We show that Hilbert–Schmidt operators can be used to define frame-like structures for $L^2(\mathbb{R}^d )$ over lattices in $\mathbb{R}^{2d} $ include multi-window Gabor frames as a special case. These are called g-frames

In this paper, we introduced and characterized the controlled $g$-duals of a frame in separable Hilbert space $\mathcal{H}$ . Afterwards, obtained new $C$-controlled $g$-dual frames from given frames. addition, approximation for was defined some their properties were investigated. Finally, relationship between approximately dual $g$-dual.

In this paper, we study continuous frames from projective representations of locally compact abelian groups type $$\widehat{G}\times G$$ . particular, using the Fourier transform on groups, obtain a characterization maximal spanning vectors. As an application, for G, compactly generated Euclidean group or local field with odd residue characteristic, prove existence vectors, hence phase retrieva...

Motion-JPEG is a common video format for compression of motion images with highquality using JPEG standard for each frame of the video. During transmission through a noisychannel some blocks of data are lost or corrupted, and the quality of decompression frames decreased.In this paper, for reconstruction of these blocks, several temporal-domain, spatial-domain, andfrequency-domain error conceal...

finite normalized tight frames are interesting because they provide decompositionsin applications and some physical interpretations. in this article,we give a recursive method for constructing them.