23 March 1995 Parallel algorithms and architectures for a family of Haar-like transforms
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In this work we introduce a new wide family of 'unbounded' DOTs based on parametric representations of transform matrices. This family contains the generalized Haar transform. A computational model corresponding to linear MISD type (pipelined) algorithms is introduced. Lower bounds are found for the complexity of linear transforms relative to the proposed model. Unified pipelined-parallel algorithms with various level of parallelism which can be implemented on MISD systems to compute unbounded DOTs are developed. It is shown that the proposed algorithms are asymptotically optimal, i.e. the order of the upper bounds coincide with the order of the lower bounds. A unified processor architecture realizing the proposed algorithms is developed. Each processor is universal for a family of unbounded DOTs, meaning that each transform of the family is effectively realized in the processors. The processors can be implemented using different number of processor elements based on the same architecture. Although the processors are universal their area-time complexities are comparable with complexities of known Haar processors.
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Jaakko T. Astola, Jaakko T. Astola, Sos S. Agaian, Sos S. Agaian, David Zaven Gevorkian, David Zaven Gevorkian, } "Parallel algorithms and architectures for a family of Haar-like transforms", Proc. SPIE 2421, Image and Video Processing III, (23 March 1995); doi: 10.1117/12.205486; https://doi.org/10.1117/12.205486

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