The usage of linear transformations has great relevance for data decorrelation applications, like image and video compression. In that sense, the discrete Tchebichef transform (DTT) possesses useful coding and decorrelation properties. The DTT transform kernel does not depend on the input data and fast algorithms can be developed to real-time applications. However, the DTT fast algorithm presented in literature possess high computational complexity. In this paper, we introduce a new low-complexity approximation for the DTT. The fast algorithm of the proposed transform is multiplication free and requires a reduced number of additions and bit-shifting operations. Image and video compression simulations in popular standards show good performance of the proposed transform. Regarding hardware resource consumption for FPGA shows a 43.1 reduction in configurable logic blocks and ASIC place and route realization shows a 57.7 reduction in the area-time figure compared with the 2D version of the exact DTT.
To the best of our knowledge, the only DTT approximation archived in literature was proposed in @cite_69 . That approximation was obtained by means of a parameterization of integer functions combined with a normalization of transformation matrix columns. The derived approximation in @cite_69 furnishes good coding capabilities, but it lacks orthogonality or near-orthogonality properties. As a consequence, the forward and inverse transformations are quite distinct and possess unbalanced computational complexities.
@cite_69
2031754465 2050320982 1978702630 2799119527
In this letter, we introduce a low-complexity approximation for the discrete Tchebichef transform (DTT). The proposed forward and inverse transforms are multiplication-free and require a reduced number of additions and bit-shifting operations. Numerical compression simulations demonstrate the efficiency of the proposed transform for image and video coding. Furthermore, Xilinx Virtex-6 FPGA based hardware realization shows 44.9 reduction in dynamic power consumption and 64.7 lower area when compared to the literature. In this letter, we provide a theoretical analysis of optimal predictive transform coding based on the Gaussian Markov random field (GMRF) model. It is shown that the eigen-analysis of the precision matrix of the GMRF model is optimal in decorrelating the signal. The resulting graph transform degenerates to the well-known 2-D discrete cosine transform (DCT) for a particular 2-D first order GMRF, although it is not a unique optimal solution. Furthermore, we present an optimal scheme to perform predictive transform coding based on conditional probabilities of a GMRF model. Such an analysis can be applied to both motion prediction and intra-frame predictive coding, and may lead to improvements in coding efficiency in the future. Transform coding using the discrete cosine transform (DCT) has been widely used in image and video coding standards, but at low bit rates, the coded images suffer from severe visual distortions which prevent further bit reduction. Postprocessing can reduce these distortions and alleviate the conflict between bit rate reduction and quality preservation. Viewing postprocessing as an inverse problem, we propose to solve it by the maximum a posteriori criterion. The distortion caused by coding is modeled as additive, spatially correlated Gaussian noise, while the original image is modeled as a high order Markov random field based on the fields of experts framework. Experimental results show that the proposed method, in most cases, achieves higher PSNR gain than other methods and the processed images possess good visual quality. In addition, we examine the noise model used and its parameter setting. The noise model assumes that the DCT coefficients and their quantization errors are independent. This assumption is no longer valid when the coefficients are truncated. We explain how this problem can be rectified using the current parameter setting. This paper proposes an end-to-end approach for single-channel speaker-independent multi-speaker speech separation, where time-frequency (T-F) masking, the short-time Fourier transform (STFT), and its inverse are represented as layers within a deep network. Previous approaches, rather than computing a loss on the reconstructed signal, used a surrogate loss based on the target STFT magnitudes. This ignores reconstruction error introduced by phase inconsistency. In our approach, the loss function is directly defined on the reconstructed signals, which are optimized for best separation. In addition, we train through unfolded iterations of a phase reconstruction algorithm, represented as a series of STFT and inverse STFT layers. While mask values are typically limited to lie between zero and one for approaches using the mixture phase for reconstruction, this limitation is less relevant if the estimated magnitudes are to be used together with phase reconstruction. We thus propose several novel activation functions for the output layer of the T-F masking, to allow mask values beyond one. On the publicly-available wsj0-2mix dataset, our approach achieves state-of-the-art 12.6 dB scale-invariant signal-to-distortion ratio (SI-SDR) and 13.1 dB SDR, revealing new possibilities for deep learning based phase reconstruction and representing a fundamental progress towards solving the notoriously-hard cocktail party problem.