⚡ electrical engineering

PaaF: Raising the perceived quality of INR-Based Image Compression

This paper introduces PaaF, a novel INR-based image codec that leverages improved architectural design, adaptive quantization, and efficient entropy coding to significantly enhance rate-distortion performance and perceptual quality while addressing the limitations of long encoding times and metric gaps in existing implicit neural representation methods.

Original authors: Lorenzo Catania, Dario Allegra

Published 2026-06-23

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CC BY 4.0

Original authors: Lorenzo Catania, Dario Allegra

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you have a giant, high-resolution photograph. Traditionally, to send this photo over the internet, you chop it up into tiny blocks, analyze the colors, and write down a set of instructions (like "make this block red, that one blue") to recreate it later. This is how JPEG and other standard formats work.

But what if, instead of chopping the photo into blocks, you treated the entire image as a mathematical recipe?

That is the core idea behind PaaF (Picture as a Function), a new method described in this paper. Here is how it works, explained simply:

1. The "Magic Recipe" vs. The "Block Puzzle"

Think of a traditional image file like a Lego set. You have a box full of specific bricks (pixels) that you have to sort, pack, and ship. When you get the box, you have to rebuild the picture brick by brick. If you lose a few bricks, the picture looks broken.

PaaF treats the image like a magic recipe or a function. Instead of sending the bricks, you send a short, compact set of instructions (a neural network) that says: "If you ask for the color at coordinate X, Y, here is exactly what color it should be."

The Benefit: You can ask for the color of a single pixel, or a million pixels, and the recipe gives you the answer instantly. It doesn't matter how big the image is; the recipe stays the same size.

2. The Problem with Previous "Recipes"

Scientists had tried this "recipe" idea before (using something called Implicit Neural Representations, or INRs), but it had two big flaws:

It took forever to write the recipe: Creating the instructions used to take hours, like trying to write a novel by hand when you could just type it.
The picture looked blurry: The recipes weren't detailed enough, so the reconstructed images often looked fuzzy or lost fine details compared to standard JPEGs.

3. How PaaF Fixes the Recipe

The authors of this paper built a better "kitchen" to write these recipes. They introduced three main upgrades:

A Smarter Architect (The Network Design):
Imagine a construction crew that knows exactly how to build a skyscraper. Previous methods used a crew that was too big and clumsy. PaaF uses a streamlined, efficient crew that knows exactly how to arrange the "bricks" (mathematical layers) to capture fine details without getting confused. They also use a special type of "activation" (a way the math wakes up) that is better at handling the wiggly, complex lines found in real photos.
Adaptive Quantization (The "Smart Packing" System):
When you send a recipe, you have to write down the numbers. Usually, you round these numbers to fit them into a box (e.g., "5.123" becomes "5").
- Old way: Everyone gets the same size box, even if they don't need it.
- PaaF way: It looks at the numbers and says, "This number is very important, let's give it a big box. That one is simple, let's give it a tiny box." It dynamically adjusts the size of the "box" for every single number to save space without losing quality.
Efficient Encoding (The Zip File):
Once the recipe is written and packed, PaaF uses a very efficient compression tool (like a super-smart Zip file) to shrink the file size even further before sending it.

4. The Results: Sharper Pictures, Faster Decoding

The paper tested PaaF against other "recipe" methods and even standard JPEGs.

Better Quality: In tests, PaaF produced clearer images with fewer blurry spots or weird wavy lines, especially in complex areas like tree leaves or brick walls.
Better Efficiency: It managed to get the same (or better) picture quality using fewer "bits" (data) than the other recipe methods.
Fast Decoding: While it still takes a little time to write the recipe (encoding), reading the recipe (decoding) is incredibly fast. Because the recipe is just a set of math instructions, a computer can calculate the colors for millions of pixels all at once (in parallel), making it very fast to view the image.

The Bottom Line

The paper concludes that PaaF is a major step forward for this specific type of image compression. It proves that you don't need to chop images into blocks to get good quality; you can use a mathematical function instead.

The Catch: The paper notes that currently, you have to "train" (write) a new recipe for every single image you want to compress. It's not a "one-size-fits-all" tool yet. However, the decoding process is so fast and efficient that this method shows great promise for the future of how we might store and send images, potentially moving us away from the old "block-based" systems entirely.

Technical Summary: PaaF – Raising the Perceived Quality of INR-Based Image Compression

Problem Statement
Implicit Neural Representations (INRs) offer a paradigm for image compression where images are represented as functions mapping coordinates to colors, approximated by neural networks. While this approach enables resolution independence and parallelizable decoding, existing INR-based codecs suffer from two primary limitations: prohibitively long encoding times (often hours) and a persistent performance gap in classic quality metrics (such as PSNR) compared to traditional codecs (e.g., JPEG) and learned latent-based methods. Previous attempts to improve INR compression, such as meta-learning or hybrid approaches, have either introduced constraints tied to specific training data or added complexity to the decoding process.

