Abstract
Compressed sensing (CS) offers a framework for image acquisition, which has excellent potential in image sampling and compression applications due to the sub-Nyquist sampling rate and low complexity. In engineering practices, the resulting CS samples are quantized by finite bits for transmission. In circumstances where the bit budget for image transmission is constrained, knowing how to choose the sampling rate and the number of bits per measurement (bit-depth) is essential for the quality of CS reconstruction. In this paper, we first present a bit-rate model that considers the compression performance of CS, quantification, and entropy coder. The bit-rate model reveals the relationship between bit rate, sampling rate, and bit-depth. Then, we propose a relative peak signal-to-noise ratio (PSNR) model for evaluating distortion, which reveals the relationship between relative PSNR, sampling rate, and bit-depth. Finally, the optimal sampling rate and bit-depth are determined based on the rate-distortion (RD) criteria with the bit-rate model and the relative PSNR model. The experimental results show that the actual bit rate obtained by the optimized sampling rate and bit-depth is very close to the target bit rate. Compared with the traditional CS coding method with a fixed sampling rate, the proposed method provides better rate-distortion performance, and the additional calculation amount amounts to less than 1%.
Highlights
Compressed sensing (CS), known as compressive sensing or compressive sampling, shows that a small group of linear, non-adaptive measurements can reconstruct finite-dimensional signals with sparse or compressible representations [1,2,3,4,5,6]
In order to estimate the model parameters of the proposed average codeword length model and the relative peak signal-to-noise ratio (PSNR) model, 100 images in the BSDS500 dataset [35] were randomly selected for training, and the BSD68 dataset [36] was used for testing, each image being cropped to a 256 × 256 size
Rate-distortion optimization plays a crucial role for the image/video encoder
Summary
Compressed sensing (CS), known as compressive sensing or compressive sampling, shows that a small group of linear, non-adaptive measurements can reconstruct finite-dimensional signals with sparse or compressible representations [1,2,3,4,5,6]. We introduce a uniform scalar quantization and entropy coder to the CS, developing a CS-based imaging framework with RDO wherein the sampling rate and bit-depth are jointly optimized. One of the main contributions of this paper is the bit-rate model, which reveals the relationship between bit rate, sampling rate, bit-depth, and characteristics of partial measurements Another contribution is to introduce a relative peak signal-to-noise ratio (PSNR) model and use a feedforward neural network to teach the relative PSNR model to estimate distortion.
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