Algorithms for video image analysis in diagnosing types of diseases based on wavelet wave functions

The subject of the research is dictated by the necessity to develop and utilize highly sensitive quantum, wave technologies, and quantum sensors in data analysis, pattern recognition, automated diagnostics of disease types using modern sensors in the macroworld, medical visualization of human organs [14], presented in the form of images F(x,y) as well as data captured as time series f(t) and images F(x,y) together, using one-dimensional wavelet wave functions of two types a1 and a2, varying within the interval ±π introduced and utilized in this work [2].

Purpose of research: the development of highly efficient algorithms and software packages for joint analysis of interrelated data presented in the form of time series and images obtained by various methods and sensors: X-ray, ultrasound, different types of tomography: computed (CT), magnetic resonance (MRI), positron emission (PET), including methods of photonics, multi-channel electrocardiographs (ECG) and electroencephalographs (EEG), radiothermographs, and other multi-channel devices used in functional diagnostics, image recognition, diagnosis of disease types in human organs in medicine, and much more, displayed by modern sensors based on quantum technologies [11–13] using wave functions of 2 types, – changes in frequency and temporal (spatial) components of observation data by phase, respectively, – a1 and a2 waves, extracted from «quanta of information» f(x) and F(x,y) [1], reflecting the states of human organs in the corresponding.

Research methods: a) transformation of «quanta of information» f(x) and images F(x,y) of sets of studied objects into two types of wave functions: phase-frequency a1=φ(a,b̅) and phase-time (spatial) a2=-φ(a̅,b) characteristics [1; 6], calculated through sequences of single-level discrete two-dimensional wavelet transformation dwt2, – separating the video image F(x,y) into matrices of details [4; 6]: approximations (cA), horizontals (cH), verticals (cV), diagonals (cD) for each of the colors (red (R), green (G), blue (B)), if the image is colored, functions of one-dimensional continuous wavelet transformation cwt(f(t),1:k,'cgau5') and multi-channel averaging operations of wavelet coefficient φ(a,b) matrices from the outputs of wavelet transformations cwt of video image F(x,y) details by columns and rows, i.e. performing operations a1=φ(a,b̅) and a2=-φ(ɑ̅,b); b) selection on the constructed images in Surfer of wavelet coefficients φ(a,b) of variable f(t) multi-frequency sawtooth wave functions of type a2 of 4 types of details AHVD, used for diagnosing types of diseases; c) statistical analysis of the correlations of wave functions of types a1 or a2 of the diagnosed disease with similar characteristics of sets of diseases in known types of organ diseases.

Objects of research: time series f(t) and images F(x,y) of the examined, particularly video images of the eye's fundus for diagnosed types of eye diseases, multichannel phase-frequency a1=φ(a,b̅) and phase-spatial a2=-φ(a̅,b) characteristics – wave functions of the original data and calculated using wavelet transforms dwt2 and cwt and matrix averaging φ(a,b) operations across rows and columns.

Research findings: a) the possibility of transforming «quanta of information»: time series f(t) used in medicine, video images F(x,y) in particular, of eye diseases, into two types of wave functions a1 and a2 using wavelet transformations, corresponding to the corpuscular-wave nature of the micro and macro world has been implemented; b) the possibility of automated diagnosis of types of eye diseases using correlations of the computed wave functions of types a1 and a2 of the diagnosed disease with the wave functions a1 and a2 of the sets of diseases in known types of diseases has been realized; c) it is shown that when correlating the wave functions of a diagnosed disease of a certain type with the wave functions of sets of known disease types, the average values in the columns of the correlation matrix have different values; in the column of correlations for diseases of the same type, the mean value is maximal, while the standard deviation std is not always minimal, depending on the composition of the images in the types, which is an indication of detecting the disease type in the correlation matrix; d) correlational links have been established between types of diseases in the diagnosis of disease types using wavelet functions a1 and a2, characterizing the strength of the links between types of diseases caused by the commonality of properties of the structural tissues of the visual organ, where types of eye diseases develop, as well as the origin of diseases; (e) a reliable method has been found for localizing the type of diagnosed disease in the correlation matrix of characteristics a1 or a2 of the disease with the characteristics of sets of images of diseases in known types of diseases, based on the correlation of the characteristics of the diagnosed disease and the characteristics of the image provided by the researcher, the types of diseases of which match, with the characteristics of sets of diseases in known types of diseases; (f) a reliable method has been found to separate types of diseases with a probability p>0,95 based on maximizing the observed value t_test of the criterion when testing the hypothesis of equality of means of two populations by eliminating the correlation coefficients in two parts of the column; (g) the requirements for the formation of sets of input data, «quanta of information» have been established to obtain reliable diagnoses of disease types; these include: increasing the capacities of input data sets in disease types; increasing the detail in observations, including increasing the orders of calculated a1 and a2 waves in wavelet transformations.