Framelets: MRA-based constructions of wavelet frames

Framelets: Mra-based Constructions of Wavelet Frames

We are interested here in wavelet frames and their construction via multiresolution analysis (MRA); of particular interest to us are tight wavelet frames. The redundant representation offered by wavelet frames has already been put to good use for signal denoising, and is currently explored for image compression. Motivated by these and other applications, we explore in this article the theory of...

MRA-Based Wavelet Frames and Applications

Digital Gabor Filters Do Generate MRA-based Wavelet Tight Frames

Gabor frames, especially digital Gabor filters, have long been known as indispensable tools for local time-frequency analysis of discrete signals. With strong orientation selectivity, tensor products discrete (tight) Gabor frames also see their applications in image analysis and restoration. However, the lack of multi-scale structures existing in MRA-based wavelet (tight) frames makes discrete ...

Constructions of periodic wavelet frames using extension principles ∗

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...

MRA Based Wavelet Frames and Applications: Image Segmentation and Surface Reconstruction

Theory of wavelet frames and their applications to image restoration problems have been extensively studied for the past two decades. The success of wavelet frames in solving image restoration problems, which includes denoising, deblurring, inpainting, computed tomography, etc., is mainly due to their capability of sparsely approximating piecewise smooth functions such as images. However, in co...