Abstract:
A wide dynamic range image sensor method combines the response of high-gain sensing cells and low-gain sensing cells with better linearity than the prior art. A search is made in successive central regions within the response curve of the high-gain and low-gain cells to find a highest slope linear fit. This highest slope and the corresponding offset are used in mixing the high-gain and low-gain responses to achieve a wide dynamic range.

Description:
TECHNICAL FIELD OF THE INVENTION 
     The technical field of this invention is image sensors. 
     BACKGROUND OF THE INVENTION 
     This invention is an improved method of mixing high-gain and low-gain sensing cells for a wide dynamic range image. These type image sensors enable a greater dynamic range sensing from a single exposure due to the differing gain factors of the two sensing cell types. 
     SUMMARY OF THE INVENTION 
     A wide dynamic range image sensor method combines the response of high-gain sensing cells and low-gain sensing cells with better linearity than the prior art. A search is made in successive central regions within the response curve of the high-gain and low-gain cells to find a highest slope linear fit. This highest slope and the corresponding offset are used in mixing the high-gain and low-gain responses to achieve a wide dynamic range. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       These and other aspects of this invention are illustrated in the drawings, in which: 
         FIG. 1  illustrates the block diagram of a typical prior art image sensing system; 
         FIG. 2  illustrates sensor gain curves of the ideal relationship between output signal and incoming light according to the prior art; 
         FIG. 3  illustrates the concept of how to achieve wide dynamic range in accordance with the prior art; 
         FIG. 4  illustrates a block diagram of a prior art wide dynamic range image sensing system; 
         FIG. 5  illustrates sensor gain curves of a realistic view of the relationship between output signal and incoming light; 
         FIG. 6  illustrates the results of applying linearization to the non-linear gain curve of  FIG. 5 ; 
         FIG. 7  illustrates the measured relationship between S 1  and S 2  of the collocated sensor pairs; 
         FIG. 8  which is a close view of the mostly linear region of the S 1  and S 2  relationship of  FIG. 7 ; 
         FIG. 9  illustrates a flow chart of the method of this invention; 
         FIG. 10  illustrates an estimated linear curve not taking into account end non-linearities; and 
         FIG. 11  illustrates an estimated linear curve using this invention which searches for the most linear section of the curve. 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
       FIG. 1  illustrates the typical block diagram  100  of a prior art image processing system (ISP). Such ISPs are employed in the prior art in digital image capturing systems such as digital still cameras (DSC) to construct an image frame from sensor input. ISP  100  illustrated in  FIG. 1  includes: image sensor  101 ;  3 A function block  102 ; CFA interpolation block  103 ; gamma correction block  104 ; color space conversion block  105 ; pre-processing block  106  and compression block  107 . 
     Image sensor  101  is generally a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS) imager. Image sensor  101  captures incoming light and converts it into an electric signal. As illustrated in  FIG. 1 , this electric signal typically is represented in a color filter array (CFA) format. The CFA format will be further detailed below. 
     The  3 A function block  102  embodies three typical ISP operations. These are: automatic focus (AF); automatic exposure (AE); and automatic white balance (AWB). The camera optics projects external objects onto image sensor  101 . In most cases, the initial image captured through the camera optics suffers low contrast, insufficient or excessive exposure and irregular colors. AF controls camera optics to maximize contrast. AE controls camera optics to obtain a proper exposure. Automatic white balance controls the camera to automatically correct irregular colors. 
     Single sensor digital cameras widely used in consumer products generally employ a color filter array (CFA) to represent multiple color spectral components red, green and blue. This contrasts with 3 sensor cameras intended for professional use. According to the CFA technique each pixel obtains only one color sample either red, green or blue. The two color components for that pixel must be interpolated from neighboring pixels. This color plane interpolation is known as CFA interpolation. CFA interpolation block  103  provides this function in imaging system  100 . As a result of this CFA interpolation the number of pixels to be processed is tripled through. In the example of  FIG. 1  the resulting signal is in a RGB 4:4:4 format. 
     Gamma correction block  104  provides an internal adjustment to compensate for nonlinearities in imaging systems. In particular, cathode ray tube (CRT) and liquid crystal display (LCD) thin film transistor (TFT) monitors and printers. Gamma correction block  104  provides a power-law relationship that approximates the relationship between the encoded luminance in a rendering system and the actual desired image brightness. A CRT converts a signal to light in a nonlinear way because the electron gun of a CRT is a nonlinear device. To compensate for the nonlinear effect, gamma correction block  104  provides an inverse transfer function before encoding. This inverse compensation causes the end-to-end response to be linear. Thus the transmitted signal is deliberately distorted so that, after it has been distorted again by the display device, the viewer sees the correct brightness. 
