In this paper, based on the parametric model of the matrix of discrete cosine transform (DCT), and using an exhaustive search of the parameters’ space, we seek for the best approximations of 8-point DCT at the given computational complexities by taking into account three different scenarios of practical usage. The possible parameter values are selected in such a way that the resulting transforms are only multiplierless approximations, i.e., only additions and bit-shift operations are required. The considered usage scenarios include such cases where approximation of DCT is used: (i) at the data compression stage, (ii) at the decompression stage, and (iii) both at the compression and decompression stages. The obtained results in effectiveness of generated approximations are compared with results of popular known approximations of 8-point DCT of the same class (i.e., multiplierless approximations). In addition, we perform a series of experiments in lossy compression of natural images using popular JPEG standard. The obtained results are presented and discussed. It should be noted, that in the overwhelming number of cases the generated approximations are better than the known ones, e.g., in asymmetric scenarios even by more than 3 dB starting from entropy of 2 bits per pixel. In the last part of the paper, we investigate the possibility of hardware implementation of generated approximations in Field-Programmable Gate Array (FPGA) circuits. The results in the form of resource and energy consumption are presented and commented. The experiment outcomes confirm the assumption that the considered class of transformations is characterized by low resource utilization.

本文基于离散余弦变换（DCT）矩阵的参数模型，并通过对参数空间的详尽搜索，在给定的计算复杂度下，寻求8点DCT的最佳近似值。解释了三种不同的实际使用场景。选择可能的参数值，使得所得的变换仅是无乘数近似值，即，仅需要加法和移位操作。考虑的使用场景包括使用DCT近似的情况：（i）在数据压缩阶段，（ii）在解压缩阶段，和（iii）在压缩和解压缩阶段。将所获得的生成近似效果的结果与同类的8点DCT的流行已知近似结果（即无乘数近似）进行比较。此外，我们使用流行的JPEG标准进行了一系列自然图像的有损压缩实验。提出并讨论了获得的结果。应当指出，在绝大多数情况下，例如在非对称情况下，从每个像素2位的熵开始，所生成的近似值甚至比已知的近似值要好3dB以上。在本文的最后一部分，我们研究了在现场可编程门阵列（FPGA）电路中硬件实现生成的近似值的可能性。以资源和能源消耗的形式给出结果并进行评论。