytesIO()
webp.save(buff, format='WEBP', lossless=True)
webp_bytes = buff.getbuffer()
```
```python
print("compression_ratio: ", x.numel()/len(webp_bytes))
webp
```
compression_ratio: 9.83650170496386
# Decoding
```python
with torch.no_grad():
z_hat = walloc.pil_to_latent(
[Image.open(buff)],
codec.latent_dim,
codec.latent_bits,
3)
X_hat = codec.decoder(rearrange(z_hat, 'b c h w -> b c (h w)')[:,:,:ℓ])
x_hat = codec.wavelet_synthesis(X_hat,codec.J)
x_hat = codec.post(x_hat)
x_hat = codec.clamp(x_hat[0,:,:L])
```
```python
start, end = 0, 1000
plt.figure(figsize=(8, 3), dpi=180)
plt.plot(x[0, start:end], alpha=0.5, c='b', label='Ch.1 (Uncompressed)')
plt.plot(x_hat[0, start:end], alpha=0.5, c='g', label='Ch.1 (WaLLoC)')
plt.plot(x[1, start:end], alpha=0.5, c='r', label='Ch.2 (Uncompressed)')
plt.plot(x_hat[1, start:end], alpha=0.5, c='purple', label='Ch.2 (WaLLoC)')
plt.xlim([400,1000])
plt.ylim([-0.6,0.3])
plt.legend(loc='lower center')
plt.box(False)
plt.xticks([])
plt.yticks([]);
```
```python
!jupyter nbconvert --to markdown README.ipynb
```
[NbConvertApp] Converting notebook README.ipynb to markdown
[NbConvertApp] Support files will be in README_files/
[NbConvertApp] Writing 1409744 bytes to README.md
```python
!sed -i 's|!\[png](README_files/\(README_[0-9]*_[0-9]*\.png\))||g' README.md
```