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Deep Convolutional AutoEncoder-based Lossy Image Compression
Zhengxue Cheng, Heming Sun, Masaru Takeuchi, Jiro Katto
TL;DR
Image compression needs alternatives to fixed traditional transforms that may not flexibly suit all image contents and formats. The paper replaces those transforms with a trained symmetric CAE, rotates its feature maps with PCA, and then quantizes and entropy-codes them. On Kodak images, the method achieves a 13.7% BD-rate decrement versus JPEG2000 while maintaining complexity comparable to JPEG and JPEG2000.
Problem
Traditional codecs use fixed transform matrices and are not expected to provide optimal, flexible coding for all image contents and formats.
Method
A symmetric CAE replaces conventional transforms, is trained with an approximated rate-distortion objective, and uses PCA rotation before quantization and entropy coding.
Results
13.7% BD-rate saving versus JPEG2000 is achieved on 24 Kodak database images, with PSNR used for quality evaluation.
Takeaways & Limitations
The method outperforms JPEG and JPEG2000 in PSNR and has complexity comparable to JPEG and JPEG2000.
Abstract
from arXiv · showhide
Image compression has been investigated as a fundamental research topic for many decades. Recently, deep learning has achieved great success in many computer vision tasks, and is gradually being used in image compression. In this paper, we present a lossy image compression architecture, which utilizes the advantages of convolutional autoencoder (CAE) to achieve a high coding efficiency. First, we design a novel CAE architecture to replace the conventional transforms and train this CAE using a rate-distortion loss function. Second, to generate a more energy-compact representation, we utilize the principal components analysis (PCA) to rotate the feature maps produced by the CAE, and then apply the quantization and entropy coder to generate the codes. Experimental results demonstrate that our method outperforms traditional image coding algorithms, by achieving a 13.7% BD-rate decrement on the Kodak database images compared to JPEG2000. Besides, our method maintains a moderate complexity similar to JPEG2000.
I. INTRODUCTION
Traditional codecs use fixed transforms and are not expected to be optimal and flexible for all image contents and formats. This paper proposes a CAE-based lossy compression architecture with PCA rotation and reports improved coding performance.
- Traditional JPEG and JPEG2000 codecs rely on fixed DCT or wavelet transforms, quantization, and entropy coding.
- Deep learning and autoencoders can extract compressed image codes with minimized loss and may adapt more quickly to new media contents and formats.
- The paper proposes a convolutional autoencoder architecture for lossy image compression.
- The method replaces conventional transforms with a symmetric CAE, trains it with an approximated rate-distortion loss, and applies PCA rotation before quantization and entropy coding.
- The proposed method is reported to outperform JPEG and JPEG2000 in PSNR and achieve a 13.7% BD-rate decrement versus JPEG2000 on Kodak images.
II. PROPOSED CONVOLUTIONAL AUTOENCODER BASED IMAGE COMPRESSION
The proposed codec uses a CAE-based encoder-decoder pipeline with preprocessing, CAE computation, PCA rotation, quantization, and entropy coding. It is trained in two stages to improve rate-distortion performance and coding efficiency.
- The encoder pipeline includes preprocessing, CAE computation, PCA rotation, quantization, and entropy coding, while the decoder mirrors the encoder architecture.
- The method first designs and trains a symmetric CAE using an approximated rate-distortion loss with added uniform noise to imitate quantization noise.
- The second stage analyzes pretrained CAE feature maps and applies PCA rotation to produce more zeros before quantization and entropy coding.
A. CAE Network
The CAE uses symmetric convolutional and deconvolutional units to transform image components into compact representations and reconstruct them. Training approximates quantization noise within a rate-distortion objective.
- The encoder and decoder implement analysis and synthesis transforms, mapping images to compressed data y and reconstructed images through functions fθ and gφ.
- The proposed downsampling and upsampling units use paired convolution and deconvolution filters, with stride 2 producing downsampled feature maps and padding one preserving input size.
- Uniform noise approximates round-based quantization during CAE training, after which real round-based quantization is used for final compression.
- PReLU improves reconstructed-image quality relative to ReLU, especially at high bit rates.
- The loss combines reconstruction MSE with a λ-weighted compressed-data term that reflects the rate-distortion tradeoff.
