This paper proposes a spatial-Radon domain CT image reconstruction model based on data-driven tight frames (SRD-DDTF). The proposed SRD-DDTF model combines the idea of joint image and Radon domain inpainting model of [1] and that of the data-driven tight frames for image denoising [2]. It is different from existing models in that both CT image and its corresponding high quality projection image...

We prove the existence of tight frames whose elements lie on an arbitrary ellipsoidal surface within a real or complex separable Hilbert space H , and we analyze the set of attainable frame bounds. In the case whereH is real and has finite dimension, we give an algorithmic proof. Our main tool in the infinite dimensional case is a result we have proven which concerns the decomposition of a posi...

Digital Gabor filters are indispensable tools of local time-frequency analysis in signal processing. With strong orientation selectivity, discrete (tight) Gabor frames generated by 2D Gabor filters also see their wide applications in image processing and volume data processing. However, owing to the lack of multi-scale structures, discrete Gabor frames are less effective than multiresolution an...

Since the extension principles of constructing wavelet frames were presented, a lot of symmetric and compactly supported wavelet frames with high vanishing moments have been constructed. However the problem of constructing periodic wavelet frames with the help of extension principles is open. In this paper, we will construct tight periodic wavelet frames using the unitary extension principle an...

The oblique extension principle introduced in [3, 5] is a general procedure to construct tight wavelet frames and their associated filter banks. Symmetric tight framelet filter banks with two high-pass filters have been studied in [13, 16, 17]. Tight framelet filter banks with or without symmetry have been constructed in [1]–[21] and references therein. This paper is largely motivated by severa...