     Color space conversion block  105  changes change the way that colors are represented in images. Current devices represent colors in many different ways. The YUV color space dominates in digital camera applications because it is supported by compression standards such as JPEG and MPEG. These compression standards are an essential component for digital cameras. Therefore color space conversion block  105  converts RGB image signals from gamma correction block  104  to YUV image signals. This conversion is usually performed using a 3 by 3 transform matrix. In the example of  FIG. 1  color space conversion block  105  outputs the image signal in a YUV 4:4:4 format. 
     Pre-processing block  106  provides several functions including edge enhancement, false color correction, chroma format conversion and the like. The edge enhancement and false color correction improve subjective image quality. These functions are optional, but are provided in most recent products. Chroma format conversion is essential. The image format needs to be converted from YUV 4:4:4 to either the YUV 4:2:2 or the YUV 4:2:0 used in JPEG and MPEG standards. The ISP algorithm is generally understood as complete with block pre-processing block  106 . 
     Compression block  107  is illustrated in  FIG. 1  but is generally believes to be outside the ISP algorithm. The image compression technique used in compression block  107  varies depending on the application. For DSC JPEG compression is generally considered mandatory. MPEG compression, some lossless codec and even proprietary schemes are often employed. 
     This invention is applicable to a so-called wide dynamic range (WDR) sensor. A WDR sensor is an innovative image capturing device. There are several schemes to realize wide dynamic range sensor. This invention is applicable to a device equipped with two types of sensing cells. Each sensing cell type has a corresponding gain factor or sensitivity to input light. The first sensor type is a high-gain cell S 1 . The second sensor type is a low-gain S 2 . It is assumed that conventional image sensors have only high-gain cells.  FIG. 2  illustrates the sensor gain curves representing the ideal relationship between output signal and incoming light. The incoming light intensity is designated [e−] for electron representing units of input light intensity. The sensor output is designated [LSB] for least significant bit representing sensor output signal. The gain curve  201  of S 1  and gain curve  202  of S 2  are both designed to be linear over the entire dynamic range. Therefore, we define that S 1  has a linear gain factor of α1 and S 2  has a linear gain factor of α2 both expressed in units of [LSB/e−]. As its name implies S 1  has larger gain than S 2 , thus α1&gt;α2. Both S 1  and S 2  have the same saturation point MaxRaw. Note gain curve  201  saturates at an inflection point where further increases in light intensity produce no further increase in signal output. A single pixel includes pair of sensing cells S 1  and S 2  called a collocated pair. These are provided in a pixel array to constitute the entire image sensor. Thus a WDR sensor has twice as many sensing cells as an ordinary image sensor. 
       FIG. 3  illustrates the main concept of how to achieve wide dynamic range.  FIG. 3  shows gain curve  201  of S 1  and gain curve  202  of S 2  as illustrated in  FIG. 2  and projected low-gain curve  203 . Let switching point P SW1  denote the minimum input light that yields an output signal MaxRaw with sensor type S 1 . Suppose a conventional image sensor that has only sensor type S 1  receives light whose intensity is larger than P SW0 . According to the S 1  gain curve  201 , the output signal gets saturated after applying the gain factor α1 to the light intensity P SW0 . The sensor thus outputs MaxRaw for any incoming light whose intensity equals or exceeds P SW0 . This is called white washout. In a region of white washout precise gray level fluctuation in output signal domain is lost. All these pixels are represented by MaxRaw, which is white. White washout is a major shortcoming of conventional image sensors. Taking photo shots recursively against a static scene permits gradually tuning gain related parameters to excessive incoming light to avoid white washout. This workaround includes: increasing the shutter speed providing a shorter exposure time; reducing the iris; and decreasing the gain factor of an analog gain amplifier. This cannot be used with a dynamic scene where either the object or the light condition source or path varies with time. A similar scenario holds for black washout which is opposite to white washout where a low light intensity yields a mostly black region. 
     A WDR sensor equipped with both S 1  and S 2  sensor types can better deal with white washout and black washout. Theoretically the dynamic range of a WDR sensor is {dot over (β)} times as wide as that of conventional image sensor equipped with only S 1  sensor types, where {dot over (β)} is the ratio of α1 to α2 
               (       β   .     =       α   ⁢           ⁢   1       α   ⁢           ⁢   2         )     .         
This is called design beta. Given that {dot over (β)} is known, the S 2  output signal multiplied by {dot over (β)} (known as projected S 2  signal  203  in  FIG. 3 ) predicts a true S 1  output signal. Below the S 2  saturation point P SW0  the WDR sensor uses the S 1  signal because S 1  has a higher signal to noise ratio (SNR) than S 2 . Above the S 1  saturation point P SW0  the WDR sensor uses the projected low-gain signal  203 . The output of the WDR sensor denoted by F 0 (t) is expressed by:
 
