We give lower frame bounds for finite subfamilies of a frame of exponentials {ek}k∈Z in L2(−π, π). We also present a method for approximation of the inverse frame operator corresponding to {ek}k∈Z, where knowledge of the frame bounds for finite subfamilies is crucial.

We study the Laplacian pyramid (LP) as a frame operator, and this reveals that the usual reconstruction is suboptimal. With orthogonal filters, the LP is shown to be a tight frame, thus the optimal linear reconstruction using the dual frame operator has a simple structure as symmetrical with the forward transform. For more general cases, we propose an efficient filter bank for reconstruction in...

We give syntax and a PER-model semantics for a typed-calculus with subtypes and singleton types. The calculus may be seen as a minimal calculus of sub-typing with a simple form of dependent types. The aim is to study singleton types and to take a canny step towards more complex dependent subtyping systems. Single-ton types have applications in the use of type systems for speciication and progra...

In this paper we introduce the notion of J-fusion frame for a Krein space K. We prove some basic results regarding J-fusion frame. We also approximate J-fusion frame bounds of a J-fusion frame by the upper and lower bounds of the synthesis operator. Finally we provide a necessary and sufficient condition under which the image of J-fusion frame under a bounded invertible linear map is also a J-f...

Frames with a large minimum angle between any two distinct frame vectors are desirable in many present day applications. For unit norm frame, the absolute value of cosine is also known as coherence. Two frames equivalent if one can be obtained from other via left action an invertible linear operator. Frame angles change under Most existing works solve different optimization problems to find opt...

The class of motion estimation algorithms known as backward methods have the advantage of dense motion eld sampling, and in coding applications the decoder needs no motion information from the coder. In this paper, we rst present an overview of operator based motion compensators with interpolative and non-interpolative kernels. We then proceed with two new results. The rst ooers a new perspecti...

A basic problem of interest in connection with the study of Schauder frames in Banach spaces is that of characterizing those Schauder frames which can essentially be regarded as Schauder bases. In this paper, we study this problem using the notion of a minimal-associated sequence space and a minimal-associated reconstruction operator for Schauder frames. We prove that a Schauder frame is a near...