10/27(五)資工系/電機系 聯合專題演講

10/27 speaker:

本週五的專題演講,邀請到:中央研究院資訊科學研究所/研究員黃文良博士來為大家進行演講;黃博士於1993年在美國紐約大學取得資訊工程博士,專長領域為:Wavelet Analysis、Signal, Image and Video Processing,機會難得,敬請踴躍出席。

講題如下:

Title:

Frame-based Sparse Analysis and Synthesis  Representations for Signals

 

Abstract:

We attempt to apply frame theory to the sparse representation of signals for synthesis and analysis formulations using a synthesis dictionary for a frame and an analysis dictionary for a dual frame. Frames are the cornerstone of signal processing in the formulation of perfect reconstruction pairs of linear operators used to decompose signals into the transform domain and reconstruct the original signals from the transform coefficients. If a synthesis frame is selected for the reconstruction of any signal by minimizing the l2-norm synthesis-based problem, then the minimizer can be obtained by
decomposing the signal using its canonical dual frame. We first seek to extend this result for all signals by determining whether a dual frame can be constructed such that its frame coefficient is the minimizer of the l1-norm synthesis-based problem. Our results indicate that such a dual frame does not exist for over-complete frames. We then show that the canonical dual frame can yield the best approximation to any l1-norm minimizer. We then present general construction designs for Parseval tight frames from observations. Finally, we propose a learning algorithm, in which the optimal Parseval frame is learned for sparse representation of image blocks. Several applications are presented involving the restoration
of frame coefficients of images.