                       F   0     ⁡     (   t   )       =     {             f   1     ⁡     (   t   )               if   ⁢           ⁢   t     ≤     P     SW   ⁢           ⁢   0                       β   0     ×       f   2     ⁡     (   t   )         +     λ   0           otherwise                   (   1   )               
where: f 1 (t) is the output signal level of S 1 ; f 2 (t) is the output signal level of S 2 ; β 0  is the gradient of the relationship between collocated S 1  and S 2  signals; and λ 0  is the offset in the relationship between collocated S 1  and S 2  signals. Note β 0  and λ 0  are calculated from actual data according to the prior art method while {dot over (β)} is fixed at design time as a design parameter.
 
       FIG. 4  illustrates a block diagram of a wide dynamic range image sensor ISP algorithm  110 .  FIG. 4  illustrates: image sensor  101 ;  3 A function block  102 ; CFA interpolation block  103 ; gamma correction block  104 ; color space conversion block  105 ; pre-processing block  106  and compression block  107 . These blocks are the same as correspondingly numbered blocks illustrated in  FIG. 1 . The only major difference between non-WDR ISP algorithm  100  of  FIG. 1  and WDR ISP algorithm  110  illustrated in  FIG. 4  is the addition of mixing block  110  in WDR ISP algorithm  110 . Mixing block  110  seamlessly mixes the S 1  and S 2  signals in the manner shown in  FIG. 3 . This mixing comprises two main tasks: calculation of relationship formula between S 1  and S 2  as in Equation (1); and fitting S 2  signals into the S 1  axis by projecting S 2  signals using the relationship formula paying special attention to seamless migration from S 1  to S 2  region around transition area near MaxRaw. 
     In the prior art f 1 (t) and f 2 (t) in Equation (1) were assumed to be linear functions, thus f 1 (t)=α 1 t and f 2 (t)=α 2 t. This assumption isn&#39;t necessarily true for actual devices.  FIG. 5  illustrates S 2  gain curve  202  and more realistic S 1  gain curve  501 . S 1  gain curve  501  includes a gentler slope in a first non-linear region  511  near zero and a second non-linear region  512  near the saturation point MaxRaw. Dark current noise offset is the main causes of the non-linearity of region  511 . Rounding error is the main cause of non-linearity of region  512 . 
       FIG. 6  illustrates the results of applying equation (1) to the non-linear gain curve  501  of  FIG. 5 . Equation (1) assumes that S 1  gain curve  501  is linear between zero and P SW0 . Calculating a projection of S 2  gain curve  202  based upon this linearity assumption results in a gain curve  202  projection  601  having a slope F 0 (t).  FIG. 6  illustrates that this projected S 2  signal  601  is not smoothly connected to S 1  gain curve  501 . Using equation (1) based upon the linearity assumption results in quality degradation to the resultant image after the mixing process. 
       FIG. 6  also illustrates a better projection  602 . Projection  602  is the result of extension of the linear region of S 1  gain curve  501 . This projection has a different gradient and a different offset. Note that in projection  602  the joining is at point P SW  which is the maximum of the linear region of S 1  gain curve  501 . This results in a new projection denoted by equation (2): 
                     F   ⁡     (   t   )       =     {             f   1     ⁡     (   t   )               if   ⁢           ⁢   t     ≤     P   SW                   β   ×       f   2     ⁡     (   t   )         +   λ         otherwise                   (   2   )               
where: f 1 (t) is the output signal level of S 1 ; f 2 (t) is the output signal level of S 2 ; β is the gradient of the relationship between the linear part of the S 1  signal and the S 2  signal; and λ is the offset in the relationship between the linear part of the S 1  signal and the S 2  signal.
 
