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In this paper the authors analyze the effectiveness of parallel graphics processing unit (GPU) realizations of discrete wavelet transform (DWT) using lattice structure and matrixbased approach. Experimental verification shows that, in general, for smaller input vector sizes along with the larger filter lengths DWT computation based on the direct approach with the use of the direct matrix multiplication significantly f aster t han the application of the lattice structure factorization while for large vector sizes the lattice structure becomes more effective. The detailed results define boundaries of performance for both implementations and determine the most advantageous situations in which one might use a given approach. The results also include comparative analysis of time efficiency o f t he p resented methods for two different GPU architectures. The presented effectiveness characteristics of the considered realizations of the two selected DWT computation methods allows for making the proper choice of the particular method in future applications depending on input data sizes, filter l engths a nd u nderlying G PU architecture.

Parallel realizations of discrete transforms (DTs) computation algorithms (DTCAs) performed on graphics processing units (GPUs) play a significant role in many modern data processing methods utilized in numerous areas of human activity. In this paper the authors propose a novel execution time prediction model, which allows for accurate and rapid estimation of execution times of various kinds of structurally different DTCAs performed on GPUs of distinct architectures, without the necessity of conducting the actual experiments on physical hardware. The model can serve as a guide for the system analyst in making the optimal choice of the GPU hardware solution for a given computational task involving particular DT calculation, or can help in choosing the best appropriate parallel implementation of the selected DT, given the limitations imposed by available hardware. Restricting the model to exhaustively adhere only to the key common features of DTCAs enables the authors to significantly simplify its structure, leading consequently to its design as a hybrid, analytically-simulational method, exploiting jointly the main advantages of both of the mentioned techniques, namely: time-effectiveness and high prediction accuracy, while, at the same time, causing mutual elimination of the major weaknesses of both of the specified approaches within the proposed solution. The model is validated experimentally on two structurally different parallel methods of discrete wavelet transform (DWT) computation, i.e. the direct convolutionbased and lattice structure-based schemes, by comparing its prediction results with the actual measurements taken for 6 different graphics cards, representing a fairly broad spectrum of GPUs compute architectures. Experimental results reveal the overall average execution time and prediction accuracy of the model to be at a level of 97.2%, with global maximum prediction error of 14.5%, recorded throughout all the conducted experiments, maintaining at the same time high average evaluation speed of 3.5 ms for single simulation duration. The results facilitate inferring the model generality and possibility of extrapolation to other DTCAs and different GPU architectures, which along with the proposed model straightforwardness, time-effectiveness and ease of practical application, makes it, in the authors' opinion, a very interesting alternative to the related existing solutions.

In this paper, the authors present several self-developed implementation variants of the Discrete Wavelet Transform (DWT) computation algorithms and compare their execution times against the commonly approved ones for representative modern Graphics Processing Units (GPUs) architectures. The proposed solutions avoid the time-consuming modulo divisions and conditional instructions used for DWT filters wrapping by proper expansion of the DWTs input data vectors. The main goal of the research is to improve the computation times for popular DWT algorithms for representative modern GPU architectures while retaining the code’s clarity and simplicity. The relations between algorithms execution time improvements for GPUs are also compared with their counterparts for traditional sequential processors. The experimental study shows that the proposed implementations, in the case of parallel realization on GPUs, are characterized by very simple kernel code and high execution time performance.