Studio delle prestazioni di un sistema a fosfori per mammografia ...

where � � and � � are the image dimensions. The integration can be extended to the entire
plane if we consider Ò �� � � outside the image. Due to the Parseval theorem [13], the
same relation is valid in the spatial frequency domain for the Fourier components �Ò ����� of
Ò �� � :
� � Ð�Ñ
��� �� � � � � �
�
�
��Ò ����� � ������ (2.31)
Starting from Eq. 2.31, the noise spectral density Ï ����� is defined as:
Ï ����� � Ð�Ñ
��� � � � � � � � ��Ò ����� � (2.32)
Finally, in order to take into account the fact that the process statistics can depend on multiple
realizations, the average of the noise spectral density is computed over a large ensemble of
realizations, thus obtaining the Noise Power Spectrum (NPS):
ÆÈË ����� � Ð�Ñ
��� � � �
� �� � � ��Ò ����� � � (2.33)
The NPS (or Wiener spectrum) describes the variance in amplitude of each frequency com-
ponent of a system.
2.4 DQE
The Detective Quantum Efficiency DQE is a physical quantity that takes into account the imag-
ing system performances both from the noise and from the spatial resolution point of view. In
order to understand the underlying reasons that lead to the definition of the operative DQE def-
inition, let us consider the expected value �� ℄and the variance Î �℄of an image signal. Given
the relation � between input and output we obtain the system characteristic curve in absence
of noise:
��ÇÍÌ ℄�� ��ÁÆ℄ (2.34)
The noise can be added as a term Æ�, with a zero expectation value ��Æ�℄ � , such that the
output is:
ÇÍÌ � � ÁÆ Æ� (2.35)
27