B. PCA Rotation, Quantization, and Entropy Coder
The method applies PCA rotation to CAE feature maps to make their energy more compact, then quantizes and entropy-codes the rotated representation for compression.
- Feature-map representation: The CAE produces an H/8 × W/8 × N6 representation for each H × W × 1 input, with each map representing a high-level image feature.N6 is the number of filters in the encoder’s sixth convolutional layer.
- PCA rotation: PCA decorrelates the CAE feature maps by reshaping them as N6-dimensional data and computing their covariance structure.The PCA procedure begins with the covariance matrix of z and then computes eigenvectors.
- PCA rotation: The eigenvectors are stacked as columns of U, ordered from the largest to the smallest eigenvalue, and used to rotate the N6-dimensional data.The rotated maps place the largest values in the first feature maps and sort features in descending order.
- Feature-map ordering: The rotated feature maps are arranged in vertical-scan order, which performs slightly better than diagonal and horizontal scanning.The rotated maps show more zeros in the bottom-right and larger values in the top-left, benefiting entropy coding.
- Quantization and entropy coding: After PCA rotation, the representation is quantized, decomposed into bitplanes, and encoded with JPEG2000’s adaptive binary arithmetic coder.The quantization precision is controlled by B, set to 12 in the model; the decoder de-quantizes the bitstream before reconstructing the images.
A. Experimental Setup
The CAE is trained on ImageNet patches using specified network widths and luma inputs, while compression efficiency and reconstruction quality are evaluated with bpp, PSNR, and MS-SSIM.
- Training setup: The CAE is trained on 5500 ImageNet images split into 128×128 patches, with H and W set to 128.The luma component is used for training, and the decoder mirrors the encoder.
- Training setup: The encoder convolutional layers use filter counts {32, 32, 64, 64, 64, 32}, and mean square error is used in the loss function.The supplied passage states that the decoder mirrors the encoder.
- Evaluation metrics: Coding efficiency is measured in bits per pixel (bpp), while reconstructed-image quality is measured with PSNR and MS-SSIM.PSNR measures objective quality, whereas MS-SSIM measures perceived quality.
B. Coding Efficiency Performance
The proposed CAE achieves strong rate-distortion performance against conventional codecs and comparable performance to Balle’s method on gray images. On Kodak color images, it saves 13.7% BD-rate relative to JPEG2000.
- CAE provides better PSNR coding efficiency than both JPEG and JPEG2000 for the tested color images.
- CAE is better than JPEG and comparable with JPEG2000 in MS-SSIM and subjective reconstructed-image quality.MSE-based training favors PSNR, while fixed 128 × 128 input blocks can produce boundary artifacts.
- 13.7% BD-rate saving is achieved by the proposed method over JPEG2000 on 24 Kodak images.BD-rate is evaluated from 0.12 bpp to 2.4 bpp using PSNR.
- CAE performance is comparable with Balle’s method on average for gray images, despite using an actual entropy coder instead of ideal entropy estimation.The proposed method is better on some test images and slightly worse on others.
C. Complexity Performance
The CAE-based codec has relatively low computational complexity. With GPU implementation, its complexity is comparable to JPEG and JPEG2000, while CPU execution is lower than Balle’s method.
- Lower CPU complexity than Balle’s method is attributed to the relatively simple CAE architecture.
- Running-time comparisons measure one complete encoding and decoding process for a 768 × 512 color image.Balle’s reported time refers to a gray image.
- Comparable complexity with JPEG and JPEG2000 is achieved using the GPU implementation.
IV. CONCLUSION AND FUTURE WORK
The paper proposes a CAE-based lossy image compression architecture that replaces conventional transforms and uses PCA-rotated feature maps before coding. It reports a 13.7% BD-rate decrement versus JPEG2000 on Kodak images and identifies perceptual optimization and GAN-based coding as future directions.
- A symmetric CAE with multiple downsampling and upsampling units replaces conventional image-codec transforms.
- The CAE is trained with an approximated rate-distortion function, while PCA rotation produces a more energy-compact feature representation.
- 13.7% BD-rate decrement versus JPEG2000 is achieved on Kodak database images.
- Future work will add perceptual quality metrics to improve MS-SSIM performance and use GANs to improve coding efficiency further.