     The prior art includes three possible implementations of the computation of equation (2). These are: a default mode which β and λ are fixed on a sensor device basis; an on-the-fly mode which β and λ are derived from actual sensor data using a method of least squares (MLS); and an off-line mode that is a mixture of the default mode and on-the-fly mode. 
     However, in actual devices neither the S 1  nor S 2  gain curves of  FIG. 6  are necessarily completely linear as shown. In this case, it is better that the S 1  signals for the calculation of β and λ in Equation 2 be limited to the linear region of curve  501 . This invention is an improved technique of the prior art on-the-fly mode. 
       FIG. 7  illustrates an actual measured relationship between S 1  and S 2  of the collocated sensor pair.  FIG. 7  illustrates a calculated linearization  701  (y=βx+λ) and the projection of the low gain signal  702 . The linearization  7081  employs a MLS calculation carried out using observed S 1  and S 2  data in the non-saturation region below LowLinearMax in the S 2  axis. This value LowLinearMax is specified at design time as MaxRaw divided by design β. Collocated pairs usually show a linear relation except for the two ends near zero and near LowLinearMax. At these ends the collocated pairs don&#39;t show linearity due to offset noise and other factors. This invention removes such unreliable data from the MLS calculation.  FIG. 7  illustrates that Min and Max are set with some margin. Min is set a few percent of LowLinearMax above zero. Max is set a few percent of LowLinearMax below LowLinearMax. This is satisfactory if the region between Min and Max has a high enough linearity. In some cases, non-linear regions remain. 
     This is illustrated in  FIG. 8  which is a close view of the mostly linear region of the S 1  and S 2  relationship.  FIG. 8  illustrates linear region  801 , first non-linear region  802  near zero, second non-linear region  803  near LowLinearMax and the MLS calculated tine  805 . The example illustrated in  FIG. 8  shows the gradient β of MLS estimated curve  805  is smaller than the gradient of linear region  801 . The gradient of linear region  801  is considered more accurate. In this invention in order to obtain a more accurate β, the data set in a sub-region between Min and Max used for MLS calculation of β and λ is shifted in various positions. The sub-region yielding the maximum β is assumed the best data set for MLS. Obtaining β and λ in this way should be the most appropriate. 
     This invention is a derivative of MLS called selected representative MLS (SR-MLS). SR-MLS is better suited for calculation of the relationship formula. SR-MLS estimates the best linear expression y=βx+λ from observed data where: x denotes S 2  data; and y denotes S 1  data. Using all observed data would not be the best choice because this would require a large amount of memory, many computations and would hamper finding the genuine relationship formula. Thus this invention applies SR-MLS to representative values: (x 0 ,y 0 ), (x 1 , y 1 ), . . . (x N , y N ) for i=0, 1, 2, . . . N. Assume x j+1 =x j +x interval  for j=0, 1, 2, . . . N. In this case x interval  is the interval in the x axis between two successive representative points in the S 1  versus S 2  curve. Thus x interval  is (Max−Min)/N. The S 1  value that corresponds to x i  is represented by an average of S 1  data whose collocated S 2  signal is x i . If there is no collocated pair at representative S 2  point x i  one is computed by interpolation or extrapolation from data whose C 1  value fall near x i . 
     SR-MLS is relatively simple and the required computations are smaller than a plain MLS.  FIG. 9  illustrates a flow chart of method  900  of this invention. Method  900  operates to calibrate the linear fitting of signals S 1  and S 2 . There are several possible times which this calibration can be performed. One embodiment performs the calibration once upon initial testing of the image sensing system. Another embodiment performs the calibration upon each initial powering of the image sensing system. Other embodiments perform method  900  on the fly. These include periodically performing method  900  based upon operation time or number of exposures of the image sensing system. The actual technique employed should be selected based upon the stability of the relationship of the sensor signals S 1  and S 2 . 
     Method  900  starts at start block  901 . Method  900  obtains the representative values (x 0 , y 0 ), (x 1 , y 1 ), . . . (x N , y N ) in block  902 . Block  903  assumes the relationship of values x i  is:
 
 x   i   =x   interval   h   i   +x   0   (3)
 
where: h i =0, 1, 2, . . . , N. This assumption relates an equally-spaced sequence x i  to the integer numbers h i  that range from 0 to N. Using this relational expression, y i =βx i +λ can be transformed into y i =βx interval +(βx 0 +λ). Then, y i  can be represented as a function of h i . Thus y i =q(h i ).
 
