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Image, video and Data Compression Using New Basis Functions
These patents utilize minimization of space-spatial frequency (momentum) for image compression using waveletized, 2D discrete new basis functions. These basis functions generalize to higher dimensions with a quaternionic tensorial approaches. The quaternionic basis functions are applied to a one-dimensional signal, a 2-D image, and 3-D video, with parallel processing and can be used to structure an algebraic biology for applications in DNA compression. The patent treats each pixel in an image to mass points and has an associated moment reference to a central moment. It covers orthogonal moments such as pseudo-Zernike, Legendre, Krawtchouk, and Hermite-Gaussian (HG) moments.
The 1-D HG moment framework is used for monitoring QRS heartbeat signatures and other signals. It shows how HG basis functions can be used with complex moments and geometric moments. A hyper-complex quaternionic Hermite basis function is used for color compression. Also, quaternionic singular value decomposition (QSVD) is used to decompose the images. A quaternion Fourier transform (QFT) for lossless spectral color compression is used with quaternion Hermite transform. The three components of a quaternion assigned to the three colors red, green, and blue for improved color compression is introduced to convert absolute color space RGB into a format that separates luma (brightness) and chroma (color) encoding into YC_r C_b for improved compression. Temporal Hermite functions are used for video compressions with temporal frames just like spatial Hermite basis functions in the space domain for image compression. It is shown that Hermite functions are Eigen functions for use in parallel processing that increase computational speed. It also covers quaternionic compression for compression of DNA information. With 4 basis sets ATCG connecting the sugar phosphates in DNA and 4 letter alphabets for nitrogenous bases, 64 alphabet of triplets, 20 letter alphabet of amino acids, 2 letter alphabet (strong and weak hydrogen bonds) we can formulate an algebraic biology with these quaternionic basis functions.