ROCStat
Examination of the diagnostic validity of different wavelet data compression methods
The purpose of our study is to examine the diagnostic validity of different wavelet data compression methods compared to standard JPEG compression in different quality settings. While the JPEG approach uses rather simple discrete cosine transformations for information packaging and is widely used for the compression of arbitrary image data, the wavelet approach includes a wide range of mathematical different subclasses of transformations with different basis functions of different grades of complexity.
The first wavelet transformations were developed from the mathematical background of the windowed fast Fourier-transformation differing from Fourier techniques by the way of localization of information in the time-frequency plane. The multiscaling properties and the choice of nonredundant wavelets with different types of basis functions provide the mathematical basis for image compressions.
Wavelet applications include a wide range of techniques in signal processing like the analysis of 1D-physiological signals, noise reduction in image processing, image reconstruction and image acquisition schemes. Compression of images may result in different amounts of information loss. In regard that biomedical information is often a combination of temporally and spatially well localized and other more diffuse features which can lead to different probabilities for diagnostic decisions it will be very important to examine what amount and kind of information loss will result in false positive or false negative diagnostic desicions.
For the exact determination of the rates of false positive or false negative decisions we used a widely known psychophysical examination and scaling method: a ROC (receiver operating characteristics) analysis as experimental estimation method for the signal detection. The detection accuracy is determined by separating sensory discrimination thresholds from reaction tendencies. To construct a psychophysical scaling function additionally a cross modality matching between different compression methods were used to measure the difference decisions.
Material and Method
About 1000 slices of standard MRI-data sets including e.g., volume requiring processes like tumours, haemorrhages and cystic diseases of the brain and slices of healthy brain tissue were compressed with standard JPEG, Haar-, Adelson-, Brislawn-, Odegard- and Antonini-Wavelets, each with compression rates of 25, 50 and 75 percent and matched to a set of uncompressed slices.
The mixed image data set respectively consists of equal subsets of MRI-slices showing volume requiring processes and MRI slices of healthy brain tissue. The type of disease, the compression type and the compression rate were coded in three numbers for each MRI slice. This is necessary for the next step, the standardized image presentation with permutation by random polysampling on a calibrated monitor. The complete image data set was written on a CD-ROM.
For the experimental image presentation, the psychophysical data elevation and the statistical exploitation we developed our own tool ROCStat (Simon, Berndtgen & Mimoun, 1997) which allows an automatic image presentation, an automatic response measurement and an automatic statistic data evaluation in one process. The examination was carried out in two different procedures.
In the ROC measurement condition seven medical examiners (also students with specialization in radiology) had to judge wether and what kind of affection (tumour, haemorrhages, cystic deseases or healthy brain tissue) he had seen and the grade of severity or extension by pressing a button on scale from 1 to 10 on the monitor. After the recording of the reaction the next monitor was presented. The response and the reaction time were recorded automatically. In the control condition two MRI slices showing the same syndrome but with different compression types and compression rates were chosen and combined by random and both presented on the monitor. The combination of an MRI slice of healthy brain tissue with an MRI slice of a syndrom was also possible. It was the task of the examiner in a forced choice paradigm to deceide which of those two images was showing the more severe syndrom or at least a syndrom by pressing a button below the image. The response and the reaction time were recorded automatically, too. Both procedures were alternated by random.
The rates of hits and the rates of false alarms were computed. The sensitivity parameters d' were found out by determination of the z-values for the standard normal distribution belonging to the rates of hits and false alarms and computing the difference between them. The reaction thresholds are the probability densities of the standard normal distribution belonging to the z-values. The ROC curves were computed over the frequencies of a positive reaction in presence of a signal (= a syndrom) and a positive reaction without the existence of a signal to estimate the conditional probabilities p(y/S) and p(y/NS). Additionally we computed t-tests (niveau of significance p<0.05) to found out whether the mean reaction values were belonging to the same or a different probality distributions.
Results
On an average each session lasted three hours. The number of trials for the examiners were in a range between 122 and 307. There was nor a linear correlation neither a nonlinear correlation between the mean reaction times for each examiner and the correctness of the judgments.
Reaction times were elongated for examiners with ophthalmological syndroms like short-sightedness and strabism but not in a statistical significant way which could be interpreted as a hint that sensory thresholds are no main factor for the reaction times neccessary for medical decisions.
For all kind of compressions could be shown that a compression rate of 25 percent is the maximal possible compression rate for valid diagnostic decisions. In lower compression rates classical JPEG compression is still superior to all types of wavelet compressions with exception to Haar-Wavelets. In higher compression rates (50 and 75 percent) Brislawn-, Odegard- and Haar - Wavelet compression have proven a higher rate of hits but also of false alarms in diagnostic judgements compared to JPEG compression without any systematic interaction related to the medical examiner.
Additional there are statistical relevant interaction effects depending on the type of histological affection. For haemorrhages and cystic diseases there are tendencies of a general superiority of Haar- and Brislawn- wavelet compression while for solid tumours JPEG compression will lead to better results. But there are some limitations in our results. The control condition to construct psychophysical scaling functions showed some inconsistencies in the judgements for all our examiners. The order of the estimation of the extents/severties of affections was violated especially for Brislawn-, Odegard- and Adelson-Wavelets also in rather low compression rates.
Artifacts produced by wavelet filtering can be improved by the additional use of statistical filtering of wavelet coefficients during or after image compression.
Our future direction will lead to more elaborated investigations of interaction effects between the types of filters, the type of affection and its severity because it will be possible to find for each kind of histological syndrome the ideal basis function for a wavelet compression.
Our special thanks are contributed to Dipl.-Ing. Birgit Schwabe in the Klinikum Krefeld and to the participants of our study.