Speaker:  Zuowei Shen
Tan Chin Tuan Centennial Professor,
                Dean of  School of Sciences, National University of Singapore 
Venue:   数学楼二楼会议室

Date：    June 5， Tuesday， 3：30-4：30 pm

Abstract: We are living in the era of big data. The discovery,
interpretation and usage of the information, knowledge and resources
hidden in all sorts of data to benefit human beings and to improve
everyone¹s day to day life is a challenge to all of us. The huge amount of
data we collect nowadays is so complicated, and yet what we expect from it
is so much.  This provides many challenges and opportunities  to many
fields.  As images are one of the most useful and commonly used types of
data, in this talk, we start from reviewing the development of the wavelet
frame (or more general redundant system) based approach for image
restoration. We will observe that a good system for any data, including
images, should be capable of effectively capturing both global patterns
and local features. One of the examples of such system is the wavelet
frame. We will then show how models and algorithms of wavelet frame based
image restoration are developed via the generic knowledge of images. Then,
the specific information of a given image can be used to further improve
the models and algorithms. Through this process, we shall reveal some
insights and understandings of the wavelet frame based approach for image
restoration and its connections to other approaches, e.g. the partial
differential equation based methods. Finally,  we  will also show, by many
examples, that  ideas  given here  can go beyond image restoration and can
be used to many other applications in data science.