In [11] we met the notions of a frame and a frame morphism. These form the objects and arrows of the category Frm . We saw that the universal algebra of a frame A is best done using certain operators on A, the nuclei on A. The collection NA of all these, the assembly of A, is partially ordered by the pointwise comparison. In fact, NA is a complete lattice since it is closed under pointwise infi...

Sparse approximation has shown to be a significant tool in improving image restoration quality, assuming that the targeted images can be approximately sparse under some transform operators. However, it is impossible for a fixed system to be always optimal for all the images. In this paper, we present an adaptive wavelet tight frame technology for sparse representation of an image with multiplic...

this paper is a continuation of [uniformities and covering properties for partial frames (i)], in which we make use of the notion of a partial frame, which is a meet-semilattice in which certain designated subsets are required to have joins, and finite meets distribute over these. after presenting there our axiomatization of partial frames, which we call $sels$-frames, we added structure, in th...

We consider the decomposition of bounded linear operators on Hilbert spaces in terms functions forming frames. Similar to singular-value decomposition, resulting frame decompositions encode information structure and ill-posedness problem can be used as basis for design implementation efficient numerical solution methods. In contrast presented derived explicitly a wide class operators, particula...

partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...

The analysis sparsity model is a very effective approach in modern Compressed Sensing applications. Specifically, redundant operators can lead to fewer measurements needed for reconstruction when employing the \(l_1\)-minimization Sensing. In this paper, we pick an eigenvector of Zauner unitary matrix and –under certain assumptions on ambient dimension– build spark deficient Gabor frame. operat...

Internet of Things (IoT) solutions are increasingly being deployed for smart applications. With the rise of smart cities there is a need for low cost and long range Low Power Wide Area Network (LPWAN) technologies. LoRaWAN is an energy efficient and cheap LPWAN solution. It is rapidly being adopted all around the world. LoRaWAN however does not provide communication robustness in its basic conf...

Using the notions of frame transform and of square integrable projective representation of a locally compact group G, we introduce a class of isometries (tight frame transforms) from the space of Hilbert-Schmidt operators in the carrier Hilbert space of the representation into the space of square integrable functions on the direct product group G × G. These transforms have remarkable properties...