The present invention pertains to a decoding device and decoding method and an encoding device and encoding method, whereby intra-prediction modes for images having a hierarchical structure can be shared using a low processing load.
A decoding program, method and device of encoded data in which an original stream can be recovered completely when decoded data is encoded again by making a computer function as a means for receiving irreversibly compressed encoded data and projecting an arbitrary real vector orthogonally to one convex set X in a first vector space where its decoded signal exists, a means for judging whether convex projection has converged or not and determining a real vector x belonging to the set X and outputting it as a decoded signal if the convex projection has judged converged, and a means for projecting an arbitrary vector in the first vector space orthogonally to one convex set Y in a second vector space different from the first vector space and then repeating orthogonal projection to the sets X and Y using an encoded signal as an initial value.
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