Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce an Nth-order extension of the Riesz transform in d dimensions.  prove that this generalized transform has the following remarkable properties: shift-invariance, scale-invariance, inner-product preservation, and steerability. The pleasing consequence is that the transform maps any primary wavelet frame (or basis) of L 2 (ℝ d ) into another “steerable” wavelet frame, while preserving the frame bounds. The concept provides a rigorous functional counterpart to Simoncelli's steerable pyramid whose construction was entirely based on digital filter design. The proposed mechanism allows for the specification of wavelets with any order of steerability in any number of dimensions; it also yields a perfect reconstruction filterbank algorithm.  illustrate the method using a Mexican-hat-like polyharmonic spline wavelet transform as our primary frame.
['Michael Unser', 'Dimitri Van De Ville']
I am writing a research paper on a idea Higher-order riesz transforms and steerablewavelet frames
[{"from": "human", "value": "I am writing a research paper on a idea Higher-order riesz transforms and steerablewavelet frames"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  introduce an Nth-order extension of the Riesz transform in d dimensions.  prove that this generalized transform has the following remarkable properties: shift-invariance, scale-invariance, inner-product preservation, and steerability. The pleasing consequence is that the transform maps any primary wavelet frame (or basis) of L 2 (\u211d d ) into another \u201csteerable\u201d wavelet frame, while preserving the frame bounds. The concept provides a rigorous functional counterpart to Simoncelli's steerable pyramid whose construction was entirely based on digital filter design. The proposed mechanism allows for the specification of wavelets with any order of steerability in any number of dimensions; it also yields a perfect reconstruction filterbank algorithm.  illustrate the method using a Mexican-hat-like polyharmonic spline wavelet transform as our primary frame."}]