Set Partitioning in Hierarchical Frequency Bands (SPHFB)

The algorithm proposed is motivated by a detailed analysis of the wavelet coefficient set partitioning schemes found in the SPIHT algorithm. Initially, the image is transformed into the wavelet domain. The threshold of each independent subband is calculated and sent to the decoder. The subbands scanning sequence is established by the magnitude of the thresholds, subbands with larger threshold are scanned first. The subbands are partitioned into sets of type Sq (where q = l....L + l with L = decomposition levels) of mxn adjacent coefficients, according to the subband they belong to. The resolution of a set in a finer subband is four times the resolution of a set in the next coarser subband. Initially, the type of a set is the same if it belongs to a subband with the same resolution, and different if the set belongs to a subband with a different resolution, except for the coarsest subband whose sets size is of one coefficient only (set of type S _L+1). We say a subband is significant when the current threshold is equal to the threshold of the correspondent subband. Then, the sets inside the subbands are scanned. Significant sets are signaled with a ´1´ and split into four subsets. Subset are also scanned and treated as sets of one fourth of resolution. The new sets are scanned again until subsets of type S_L+i (one coefficient) are gotten. If the coefficient is non-significant a ´0´ is sent to the decoder, otherwise a ´ 1´ is sent followed by a bit of sign corresponding to the sign of the coefficient. After a sorting pass, a refinement pass is carried out. Refinement is performed on significant S_L+1 sets from previous passes, according to the current threshold (k_n), and is performed by sending the k_nth bit of the previous significant coefficient. Afterwards, the threshold is decremented by one and the subbands scanning process is repeated. Previous knowledge of the maximum bit depth (threshold) of a subband, a- voids sending to the decoder extra zeros to signal the sets inside the subband are non-significant and, at the same time, allows the encoder to send the most significant subbands and high energy areas first.