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Figure 9 shows the BER degradation at with respect to the reference system, for a fixed ratio and various values of the block length.
Category 3. Some pixel grayscale values of the block under consideration are very close to the upper bound of the histogram (255 for an 8-bit grayscale image).
Category 2. Some pixel grayscale values of the block under consideration are very close to the lower bound of the histogram (0 for an 8-bit grayscale image).
This is achieved by grading each block with a score that evaluates the difference between the maximal 5 values of the block and the block average values, normalized by the standard deviation.
Category 4. Some pixel grayscale values of the block under consideration are close to the upper bounds, while some pixel grayscale values are close to the lower bounds of the histograms.
The matrices S and T are (2 Ntimes2 N) block tridiagonal, y is the 2N-component solution vector, and w denotes the 2N component column vector of known boundary values and right-hand side function values of the block system (51).
Similar(51)
However, computing the DFT of every block requires the MDCT values of the corresponding block, previous block, and succeeding block, which causes an inevitable algorithm delay of one block.
The solution of (5) is obtained by performing the water-filling power allocation over the singular values of the block-diagonal matrix H e = diag H 1, e, H 2, e, …, H K 0, e for the sum-power constraint of P[4], where H k,e, k = 1, 2,..., K0 is defined by (4).
Each category is represented by an histogram of the corresponding pixel values of the blocks in the spatial domain.
While comparing the presented graphs, it is easy to notice that the introduction of priorities (Figs. 5, 6, and 7) influences the values of the blocking probability.
In the hybrid algorithm proposed by [24], the audio signal is partitioned into blocks, and the watermark bits are embedded using dither modulation quantization of the singular values of the blocks.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com