Lossy JPEG Compression in Quantitative Angiography: the Role of X-ray Quantum Noise

Abstract

In medical imaging, contrary to applications in the consumer market, the use of irreversible or lossy compression is still in its beginnings. This is due to the suspected risk of compromising the diagnostic content. Many studies have been performed, but it was not until 2008 that national activities in different countries resulted in recommendations for the safe use of irreversible image compression in clinical practice. Quantitative coronary angiography (QCA), however, poses a special problem, since here a large variation in published maximum compression factors has strengthened the general concerns about the use of lossy techniques. Up to now, the reason for the variation has not been thoroughly investigated. Reasons for the discrepancies in published compression factors are determined in this study. Since JPEG compression reduces the quantum noise of the X-ray images, the impact of compression is overestimated when interpreting any change in local diameter as an error. By taking into consideration the quantitative effect of quantum noise in QCA, it is shown that the influence of JPEG compression can be neglected for compression factors up to ten at clinically applicable X-ray doses. This limit is comparable to that found by visual analysis for aesthetic image quality. Future studies on image compression effects should take the interaction with quantum noise explicitly into consideration.

Appendix

For a vessel with constant true diameter (phantom), the total standard deviation σ of the measured diameter along the vessel in the compressed image

$$ \sigma_{total}^2 = \frac{1}{N} \cdot \sum\limits_{l = 1}^N {{{\left( {d(l) - \mu } \right)}^2}}, \mu = \frac{1}{N} \cdot \sum\limits_{l = 1}^N {d(l)} $$

l =   1... N:

location along the vessel where the vessel diameter is measured

d(l):

local diameter at location l measured in compressed image

can be transformed as follows, grouping the diameter values by the corresponding values in the uncompressed image instead of by location:

$$ \begin{array}{*{20}{c}} {\sigma_{total}^2 = \frac{1}{N} \cdot \sum\limits_{l = 1}^N {{d^2}(l)} - {\mu^2} = \frac{1}{N} \cdot \left( {\left( {\sum\limits_l^{{N_1}} {d_1^2(l)} + \sum\limits_l^{{N_2}} {d_2^2(l)} + \ldots + \sum\limits_l^{{N_n}} {d_n^2(l)} } \right)} \right) - {\mu^2}} \\{ = \frac{1}{N} \cdot \left( {\left( {\sum\limits_j^{{N_1}} {d_{1j}^2} + \sum\limits_j^{{N_2}} {d_{2j}^2} + \ldots + \sum\limits_j^{{N_n}} {d_{nj}^2} } \right)} \right) - {\mu^2}} \\\end{array} $$

d _i (l):

local diameter at location l with corresponding diameter value d0 _i in the uncompressed image; the diameter d0 _i describes the influence of quantum noise

d _ij :

local diameter with corresponding diameter value d0 _i in uncompressed image with index j differentiating the different values

N _i :

frequency of occurrence of $d{0_i};{ }{N_1} + {N_2} + \ldots + {N_n} = N$

Using the relationship

$$ \frac{1}{{{N_i}}} \cdot \sum\limits_j^{{N_i}} {d_{ij}^2 = \sigma_i^2 + \mu_i^2} $$

σ _i :

standard deviation of the N _i diameter values with initial diameter d0 _i around the mean value μ _i

it results in

$$ \begin{array}{*{20}{c}} {\sigma_{total}^2 = \frac{1}{N} \cdot \left( {{N_1} \cdot \left( {\sigma_1^2 + \mu_1^2} \right) + {N_2} \cdot \left( {\sigma_2^2 + \mu_2^2} \right) + \ldots + {N_n} \cdot \left( {\sigma_n^2 + \mu_n^2} \right)} \right) - {\mu^2}} \\{ = \underbrace {\frac{1}{N} \cdot \left( {{N_1} \cdot \sigma_1^2 + {N_2} \cdot \sigma_2^2 + \ldots + {N_n} \cdot \sigma_n^2} \right) + }_{\sigma_{compression}^2}\underbrace {\frac{1}{N} \cdot \left( {{N_1} \cdot \mu_1^2 + {N_2} \cdot \mu_2^2 + \ldots + {N_n} \cdot \mu_n^2} \right) - {\mu^2}}_{\sigma_{roentgen}^2}} \\\end{array} $$

Thus, the total standard deviation of diameter is divided into compression dependent σ _compression and σ _roentgen that comes from the distribution of diameter values in the uncompressed image. Without compression, the equation above describes the standard deviation of diameter d0 due to quantum noise. In this case, μ _i corresponds to d0 _i , and σ _i results in zero.