Approximation of the Inverse Frame Operator and Applications to Gabor Frames

Approximation of the inverse frame operator and applications to Gabor frames.

tight frame approximation for multi-frames and super-frames

در این پایان نامه یک مولد برای چند قاب یا ابر قاب تولید شده تحت عمل نمایش یکانی تصویر برای گروه های شمارش پذیر گسسته بررسی خواهد شد. مثال هایی از این قاب ها چند قاب های گابور، ابرقاب های گابور و قاب هایی برای زیرفضاهای انتقال پایاست. نشان می دهیم که مولد چند قاب تنک نرمال شده (ابرقاب) یکتا وجود دارد به طوری که مینیمم فاصله را از ان دارد. همچنین مسایل مشابه برای قاب های دوگان مطرح شده و برخی ...

Frames of exponentials: lower frame bounds for finite subfamilies and approximation of the inverse frame operator

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.

Frame Representations and Parseval Duals with Applications to Gabor Frames

Let {xn} be a frame for a Hilbert space H. We investigate the conditions under which there exists a dual frame for {xn} which is also a Parseval (or tight) frame. We show that the existence of a Parseval dual is equivalent to the problem whether {xn} can be dilated to an orthonormal basis (under an oblique projection). A necessary and sufficient condition for the existence of Parseval duals is ...

Approximating the Inverse Frame Operator from Localized Frames

This investigation seeks to establish the practicality of numerical frame approximations. Specifically, it develops a new method to approximate the inverse frame operator and analyzes its convergence properties. It is established that sampling with well-localized frames improves both the accuracy of the numerical frame approximation as well as the robustness and efficiency of the (finite) frame...