Discrete Cosine Transform (DCT Encoding)

DCT is used in numerous applications in science and engineering, from lossy compression of audio (e.g. MP3) and images (e.g. JPEG) (where small high-frequency components can be discarded), to spectral methods for the numerical solution of partial differential equations. The use of cosine rather than sine functions is critical in these applications: for compression, it turns out that cosine functions are much more efficient, whereas for differential equations the cosines express a particular choice of boundary conditions.

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Discrete Wavelet Transform (Wavelet Encoding)

In numerical analysis and functional analysis, a discrete wavelet transform (DWT) is any wavelet transform for which the wavelets are discretely sampled. As with other wavelet transforms, a key advantage it has over Fourier transforms is temporal resolution: it captures both frequency and location information (location in time).

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Together DCT and Wavelet-based video encoding technologies have been widely adopted in many sectors. TRUDEF™ offers solutions designed to compete for market share from these video encoding technologies.

Fractal Transform (Fractal Encoding)

Fractal compression is founded on the fact that in a string of images, similar patterns are repeated. A fractal algorithm mathematically encodes these patterns into data called “fractal codes”. When images are viewed; fractal code containing the geometric patterns of the original are remapped back into pixels, self-similar patterns are reused during this decoding process.

An inherent feature of fractal compression is its ability to decompress images into different resolutions than the original while maintaining a high level of image quality. This is a powerful method of saving bandwidth by allowing users to watch video at higher resolutions than what is transmitted over a network or storage requirements for local access. Up scaling is valuable for transforming archived content originally shot in lower resolution formats to modern HD formats while maintaining as much of the original detail as possible.

TMMI’s fractal based encoding will allow HDTV broadcasters to upscale video for the next generation HDTV resolutions with little or no increase in bandwidth usage. The fractal encoding process is computationally intensive; however, decoding is done in near real-time. During the 1990′s the available slow 16 bit and 32 bit hardware limited the practical use of fractal compression. Today’s multi-core 64 bit hardware is significantly more powerful and low cost distributed processing fractal compression is now commercial viable.

Fractal Scaling is an effective method of saving bandwidth while providing higher resolutions. When screen resolution is doubled it contains 4X as many pixels: 1920×1080=2,073,600 pixels, doubling the resolution to 3840×2160=8,294,400 pixels.