Related papers: Image Compression predicated on Recurrent Iterated…
This paper introduces a new class of iterated function systems (IFSs) called R-IFSs, which include both rotation/reflection maps and contraction maps. The study of R-IFSs is motivated by the recent research direction on enriching IFSs by…
We use neural network algorithms for finding compression methods of images in the framework of iterated function systems which is a collection of the transformations of the interval $(0, 1)$ satisfying suitable properties.
We consider a construction of recurrent fractal interpolation surfaces with function vertical scaling factors and estimation of their box-counting dimension. A recurrent fractal interpolation surface (RFIS) is an attractor of a recurrent…
For lossy image compression systems, we develop an algorithm, iterative refinement, to improve the decoder's reconstruction compared to standard decoding techniques. Specifically, we propose a recurrent neural network approach for…
We investigate the use of iterated function system (IFS) models for data analysis. An IFS is a discrete dynamical system in which each time step corresponds to the application of one of a finite collection of maps. The maps, which represent…
We provide an overview of iterated function systems (IFS), where randomly chosen state-to-state maps are applied iteratively to a state. We aim to summarize the state of art and, where possible, identify fundamental challenges and…
Recently Implicit Neural Representations (INRs) gained attention as a novel and effective representation for various data types. Thus far, prior work mostly focused on optimizing their reconstruction performance. This work investigates INRs…
Computed tomography (CT) reconstructs volumetric images using X-ray projection data acquired from multiple angles around an object. For low-dose or sparse-view CT scans, the classic image reconstruction algorithms often produce severe noise…
Iterated functions system (IFS) is defined by specifying a set of functions in a classical phase space, which act randomly on an initial point. In an analogous way, we define a quantum iterated functions system (QIFS), where functions act…
Implicit Neural Representations (INRs) are a novel paradigm for signal representation that have attracted considerable interest for image compression. INRs offer unprecedented advantages in signal resolution and memory efficiency, enabling…
We develop a qualitative-dynamics framework for general Iterated Function Systems (IFSs) on locally compact spaces. Our approach extends to IFSs a framework recently developed in the semiflows setting by James Yorke and the present author…
To improve the compressive sensing MRI (CS-MRI) approaches in terms of fine structure loss under high acceleration factors, we have proposed an iterative feature refinement model (IFR-CS), equipped with fixed transforms, to restore the…
A finite family $\mathcal{F}=\{f_1,\ldots,f_n\}$ of continuous selfmaps of a given metric space $X$ is called an iterated function system (shortly IFS). In a case of contractive selfmaps of a complete metric space is well-known that IFS has…
We describe an image compression method, consisting of a nonlinear analysis transformation, a uniform quantizer, and a nonlinear synthesis transformation. The transforms are constructed in three successive stages of convolutional linear…
The paper is devoted to searching algorithms which will allow to generate images of attractors of \emph{generalized iterated function systems} (GIFS in short), which are certain generalization of classical iterated function systems, defined…
Iterated function systems (IFS) can be a surprisingly useful tool for studying structure in data. Here we present results stemming from a 2013 computational study by the author using IFS. The results include fractal patterns that reveal…
We present a general theory of fractal transformations and show how it leads to a new type of method for filtering and transforming digital images. This work substantially generalizes earlier work on fractal tops. The approach involves…
We introduce an harmonic analysis for iterated function systems (IFS) (X, mu) which is based on a Markov process on certain paths. The probabilities are determined by a weight function W on X. From W we define a transition operator R_W…
The iterative refinement method (IRM) has been very successfully applied in many different fields for examples the modern quantum chemical calculation and CT image reconstruction. It is proved that the refinement method can create an exact…
Scalable image compression is a technique that progressively reconstructs multiple versions of an image for different requirements. In recent years, images have increasingly been consumed not only by humans but also by image recognition…