Compression for Multimedia by Irina Bocharova

By Irina Bocharova

Supplying an intensive theoretical knowing of lossy compression innovations for picture, video, speech, and audio compression, this booklet additionally covers the main beneficial properties of every method, in addition to functional purposes, implementation concerns, and layout trade-offs. It provides comparisons of multimedia criteria when it comes to attaining recognized theoretical limits, when universal and distinguishing positive factors of the prevailing criteria are defined and on the topic of the historical past concept. there's distinct insurance of such subject matters because the H.264 video coding usual, low-complexity code-based vector quantizers, and the Blahut rate-distortion set of rules. Examples in accordance with actual multimedia info also are integrated, plus end-of-chapter difficulties to check knowing, algorithms that let the reader to symbolize speech and audio signs successfully, and an appendix at the fundamentals of lossless coding. With a great stability of conception and perform, this e-book is perfect for undergraduate and graduate scholars, and can be an invaluable reference for practitioners.

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Below, we formulate without proof the rate-distortion theorem and its converse for a discrete-time stationary random process. 1 For a discrete-time stationary and ergodic continuous source with ratedistortion function H (D) with respect to the squared error d(x, y) = (x − y)2 , there exists an n 0 such that for all n > n 0 and for any δ1 > 0 and δ2 > 0 there exists an (R, Dn )-code of code length n with code rate R ≤ H (D) + δ1 for which the mean squared error Dn is less than or equal to D + δ2 .

When the codebook is found, the quantization procedure itself consists in finding for any input vector x one of the vectors yi , i = 1, 2, . . , M closest to x in terms of the squared error x − y 2 . The main shortcoming of vector quantization is its high computational complexity. To find the closest approximating vector it is necessary to perform an exhaustive search among M = 2n R0 vectors. 5 bit/sample and n = 32, then the size of the codebook is equal to M = 216 . It is possible to reduce the computational complexity of vector quantization by using structured codebooks.

The Voronoi cells of such a vector quantizer are n-dimensional cubes. In the general case lattice quantizers have nonrectangular Voronoi regions. In the next chapter we discuss the so-called shaping gain that is the gain in the average distortion obtained for lattice quantizers compared to scalar quantizers by manipulating the shape of the Voronoi cells. Notice that spherical Voronoi regions maximize the shaping gain but they cannot cover Rn . 3 Vector quantization To demonstrate the advantage of lattice quantizers in terms of computational complexity we consider the following example.

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