Compressive Sensing Based Image Codec With Partial Pre-Calculation

Abstract

This study relocates partial reconstruction to the encoder upon observing sparser data post-partial reconstruction. This optimization reduces decoder processing time and mitigates degradation from subsequent quantization by capitalizing on sparsity.

Leveraging the deterministic sensing matrix’s sparsity simplifies complex partial reconstruction to matrix-based multiplications, significantly reducing processing time. This approach parallels common intra-prediction but with reduced complexity.

Consequently, compared to the state-of-the-art, this work decreases 22.61 % bpp with 17.72 % increased quality. Meanwhile, time speeds up to 649.13× on the encoder, 11.03× on the decoder, and 288.46× in total.

Motivation

Figure 1. Different codec architectures comparing with our proposal. The * represents merit, and the + represents demerit.
The issues in the existing works are as follows.

The PIC (1) requires a higher frequency than the original signal during the Analog-to-Digital conversion, resulting in increased hardware costs.
The CSICS (2) reduces hardware requirements during sampling but suffers from low compression ratios and time-consuming reconstruction.
The CSMC (3) enhances compression ratios but sacrifices image quality and significantly increases encoding and decoding times.
Our proposed framework (4) to overcome the above issues.

Methods

1. The overall framework

TMMproposal

Figure 2. The proposed Compressive Sensing based Image Codec with Partial Pre-calculation (CSCP) framework.
The main contributions of our novel framework are as follows.

Integrating quantization and Huffman Coding in the frequency domain to enhance compression ratio after partial pre-calculation.
By leveraging sparsity in the frequency domain, image quality degradation due to quantization is minimized.
Simplifying partial pre-calculation to single matrix multiplication, facilitated by the chosen measurement matrix, further reduces time costs in the encoder.
Additionally, this partial pre-calculation serves a similar function to the commonly used intra-prediction in existing works but with a sparser output and significantly reduced time requirements.
Moving partial pre-calculation from the reconstruction process to the encoder significantly reduces decoding time.
In summary, our proposed codec not only significantly reduces decoding time but also improves compression ratios.

2. The proposed Matrix Multiplication based Fast Reconstruction (MMFR).

ISCASproposal

Figure 3. Comparison between the original reconstruction procedure (1)
and our proposed Matrix Multiplication based Fast Reconstruction (MMFR)(2).
The main contributions of MMFR are as follows.

Observing from the sensing matrix, the first M vectors are non-zero vectors.
In other words, only the M first elements of the data in the frequency domain are kept for reconstructing signal .
With unnecessary vectors removed, the sensing matrix is reduced to .
This allows the reconstruction procedure to be implemented by several add and shift operators, thus significantly reducing the complexity of the calculation.

3. The proposed One-row-two-tables strategy.

Figure 4. The proposed One-Row-Two-Tables strategy.
The main contributions of One-row-two-tables strategy are as follows.

Regarding the data distribution feature, the quantized data in a single row block is split into two Huffman coding units:
the first element in each block and the other elements.
This strategy requires lower time cost to further improve the compression ratio.

Experimental Results

[1] HINTRA19: Peetakul, Jirayu, Jinjia Zhou, and Koichi Wada. "A measurement coding system for block-based compressive sensing images by using pixel-domain features." 2019 Data Compression Conference (DCC). IEEE, 2019.
[2] APMC 21: Wan, Rentao, et al. "APMC: adjacent pixels based measurement coding system for compressively sensed images." IEEE Transactions on Multimedia 24 (2021): 3558-3569.

Table 1. The performance comparison with existing CS codecs.

Table 2. The comparison of time overhead with existing CS codec.

Acknowledgement

This work was supported by JSPS KAKENHI Grant Number JP22K12101.

BibTeX

@ARTICLE{10297548,
  author={Xu, Jiayao and Yang, Jian and Kimishima, Fuma and Taniguchi, Ittetsu and Zhou, Jinjia},
  journal={IEEE Transactions on Multimedia}, 
  title={Compressive Sensing Based Image Codec With Partial Pre-Calculation}, 
  year={2024},
  volume={26},
  number={},
  pages={4871-4883},
  keywords={Image coding;Image reconstruction;Decoding;Compressed sensing;Codecs;Quantization (signal);Reconstruction algorithms;Compressive sensing;image compression;codec design;reconstruction algorithm},
  doi={10.1109/TMM.2023.3327534}}