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We have shown that the remote sensing optical imaging to achieve detailed sub-pixel decomposition is a unique application of blind source separation (BSS) that is truly linear of far away weak signal, instantaneous speed of light without delay, and along the line of sight without multiple paths. In early papers, we have presented a direct application of statistical mechanical de-mixing method called Lagrange Constraint Neural Network (LCNN). While the BSAO algorithm (using a posteriori MaxEnt ANN and neighborhood pixel average) is not acceptable for remote sensing, a mirror symmetric LCNN approach is all right assuming a priori MaxEnt for unknown sources to be averaged over the source statistics (not neighborhood pixel data) in a pixel-by-pixel independent fashion. LCNN reduces the computation complexity, save a great number of memory devices, and cut the cost of implementation. The Landsat system is designed to measure the radiation to deduce surface conditions and materials. For any given material, the amount of emitted and reflected radiation varies by the wavelength. In practice, a single pixel of a Landsat image has seven channels receiving 0.1 to 12 microns of radiation from the ground within a 20x20 meter footprint containing a variety of radiation materials. A-priori LCNN algorithm provides the spatial-temporal variation of mixture that is hardly de-mixable by other a-posteriori BSS or ICA methods. We have already compared the Landsat remote sensing using both methods in WCCI 2002 Hawaii. Unfortunately the absolute benchmark is not possible because of lacking of the ground truth. We will arbitrarily mix two incoherent sampled images as the ground truth. However, the constant total probability of co-located sources within the pixel footprint is necessary for the remote sensing constraint (since on a clear day the total reflecting energy is constant in neighborhood receiving pixel sensors), we have to normalized two image pixel-by-pixel as well. Then, the result is indeed as expected.
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