# CMOS Fixed Pattern Noise Removal Based on Low Rank Sparse Variational Method
## 2 Existing Methods
### Calibration-Based Method  
The main representative methods based on calibration are as follows: the two-point method [7; 8; 9], the subsection correction method [10; 11], the S-curve method [12; 13], the polynomial fitting method [14]. 1. Two-point correction method  
The basic idea of two-point correction method is to assume that the photoelectric response characteristic of each pixel is a stable linear relationship, which can be expressed by \(M=k\cdot n+B\), where \(k\) is the slope of photoelectric response curve, \(B\) is the offset, \(n\) is the number of incident photons or the energy of incident light. The correction of nonuniformity can be completed by the following steps: (1) calculate the slope correction coefficient g of each pixel; (2) calculate the offset correction coefficient O of each pixel; (3) under the effect of Formula \(M=m\cdot G+O\), correct the slope \(k\) of each pixel to \(K\), and the offset \(b\) to \(B\), as shown in Figure 4. \(K\) is the average of all pixel slopes, and \(B\) is the average of all pixel offsets. Figure 3: Summary of FPN correction methods. Figure 2: Images taken by CIS with fixed pattern noise (FPN) noise (including two-ended output structure). The premise for the two-point method to be feasible is that the photoelectric response characteristics of each pixel are stable and linear. This is because b in \(m=k\cdot N+b\) contains CFPN, as shown in Formula 1. CFPN is due to the bias voltage mismatch of the last op amp, and its mismatch voltage will drift to a certain extent with the working environment and working time [15; 16]. Figure 5 shows the whole process of gradual failure of the correction factor as b drifts. First, after 15 min of CIS operation, the corrected parameters \(G\) and \(O\) are calculated immediately. Next, an image is collected and nonuniformity correction is performed using the currently obtained \(G\) and \(O\) values. A very good correction result can be obtained at this point, as shown in Figure 5a. After working for CIS for 1 h, the images were collected again, and the original \(G\) and \(O\) were used for non-uniformity correction. The expected uniform correction results are not obtained at this time, and there is a significant residual of CFPN noise, as shown in Figure 5b. Similarly, CIS works for 3 h, and then collects the image again, and uses the original correction parameters \(G\) and \(O\) to correct the nonuniformity. The final result is shown in Figure 5c. From the above experiments, it can be very obvious that the calibration-based method can achieve very effective correction in the short term. As time goes by, the original correction parameters become invalid gradually. Therefore, in order to get good correction effect, the calibration parameters \(G\) and \(O\) need to be calibrated periodically. 2. Segmental Correction Method  
Because the linearity of the photoelectric response curve of CIS is not ideal, it shows some nonlinearity, as shown in Figure 6. It can be understood that \(k\), \(b\) change with the energy of the incident light, that is, \(K\) (\(N\)), \(b\) (\(N\)) are a function of the incident energy. Unified use of the same set of correction parameters \(G\), \(O\) will reduce the accuracy of the correction. In order to obtain a higher correction accuracy, piecewise linear fitting can be used. The curve can be approximated as a combination of several linear segments, each of which is corrected by a two-point method. With the drift of CIS parameters, the piecewise correction method will also encounter the problem of gradually invalidating. Therefore, we need to calibrate the parameters regularly and repeatedly. Figure 4: Correction process diagram of two-point method (x coordinate: incident light energy y coordinate: gray value). Figure 5: The effect of flat field correction (**a**) corrected results after CIS working for 15 min; (**a**) corrected results after CIS working for 15 min; (**b**) corrected results after CIS working for 1 h; (**c**) corrected results after CIS working for 3 h.  
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