Breast cancer continues to be a significant public health problem in the world. The diagnosing mammography method is the most effective technology for early detection of the breast cancer. However, in some cases, it is difficult for radiologists to detect the typical diagnostic signs, such as masses and microcalcifications on the mammograms. Dense region in digital mammographic images are usual...

Frame theory is an active research area in mathematics, computer science and engineering with many exciting applications a variety of different fields. In this paper we study the notion dual continuous K-frames Hilbert spaces. Also establish some properties.

A dimension invariance property of finite frames of translates and Gabor frames is discussed. Under appropriate support conditions among the frame and dual frame generating functions, we show that a pair of dual frames evaluated in a given space remains a valid dual set if they are naturally embedded in the underlying space of almost arbitrarily enlarged dimension. Consequently, the evaluation ...

In this note we will show that the so called Sobolev dual is the minimizer over all linear reconstructions using dual frames for stable r order Σ∆ quantization schemes under the so called White Noise Hypothesis (WNH) design criteria. We compute some Sobolev duals for common frames and apply them to audio clips to test their performance against canonical duals and another alternate dual correspo...