Thermodynamic free-energy minimization for unsupervised fusion of dual-color infrared breast images

This paper presents algorithmic details of an unsupervised neural network and unbiased diagnostic methodology, that is, no lookup table is needed that labels the input training data with desired outputs. We deploy the smart algorithm on two satellite-grade infrared (IR) cameras. Although an early malignant tumor must be small in size and cannot be resolved by a single pixel that images about hundreds cells, these cells reveal themselves physiologically by emitting spontaneously thermal radiation due to the rapid cell growth angiogenesis effect (In Greek: vessels generation for increasing tumor blood supply), shifting toward, according to physics, a shorter IR wavelengths emission band. If we use those exceedingly sensitive IR spectral band cameras, we can in principle detect whether or not the breast tumor is perhaps malignant through a thin blouse in a close-up dark room. If this protocol turns out to be reliable in a large scale follow-on Vatican experiment in 2006, which might generate business investment interests of nano-engineering manufacture of nano-camera made of 1-D Carbon Nano-Tubes without traditional liquid Nitrogen coolant for Mid IR camera, then one can accumulate the probability of any type of malignant tumor at every pixel over time in the comfort of privacy without religious or other concerns. Such a non-intrusive protocol alone may not have enough information to make the decision, but the changes tracked over time will be surely becoming significant. Such an ill-posed inverse heat source transfer problem can be solved because of the universal constraint of equilibrium physics governing the blackbody Planck radiation distribution, to be spatio-temporally sampled. Thus, we must gather two snapshots with two IR cameras to form a vector data X(t) per pixel to invert the matrix-vector equation X=[A]S pixel-by-pixel independently, known as a single-pixel blind sources separation (BSS). Because the unknown heat transfer matrix or the impulse response function [A] may vary from the point tumor to its neighborhood, we could not rely on neighborhood statistics as did in a popular unsupervised independent component analysis (ICA) mathematical statistical method, we instead impose the physics equilibrium condition of the minimum of Helmholtz free-energy, H = E - T o S . In case of the point breast cancer, we can assume the constant ground state energy E o to be normalized by those benign neighborhood tissue, and then the excited state can be computed by means of Taylor series expansion in terms of the pixel I/O data. We can augment the X-ray mammogram technique with passive IR imaging to reduce the unwanted X-rays during the chemotherapy recovery. When the sequence is animated into a movie, and the recovery dynamics is played backward in time, the movie simulates the cameras' potential for early detection without suffering the PD=0.1 search uncertainty. In summary, we applied two satellite-grade dual-color IR imaging cameras and advanced military (automatic target recognition) ATR spectrum fusion algorithm at the middle wavelength IR (3 - 5μm) and long wavelength IR (8 - 12μm), which are capable to screen malignant tumors proved by the time-reverse fashion of the animated movie experiments. On the contrary, the traditional thermal breast scanning/imaging, known as thermograms over decades, was IR spectrum-blind, and limited to a single night-vision camera and the necessary waiting for the cool down period for taking a second look for change detection suffers too many environmental and personnel variabilities.