Methodology: PaaF (Picture as a Function)
The authors propose PaaF, a purely INR-based image codec designed to enhance rate-distortion performance while maintaining the simplicity and parallelizability of INR decoding. The methodology integrates several novel technical components:

Coordinate-Based Representation & Preprocessing:
- Images are mapped from pixel coordinates $(p_x, p_y)$ to normalized coordinates $(c_x, c_y) \in [-1, 1]$ .
- A colorspace transformation converts RGB to YCbCr, followed by per-channel mean subtraction and normalization to $[-1, 1]$ . This empirically improves reconstruction quality.
Exponential Architectural Configuration:
- To optimize the bits-per-pixel ratio, the network employs an exponential heuristic for layer feature counts. Feature counts decrease exponentially with layer depth, creating depth-proportional bottlenecks.
- Weight restarts and perturbation ranges also decay exponentially during training.
Self-Modulating SIREN Activations:
- The network utilizes a single lean module where all layers (except the tail) employ self-modulating sinusoidal activations (SIRENs).
- Unlike traditional SIRENs that require auxiliary modulation networks, PaaF deterministically samples phase offsets ( $\phi_i$ ) and period modulations ( $\omega_i$ ) based on the output feature index. These parameters are regenerable via shared pseudo-random number generator settings, eliminating the need to transmit them in the bitstream.
Fine-Grained Adaptive Quantization:
- The paper introduces a non-uniform quantization scheme motivated by the observation that post-training weights follow a Laplacian distribution.
- Instead of fixed-bit strategies, PaaF uses a scale factor $s$ and a symbol count $M = 2^e$ (where $e$ is not necessarily an integer) to map values to discrete integers.
- An efficient dichotomic search is employed to find the optimal $e$ that minimizes the rate-distortion trade-off, balancing rate reduction against quality drop.
Entropy Coding and Training Pipeline:
- Quantized parameters are compressed using Brotli and a range coder, selecting the best distribution (Laplacian or Gaussian) for the specific dataset.
- The training pipeline involves iterative fitting with weight perturbation and dataset subdivision (pixel unshuffling) to reduce per-step compute. Quantization is integrated into the selection process at the end of each epoch, followed by full quantization-aware fine-tuning.
Loss Functions:
- The authors tailor loss functions to specific presets:
  - PSNR: Uses a mathematically stable approximation of $\log(\cosh(x))$ .
  - MS-SSIM: Combines L1 loss and SSIM.
  - Visual: A combination of LogCosh and SSIM, designed to optimize perceptual quality.

Key Contributions

PaaF Codec: A novel, open-source image codec based purely on INRs that departs from hybrid or latent-based solutions.
Architectural Innovations: Introduction of self-modulating SIREN layers that remove the need for auxiliary modulation networks and a novel exponential configuration for network depth.
Adaptive Quantization: A flexible quantization scheme that replaces fixed-bit strategies, allowing for non-power-of-2 symbol counts to better fit the weight distribution.
Comprehensive Evaluation: A rigorous benchmarking of PaaF against existing purely INR-based methods (COIN, ICE, Strümpler et al., NIF) and a traditional baseline (JPEG) on the Kodak and CLIC2020 datasets.

Experimental Results

Quantitative Performance: On the Kodak dataset, PaaF outperforms all compared INR-based methods across all metrics (PSNR, MS-SSIM, LPIPS) and bitrates. On the high-resolution CLIC2020 dataset, PaaF shows particularly strong advantages in perceptual metrics (LPIPS), achieving BD-Rate gains of up to -87% over competitors in certain configurations.
Ablation Studies: Experiments confirm that the adaptive quantization scheme significantly outperforms fixed-bit quantization (6, 7, 8, and 12 bits), especially at higher quality encodings. The proposed loss function combinations (LogCosh/SSIM) also demonstrate superior performance over standard L2 or L2+SSIM combinations, particularly in LPIPS.
Qualitative Analysis: Visual comparisons show that PaaF (specifically the "Visual" preset) reduces blurriness and artifacts (such as color aliasing and wavy patterns) seen in JPEG and other INR methods, faithfully reconstructing high-frequency details like wall edges and tree leaves at low bitrates.

Significance and Claims
The paper claims that PaaF successfully narrows the gap between functional representations and established compression paradigms. By improving architectural design and introducing adaptive quantization, the authors demonstrate that purely INR-based methods can achieve consistent improvements in both quantitative metrics and perceptual quality without relying on hybrid latent representations.

The authors emphasize that while INR-based methods still require per-image training (a limitation regarding encoding time), the decoding process remains efficient, parallelizable, and capable of producing high-fidelity, artifact-free reconstructions. The work suggests that functional data representations hold significant potential to revolutionize multimedia compression, provided that computational optimizations and subjective quality studies continue to advance. The authors position PaaF not as a direct competitor to all existing codecs, but as a significant advancement within the specific domain of purely INR-based compression.