Abstract
We present a design scheme that generates tight and semi-tightframes in discrete-time periodic signals space originated fromfour-channel perfect reconstruction periodic filter banks. Filter banksare derived from interpolating and quasi-interpolating polynomial and discrete splines. Each filter bank comprises one linear phaselow-pass filter (in most cases interpolating) and one high-passfilter, whose magnitude's response mirrors that of a low-pass filter.These filter banks comprise two band-pass filters. We introduce local discrete vanishing moments (LDVM). When the frame is tight, analysis framelets coincidewith their synthesis counterparts. However, for semi-tight frames,we swap LDVM between synthesis and analysis framelets. The designscheme is generic and it enables us to design framelets with anynumber of LDVM. The computational complexity of the the framelet transforms,which consists of calculating the forward and the inverse FFTs, doesnot depend on the number of LDVM and does depend on the size of the the impulse response fi lters. The designed frames are used for image restorationtasks, which were degraded by blurring, random noise and missingpixels. The images were restored by the application of the SplitBregman Iterations method. The frames performances are evaluated. Apotential application of this methodology is the design of asnapshot hyperspectral imager that is based on a regular digitalcamera. All these imaging applications are described.
Highlights
Restoration of multidimensional signals that were corrupted and/or damaged and/or noised is a major challenge that the signal/image processing community faces nowadays when rich multimedia content is the most popular data being transmitted over diverse networks types including mobile
The goal of our experiments is to compare between the performances of different tight and semi-tight frames in identical conditions
The performance of the tight frames T14,0 and T13,0, which were derived from the piece-wise linear splines, were significantly worse as well as the performance of the tight frames T1400,0 and T1420,0 that have many local discrete vanishing moments (LDVM)
Summary
Restoration of multidimensional signals that were corrupted and/or damaged and/or noised is a major challenge that the signal/image processing community faces nowadays when rich multimedia content is the most popular data being transmitted over diverse networks types including mobile. Quality degradation in multidimensional signals can come from sampling, acquisition, transmission through noisy channels, to name some. Restoration of multidimensional signals includes denoising, deblurring, recovering missing or damaged samples or fragments (inpainting in images), resolution enhancement and super resolution. The processing goals are to improve the visual perception of still and video signals. Tight and semi-tight frames, interpolating and quasiinterpolating polynomial, vanishing moments, split Bregman iterations, image restoration
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
