Lossy image compression is generally formulated as a joint rate-distortion optimization to learn encoder, quantizer, and decoder. However, the quantizer is non-differentiable, and discrete entropy estimation usually is required for rate control. These make it very challenging to develop a convolutional network (CNN)-based image compression system. In this paper, motivated by that the local information content is spatially variant in an image, we suggest that the bit rate of the different parts of the image should be adapted to local content. And the content aware bit rate is allocated under the guidance of a content-weighted importance map. Thus, the sum of the importance map can serve as a continuous alternative of discrete entropy estimation to control compression rate. And binarizer is adopted to quantize the output of encoder due to the binarization scheme is also directly defined by the importance map. Furthermore, a proxy function is introduced for binary operation in backward propagation to make it differentiable. Therefore, the encoder, decoder, binarizer and importance map can be jointly optimized in an end-to-end manner by using a subset of the ImageNet database. In low bit rate image compression, experiments show that our system significantly outperforms JPEG and JPEG 2000 by structural similarity (SSIM) index, and can produce the much better visual result with sharp edges, rich textures, and fewer artifacts.
For the existing image standards, , JPEG and JPEG 2000, the codecs actually are separately optimized. In the encoding stage, they first perform a linear transform to an image. Quantization and lossless entropy coding are then utilized to minimize the compression rate. For example, JPEG @cite_21 applies discrete cosine transform (DCT) on @math image patches, quantizes the frequency components and compresses the quantized codes with a variant of Huffman encoding. JPEG 2000 @cite_2 uses a multi-scale orthogonal wavelet decomposition to transform an image, and encodes the quantized codes with the Embedded Block Coding with Optimal Truncation. In the decoding stage, decoding algorithm and inverse transform are designed to minimize distortion. In contrast, we model image compression as a joint rate-distortion optimization, where both nonlinear encoder and decoder are jointly trained in an end-to-end manner.
@cite_21 @cite_2
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JPEG 2000 is an image coding system based on the discrete wavelet transform. Unfortunately, there exist several major issues with the effective implementation of the codec. For high resolution data decomposed by a separable transform, immensely many CPU cache misses occur. Following the procedure as defined in the standard, the coefficients of a single resolution appears all at once. Consequently, the entropy coder (EBCOT) needs to once again return to the data already touched. We present a software architecture designed for JPEG 2000 coders. The proposed method employs a strip-based data processing technique while it performs a single-pass multi-scale wavelet transform. The overall compression chain is driven by incoming data while the fragments of the resulting bitstream can be produced immediately after loading the corresponding data and additionally in parallel. The method is friendly to the CPU cache and can nicely exploit the SIMD extensions. The discrete wavelet transform (DWT), the technology at the heart of the JPEG 2000 image compression system, operates on user-definable tiles of the image, as opposed to fixed-size blocks of the image as does the discrete cosine transform (DCT) used in JPEG. This difference reduces artificial blocking effects but can severely stress the memory system. We examine the interaction of the DWT and the memory hierarchy, modify the structure of the DWT computation and the layout of the image data to improve cache and translation lookaside buffer (TLB) locality, and demonstrate significant performance improvements of the DWT over a baseline implementation. Our optimized DWT implementation exhibits speedups of up to 4 spl times over the DWT in a JPEG 2000 reference implementation. Transform coding using the discrete cosine transform (DCT) has been widely used in image and video coding standards, but at low bit rates, the coded images suffer from severe visual distortions which prevent further bit reduction. Postprocessing can reduce these distortions and alleviate the conflict between bit rate reduction and quality preservation. Viewing postprocessing as an inverse problem, we propose to solve it by the maximum a posteriori criterion. The distortion caused by coding is modeled as additive, spatially correlated Gaussian noise, while the original image is modeled as a high order Markov random field based on the fields of experts framework. Experimental results show that the proposed method, in most cases, achieves higher PSNR gain than other methods and the processed images possess good visual quality. In addition, we examine the noise model used and its parameter setting. The noise model assumes that the DCT coefficients and their quantization errors are independent. This assumption is no longer valid when the coefficients are truncated. We explain how this problem can be rectified using the current parameter setting. Lossy image compression is generally formulated as a joint rate-distortion optimization to learn encoder, quantizer, and decoder. However, the quantizer is non-differentiable, and discrete entropy estimation usually is required for rate control. These make it very challenging to develop a convolutional network (CNN)-based image compression system. In this paper, motivated by that the local information content is spatially variant in an image, we suggest that the bit rate of the different parts of the image should be adapted to local content. And the content aware bit rate is allocated under the guidance of a content-weighted importance map. Thus, the sum of the importance map can serve as a continuous alternative of discrete entropy estimation to control compression rate. And binarizer is adopted to quantize the output of encoder due to the binarization scheme is also directly defined by the importance map. Furthermore, a proxy function is introduced for binary operation in backward propagation to make it differentiable. Therefore, the encoder, decoder, binarizer and importance map can be jointly optimized in an end-to-end manner by using a subset of the ImageNet database. In low bit rate image compression, experiments show that our system significantly outperforms JPEG and JPEG 2000 by structural similarity (SSIM) index, and can produce the much better visual result with sharp edges, rich textures, and fewer artifacts.