Learning-based Image Compression (LIC) models are hindered by high computational complexity and encoding-decoding mismatch issues across different hardware platforms. While Post-Training Quantization (PTQ) enables efficient deployment, standard fixed-bit approaches exhibit substantial quality degradation at low precision. To address these limitations, we propose MPP-LIC, an efficient mixed-precision PTQ approach for LIC. Our approach consists of four key steps as illustrated in Fig. 1: •Step 1: acquire initial sensitivity list. We leverage the Hessian trace to estimate each block's sensitivity for following quantization. •Step 2: obtain optimized sensitivity list based on task-constraint metric. We formulate the optimized sensitivity list using a task-constrained metric that considers both quantization error and rate-distortion performance. •Step 3: allocate mixed bit-width by the sensitivity list. Under the manually specified model size constraint, we assign mixed bit-widths to each block according to the sensitivity list obtained from Step 2. •Step 4: conduct task-constraint block-wise optimization. We perform blockwise optimization on mixed- precision model using minimal calibration images.

Rate-distortion (RD) theory is a fundamental theory for lossy image compression that treats compressing the original images to a specified bitrate with minimal signal distortion, which is an essential metric in practical application. Moreover, with the development of visual analysis applications (such as classification, detection, segmentation, etc.), the semantic distortion in compressed images are also an important dimension in the theoretical analysis of lossy image compression. In this paper, we model the rate-distortion-classification (RDC) trade-off in lossy image compression based on the previous RD model. Specifically, the classification task is used as a representative image vision analysis task to calculate the semantic distortion. For the joint optimization modeling of RDC, the optimization objective function is the code rate expressed by the mutual information $I(\cdot,\ \cdot)$ with the constraints of MSE loss $\mathrm{E}[\triangle(\cdot,\ \cdot)]$ and the classification task error rate $\varepsilon$, where $\varepsilon$ is defined by Equation (2). Define the binary classifier as:

Image compression approaches based on deep learning have achieved remarkable success. Existing studies mainly focus on human vision and machine analysis tasks taking reconstructed images as input. However, those methods need images to be decoded before performing downstream visual tasks, which motivates us to explore how to directly conduct visual analysis using the compressed data without decoding. The overview of our proposed model is shown as Fig. 1(a). Specifically, a task-agnostic learning-based compression model is proposed, which effectively supports various compressed domain-based analytical tasks meanwhile reserves outstanding re-constructed perceptual quality compared with traditional and learning-based codecs. To obtain the extremely compacted data representation with essential semantic infor-mation, we take the help of the generative model on decoder part. Then, we propose a multi-task learning model which can directly obtain semantic information from the compressed visual data. The pipeline of the proposed model is detailedly illus-trated in Fig. 1(b). In addition, joint optimization strategy is adopted to achieve the best balance point among compression efficiency, reconstructed image quality, and the downstream visual tasks' performance. Experimental results verify that our proposed compressed domain-based multi-task analysis model outperforms the reconstructed image-based method on transmission efficiency, saving more than ten times of bit-rate consumption while preserving comparable visual analysis precision (i.e., classification and segmentation tasks) when compared with RGB image input models, which is evaluated on the CelebA-HO dataset.

Image compression is a key problem in this age of information explosion. With the help of machine learning, recent studies have shown that learning-based image compression methods tend to surpass traditional codecs. Image compression can be split into three steps: transform, quantization, and entropy estimation. However, the transform step in traditional codecs lacks flexibility because of the strict mathematical premise while the transform in most learning-based codecs neglects its intrinsic interpretation. After observing compression degradation degree varies on different frequency bands as illustrated as Fig. 1(a), we propose an end-to-end compression model from the frequency perspective with a frequency-pyramid transform and a frequency-aware fusion module. The right of the Fig. 1(a) displays each frequency layer's component of the proposed model from low to high-frequency splits. Intuitively, we can infer that the low-frequency part contains the global structure while the high-frequency part gets finer details, satisfying the feature of human visual system (HVS). The proposed model are detailedly shown in Fig. 1(b) that independent probability estimation models are set for each frequency split. Extensive experiments are conducted to demonstrate that our model outperforms all traditional codecs (e.g., JPEG, JPEG2000, HEVC, and VVC) on MS-SSIM metric on both Kodak and CLIC2020 professional test datasets. Taking BPG-4:4:4 as the anchor, our proposed model achieves 11.6% BD-rate reduction under PSNR measurement, which is evaluated on the Kodak dataset.