     In general, arbitrary polynomial P(h i ) of order m can be expressed as: 
                     P   ⁡     (     h   i     )       =           a   0     ⁢       P     N   ⁢           ⁢   0       ⁡     (     h   i     )         +       a   1     ⁢       P     N   ⁢           ⁢   1       ⁡     (     h   i     )         +   …   +       a   m     ⁢       P     N   ⁢           ⁢   m       ⁡     (     h   i     )           ⁢     
     ⁢           =       ∑     k   =   0     m     ⁢           ⁢       a   k     ⁢       P     N   ⁢           ⁢   k       ⁡     (     h   i     )                     (   4   )               
where: m&lt;N; a k  are coefficients of each term; and P Nk (h i ) is called orthogonal polynomial. The orthogonal polynomial is represented by:
 
                       P     N   ⁢           ⁢   k       ⁡     (     h   i     )       =       ∑     i   =   0     k     ⁢           ⁢         (     -   1     )     l     ⁢     (         k           l         )     ⁢     (           k   +   1             l         )     ⁢         (     h   i     )       (   l   )           (   N   )       (   l   )                     (   5   )               where   ⁢     :                               (         k           l         )     =       k   !         l   !     ⁢       (     k   -   1     )     !                                 
is called binomial coefficient; and (N) (1) =N(N−1) . . . (N−1+1) is called the factorial polynomial. Equation 4 can be solved for a k  due to the orthogonality of P Nk (h i ) as follows (details omitted):
 
                     a   k     =         ∑     i   =   0     N     ⁢           ⁢       P   ⁡     (     h   i     )       ⁢       P   Nk     ⁡     (     h   i     )               ∑     i   =   0     N     ⁢           ⁢       P   Nk   2     ⁡     (     h   i     )                   (   6   )               
Equation (5) is only dependent on N, k, and h i . These values are independent of the representative values of the relationship between S 1  and S 2 . The numerical values of P Nk (h i ) and
 
               ∑     i   =   0     N     ⁢           ⁢       P   Nk   2     ⁡     (     h   i     )             
in Equation (6) can be precalculated and stored on a memory prior to the calculation of Equation (5) using instantaneous representative values. This technique enables a relatively simple calculation of a k . If the relationship between S 1  and S 2  is a linear function, then equation (4) can be rewritten as:
 
 P ( h   i )=α 0   P   N0 ( h   i )+α 1   P   N1 ( h   i )  (7)
 
From equation (5) P N0 (h 1 )=1 and
 
                 P     N   ⁢           ⁢   1       ⁡     (     h   i     )       =     1   -     2   ⁢         h   i     N     .               
Substituting these expressions into equation (7) yields the more easily understood expression:
 
                     P   ⁡     (     h   i     )       =         -       2   ⁢           ⁢     a   1       N       ⁢     h   i       +     (       a   0     +     a   1       )               (   8   )               
Because P(h i ) can be replaced with y i =q(h i ) we can solve for β and λ as follows:
 
                       β   ⁢           ⁢     x   interval     ⁢     h   i       +     (       β   ⁢           ⁢     x   0       +   λ     )       =         -       2   ⁢           ⁢     a   1       N       ⁢     h   i       +     (       a   0     +     a   1       )               (   9   )               Thus   ⁢     :                             β   =     -       2   ⁢           ⁢     a   1         N   ⁢           ⁢     x   interval                   (   10   )             and                         λ   =       a   0     +     a   1     +       2   ⁢           ⁢     a   i     ⁢     x   0         N   ⁢           ⁢     x   interval                   (   11   )               
Thus estimates of both β and λ can be calculated from the representative values. In order to obtain the most effective values of β and λ, the process searches successive windows of values (x i , y i ). Each computation uses consecutive values: (x 0+s , y 0+s ), (x 1+s , y 1+s ), . . . , (x M−1+s , y M−1+s ) selected from the representative values (x 0 , y 0 ), (x 1 , y 1 ), . . . , (x M , y M ) where M&lt;N and s=0, 1, 2, . . . , N−M. The particular value of s selects a subset of the representative values (x 0 , y 0 ). The SR-MLS calculation for β and λ are carried out for all allowed values of s. The invention determines the largest value β s  among all the estimated B is considered the value. This value β s  triggers selection of the corresponding λ s  and s M . These values are applied for projection of S 2  to the S 2  axis according to Equation (2).
 
