Digital Signal Processing Reference
In-Depth Information
where is the mean.
Sample variance (also from Walpole and Myers) [13]:
P
N
k=1
(input[k]result[k])
2
N1
S
2
=
The Mean Square Error (MSE) between an image and its reconstruction (perhaps
after compression) is:
P
P
M
m=1
N
n=1
(original[m;n]reconstruction[m;n])
2
MN
MSE =
:
The Root Mean Square Error (RMSE) is given by the following formulas.
s
P
r
N
k=1
(input[k]result[k])
2
length(input)
2
N
RMSE =
=
For 2D data such as images:
s
P
r
P
M
m=1
N
n=1
(original[m;n]reconstruction[m;n])
2
MN
MSE
MN
RMSE =
=
where MSE stands for Mean Square Error.
The Signal to Noise Ratio (SNR) equation follows.
x
2
2
SNR = 10 log
10
where
x
is the mean square of the input signal [41]. A related formula commonly
used in image processing is the Peak Signal to Noise Ratio (PSNR).
MaxPossibleV alue
RMSE
PSNR = 20 log
10
where Max Possible Value comes from the encoding, e.g., 255 for grayscale [42].
