By Srdjan Stanković, Irena Orović, Ervin Sejdić
This publication is designed for college students, pros and researchers within the box of multimedia and similar fields with a necessity to benefit the fundamentals of multimedia platforms and sign processing. Emphasis is given to the research and processing of multimedia signs (audio, photographs, and video). precise perception into the main correct mathematical equipment and adjustments utilized in multimedia sign processing is given. a distinct dating among various adjustments can also be integrated, commencing new views for outlining novel transforms in particular purposes. distinctive recognition is devoted to the compressive sensing quarter, which has a good power to give a contribution to extra development of contemporary multimedia platforms. as well as the theoretical strategies, numerous regular and extra lately authorised algorithms for the reconstruction of other sorts of indications are thought of. more information and info also are supplied to permit a entire research of audio and video compression algorithms. eventually, the ebook connects those ideas to different vital components of multimedia structures, equivalent to the research of optical media, electronic watermarking, and telemedicine.
New to this edition:
Introduction of the generalization inspiration to consolidate the time-frequency sign research, wavelet transformation, and Hermite transformation
Inclusion of admired strong transformation conception utilized in the processing of noisy multimedia information in addition to
advanced multimedia facts filtering methods, together with snapshot filtering innovations for impulse noise environment
Extended video compression algorithms
Detailed insurance of compressive sensing in multimedia functions
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Additional info for Multimedia Signals and Systems: Basic and Advanced Algorithms for Signal Processing
In the case of signals corrupted by impulse noise, the commonly used alternative approach is based on median filter, obtained as a central element in the sorted sequence. The median filter is considered in more detail in Chap. 4. In the case of the STFT, we can observe the vector xðn þ mÞeÀ j2πmk=N for m ¼ [ÀN/2, . , N/2 À 1], having real and imaginary part. Now, using the loss function independent Ffεg ¼ ReðεÞ þ ImðεÞ and a marginal median filter form, we can define the marginal median STFT form as follows: È Â N N ÁÉ STFT M ðn; kÞ ¼ median Re xðn þ mÞeÀ j2πmk=N , for m 2 À , 2 2 ð1:58Þ È Â N N ÁÉ À j2πmk=N þ jmedian Im xðn þ mÞe , for m 2 À , : 2 2 For cases when the noise is a mixture of Gaussian and impulse noise (or heavytailed noise), the resulting pdf function would have a complex form which is not suitable for practical applications.
Let us mention some of the most commonly used wavelets: • The Haar wavelet is the oldest and the simplest wavelet. • Daubechies wavelets represent a set of orthonormal wavelets of limited duration. For example, Daubechies D4 wavelet has 4 coefficients; D8 has 8 coefficients, and so on. Note that the Haar wavelet is actually the Daubechies wavelet of the first order. • Bi-orthogonal wavelets are widely used in image compression. For example, JPEG2000 compression algorithm is based on bi-orthogonal Le Gall (5,3) and Cohen–Daubechies–Feauveau (CDF) (9,7) wavelets.
4, the discrete Fourier transform is given by: DFT ðkÞ ¼ N À1 X f ðnÞeÀ j N nk : 2π ð1:8Þ n¼0 The inverse discrete Fourier transform is defined as: f ð nÞ ¼ N À1 1X 2π DFT ðkÞe j N nk : N k¼0 ð1:9Þ It should be mentioned that computationally efficient algorithms known as the Fast Fourier Transform (FFT) algorithms have been derived to calculate discrete Fourier transform and its inverse. To become more familiar with the Fourier transform, we recommend considering problems found at the end of this chapter.
Multimedia Signals and Systems: Basic and Advanced Algorithms for Signal Processing by Srdjan Stanković, Irena Orović, Ervin Sejdić