     Referring back to  FIG. 9 , block  903  sets s equal to 0. Block  904  calculates β and λ according to equations (9) and (10). Test block  905  determines if the just calculated value β is greater than the tentative maximum β s . If this is true, (Yes at text block  905 ), then block  906  sets a new β s  equal to the current β and a new λ s  equal to the current λ. Block  906  saves these values corresponding to the new maximum value of β. If this is not true (No at test block  905 ), then method  900  skips block  906 . 
     Method  900  next determines if all tentative β and λ calculations are complete. Test block  907  tests to determine if s≧N-M. If not (No at test block  907 ), then all tentative β and λ calculations not are complete. Block  908  increments S. Method  900  then loops back to block  904  for another tentative β and λ calculation. If the loops in s are complete (Yes at test block  907 ), then block  909  calculates the combined function F(t) according to claim  2  from the maximum value β s  and the corresponding value λ s . The value of Psw may be empirically determined from the value of s corresponding to β s . As noted above the value of P SW  used in selected to approximate the end of the linear response region in S 1  as illustrated in  FIG. 6 . 
     Block  909  implements equation (2) which is the simplest implementation called hard switching. Another choice called soft switching achieves gradual migration from S 1  to S 2  in a transition band P SW −θ≦t≦P SW . θ is an empirical constant designation a range of the transition band and is a positive number in [e−]. θ could be a predetermined constant of P SW , such as 90%. In the S 1  non-saturation band where t≦P SW  both S 1  and S 2  signals are meaningful. A typical gradual migration is weighted average g(t): 
                     g   ⁡     (   t   )       =         μ   ⁢           ⁢       f   1     ⁡     (   t   )         +     ρ   ⁢           ⁢       f   2     ⁡     (   t   )             μ   +   ρ               (   11   )               
where: μ and ρ are proportionality constants. A most practical implementation among various derivatives of weighted averaging of the type of equation (11) has weighting coefficients linear to distance from both tips of the transition band. This linear weighted averaging g i (t) is expressed by:
 
                       g   i     ⁡     (   t   )       =           (       P   SW     -   t     )     ⁢       f   1     ⁡     (   t   )         +       (     t   -     P   SW     +   θ     )     ⁢       f   2     ⁡     (   t   )           θ             (   12   )               
Thus the output of the WDR sensor system F s (t) is:
 
     
       
         
           
             
               
                 
                   
                     
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       FIGS. 10 and 11  present the results of this invention applied to a common set of parameters set forth in Table 1. 
                                                           TABLE 1                               3640 Horizontal by               Resolution [pels]   2400 Vertical                                            MaxRaw [LSB]   4095    (12 bits)               MaxVal [LSB}   65,535    (16 bits)               Min [LSB]   296                   Max [LSB]   656                   x interval  [LSB]   36                   N   10                   M   5                          FIGS. 10 and 11  result from calculations of the S 2  versus S 1  signal curve for a particular image sensing device. Both  FIGS. 10 and 11  illustrates the actual S 2  versus S 1  signal curve  1001 . The example of  FIG. 10  estimated the linear curve by calculating y=βx+λ according to the prior art not taking into account the end non-linearities. This results in a linear approximation  1002 . The example of  FIG. 11  estimated the linear curve using this invention which searches for the most linear section of the curve. This results in a linear approximation  1102 . Estimated linear curve  1002  has gentler slope than the slope of actual curve  1001  in the linear region. Estimated linear curve  1102  formed using the technique of this invention makes a better fit for the linear section of actual curve  1001 . This better estimate would result a more appropriate projection of the S 2  signal into the S 1  axis.
 
     This invention is intended for use in a wide dynamic range sensor equipped with high-gain cell and low-gain sensing cells. This proposal addresses a practical solution for the relationship formula calculation between high-gain and low-gain signals. In actual devices this relationship has nonlinear regions before the high-gain cell saturates. The inventors have determined experimentally that the proposed method derives a more accurate relationship formula between low-gain signals and high-gain signals. This provides quality improvement of the resultant image after mixing process over the original prior art method.