Necessary and sufficient condition of the functional extremum in the tasks of digital video image compression, solved by methods of classical variation calculation

Kalistratov Dmitry Sergeevich

the compression of digital video images is considered, an example of additional compression of the high-frequency component of the wavelet - Haar transform, based on the solution of the variational calculus with compression priority adjustment on the principle of code volume - image quality is discussed, the construction of the target functional is given, an example of solving a variational task by Lagrange method of indefinite factors is presented, the necessary and sufficient conditions for its extremum are analyzed in detail.

Keywords:digital video image, compression, amount of code, image quality, priorities, functionality, extreme solution, necessary and sufficient conditions for an extremum, Euler equations, Hesse matrix