# A 4K-Capable FPGA Implementation of Single Image Haze Removal Using Hazy Particle Maps
## 2 Haze Removal with Hazy Particle Maps
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Dataset** & **Method** & **MSE** & **SSIM** & **TMQI** & **FADE** \\ \hline \multirow{4}{*}{D-HAZY} & [PERSON] & **0.0303** & **0.8348** & 0.8631 & 0.7422 \\  & [PERSON] & 0.0611 & 0.7475 & 0.8000 & 0.9504 \\  & [PERSON] & 0.0481 & 0.7984 & 0.8206 & 0.9745 \\  & [PERSON] & 0.0373 & 0.7672 & **0.8782** & **0.5054** \\ \hline \multirow{4}{*}{O-HAZE} & [PERSON] & **0.0200** & **0.7709** & 0.8403 & **0.3719** \\  & [PERSON] & 0.0283 & 0.7263 & 0.8416 & 0.4013 \\ \cline{1-1}  & [PERSON] & 0.0274 & 0.6647 & 0.8118 & 0.6531 \\ \cline{1-1}  & [PERSON] & 0.0346 & 0.7255 & **0.8921** & 0.4038 \\ \hline \multirow{4}{*}{I-HAZE} & [PERSON] & 0.0535 & 0.6580 & 0.7319 & 0.8328 \\  & [PERSON] & 0.0318 & 0.7200 & 0.7740 & **0.8053** \\ \cline{1-1}  & [PERSON] & 0.0359 & 0.6864 & 0.7512 & 1.0532 \\ \cline{1-1}  & [PERSON] & **0.0237** & **0.7672** & **0.7978** & 0.9632 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Average Mean Squared Error (MSE), Structural Similarity (SSIM), Tone-Mapped image Quality Index (TMQI), and Fog Aware Density Evaluator (FADE) results on three datasets. Figure 2: Qualitative evaluation of haze removal algorithms: (from left to right) input hazy image and dehazed images of [PERSON] et al., [PERSON] et al., [PERSON] et al., and [PERSON] et al. widely used in software for algorithm design and simulation, while fixed-point number representation is mainly used in hardware design. An \(N\)-bit fixed-point representation is actually an \(N\)-bit binary number with an 'implied binary point' separating the number into \(FC\)-bit fraction and \((N-FC)\)-bit integer parts, analogous to the decimal point between the fraction and integer digits of an ordinary decimal number. By converting a number from its floating-point representation to its fixed-point representation using Equation (9), reduced hardware utilization and increased processing speed can be achieved at the cost of losing arithmetic accuracy. Accordingly, hardware designers have to decide the number of fraction bits for every signal in the design so that the propagated loss of accuracy at the output is within a predetermined limit. In addition, they also allocate the number of integer bits to adequately accommodate the signal range. Our hardware design can achieve the computation error of less than \(\pm 0.5\) Least Significant Bit (LSB) compared with the floating-point algorithm. This computation error is calculated using Equation (10). \[FI=round\Big{(}FL\times 2^{FC}\Big{)}, \tag{9}\]  
\[E=FL_{EJ}-\frac{Fl_{EJ}}{2^{FC_{EJ}}} \tag{10}\]  
where \(E\) is the computation error, \(FL_{EJ}\) denotes the floating-point value, and \(Fl_{EJ}\) represents the fixed-point value of \(FL_{EJ}\) with \(FC_{EJ}\) fraction bits at the final output \(EJ\) in Figure 1.  
The visual evaluation in Figure 2 shows that [PERSON] et al. 's algorithm resolves completely halo artifacts that occur in [PERSON] et al. 's approach. This is achieved by employing the mHMF, which outperforms the standard median filter used in [PERSON] et al. 's method to estimate the haze distribution. Hence, it is worthwhile to design a compact hardware architecture for the mHMF that can handle large size images in real time.