# A 4K-Capable FPGA Implementation of Single Image Haze Removal Using Hazy Particle Maps
## 1 Introduction
In real-time image processing systems, a fast and compact solution for these algorithms is always essential. [PERSON] et al. proposed a fast implementation of DCP by lightening the complexity of the atmospheric light estimation and exploiting the high similarity of successive video frames [12]. In contrast, [PERSON] et al. shortened the processing time of DCP by utilizing morphological reconstruction instead of soft matting to refine the transmission map [13]. According to the provided experimental results, [PERSON] et al. 's design was able to process a 320 \(\times\) 240 image in 0.228 s (i.e., 1/0.228 \(\approx\) 4.39 frames per second (fps)), while [PERSON] et al. 's design required 0.14 s to handle a 1920 \(\times\) 1080 image (i.e., 1/0.14 \(\approx\) 7.14 fps). These faster versions of DCP are still inappropriate for real-time applications requiring a processing speed of at least 25 fps. Similarly, Table 1 shows the system complexity based on the CPU times using [PERSON] et al. 's, [PERSON] et al. 's, [PERSON] et al. 's, [PERSON] et al. 's, [PERSON] et al. 's, and [PERSON] et al. 's algorithms [6; 7; 8; 9; 11; 15]. [PERSON] et al. 's algorithm was programmed via Anaconda, while the other five algorithms were programmed via MATLAB R2019a. They were all tested on a Core i7-6700 CPU (3.4 GHz) with 16 GB RAM. For the smallest 320 \(\times\) 240 image, the fastest [PERSON] et al. 's algorithm was only able to handle up to 20 fps (= 1/0.05). For the 4K standard of a 4096 \(\times\) 2160 image, the speed of even the fastest [PERSON] et al. 's algorithm was significantly declined to 0.09 fps (\(\approx\)1/11.09), and the processing time of [PERSON] et al. 's algorithm could not be measured due to insufficient RAM. This finding suggests that the real-time processing is completely impossible, and the memory capacity is a key factor in the hardware design for haze removal. An alternative might be to implement these algorithms on a graphics processing unit (GPU) with GPU-accelerated libraries included in the Compute Unified Device Architecture toolkit. GPU can be a main means of realizing data-driven haze removal algorithms. For example, a cascaded convolutional neural network for dehazing proposed in Reference [14] was able to handle a 640 \(\times\) 480 image in 0.1029 s (i.e., 1/0.1029 \(\approx\) 9.75 fps). Unfortunately, this processing speed still does not meet the requirement of real-time processing. In addition, an in-depth study on both classical and deep learning haze removal \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Image Size** & **[PERSON] [6]** & **[PERSON] [7]** & **[PERSON] [8]** & **[PERSON] [9]** & **[PERSON] [15]** & **[PERSON] [11]** \\ \hline
320 \(\times\) 240 & 4.11 & 0.23 & 29.56 & 0.11 & 0.05 & 0.08 \\
640 \(\times\) 480 & 17.83 & 0.79 & 96.50 & 0.47 & 0.65 & 0.35 \\
800 \(\times\) 600 & 28.05 & 1.69 & 129.67 & 0.72 & 1.06 & 0.67 \\
1024 \(\times\) 768 & 46.82 & 2.18 & 173.86 & 1.18 & 1.74 & 0.96 \\
1920 \(\times\) 1080 & 143.86 & 4.27 & 583.18 & 3.14 & 4.76 & 2.25 \\
4096 \(\times\) 2160 & - & 25.76 & 2388.85 & 13.20 & 20.38 & 11.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Processing time in seconds of haze removal algorithms. methods stated that the classical ones tend to generate results favored by human perception [20]. As well as this, researchers may be increasingly interested in designing the hardware using field-programmable gate arrays (FPGA) because of the high cost of the GPU platform in terms of both market price and energy consumption [21] and the inability to handle large image sizes in real time. Several hardware implementations until now including [PERSON] et al. 's and other designs [1; 2; 22] are only appropriate for small-size imaging applications because of their low throughput. Therefore, a strategy for processing a large size image in real time is highly required. This paper presents a 4K-capable hardware design using [PERSON] et al.