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January 2000 - present
Publications
Publications (72)
Positron emission tomography (PET) is a medical imaging technique employed to identify regions of heightened metabolic activity in the body. The primary challenge of PET imaging lies in reconstructing images (2D) or volumes (3D). Reconstruction methods can be categorized into two main types: analytical and iterative. In our previous research, we de...
In this paper, we provide a precise mathematical model of crystal-to-crystal response which is used to generate the white image - a necessary compensation model needed to overcome the physical limitations of the PET scanner. We present a closed-form solution, as well as several accurate approximations, due to the complexity of the exact mathematica...
In this paper, we provide a novel method for the estimation of unknown parameters of the Gaussian Mixture Model (GMM) in Positron Emission Tomography (PET). A vast majority of PET imaging methods are based on reconstruction model that is defined by values on some pixel/voxel grid. Instead, we propose a continuous parametric GMM model. Usually, Expe...
Positron emission tomography (PET) is an important functional medical imaging technique often used in the evaluation of certain brain disorders, whose reconstruction problem is ill-posed. The vast majority of reconstruction methods in PET imaging, both iterative and deep learning, return a single estimate without quantifying the associated uncertai...
An image or volume of interest in positron emission tomography (PET) is reconstructed from gamma rays emitted from a radioactive tracer, which are then captured and used to estimate the tracer’s location. The image or volume of interest is reconstructed by estimating the pixel or voxel values on a grid determined by the scanner. Such an approach is...
This paper introduces a novel framework for single-pixel imaging via compressive sensing (CS) in shift-invariant (SI) spaces by exploiting the sparsity property of a wavelet representation. We reinterpret the acquisition procedure of a single-pixel camera as filtering of the observed signal with continuous-domain functions that lie in an SI subspac...
This paper introduces a novel framework and corresponding methods for sampling and reconstruction of sparse signals in shift-invariant (SI) spaces. We reinterpret the random demodulator, a system that acquires sparse bandlimited signals, as a system for the acquisition of linear combinations of the samples in the SI setting with the box function as...
Positron emission tomography (PET) is a noninvasive imaging modality. Analytical algorithms are faster and less demanding than iterative algorithms. Generally, iterative methods are mainly used for image reconstruction in PET due to the stochastic nature of electron-positron annihilation. Raytest ClearPET scanner is a small animal PET scanner. It t...
This paper examines the performance of principal-component-analysis (PCA) projections in compressive sensing (CS). Observed signals are assumed to follow a Gaussian distribution and have the asymptotic sparsity property in a wavelet transform domain. In order to exploit these signal priors, we propose multilevel subsampling of PCA projections in ad...
This paper introduces a novel framework for single-pixel imaging via compressive sensing (CS) in shift-invariant (SI) spaces by exploiting the sparsity property of a wavelet representation. We reinterpret the acquisition procedure of a single-pixel camera as filtering of the observed signal with continuous-domain functions that lie in an SI subspac...
This paper introduces a novel framework for single-pixel imaging via compressive sensing (CS) in shift-invariant (SI) spaces by exploiting the sparsity property of a wavelet representation. We reinterpret the acquisition procedure of a single-pixel camera as filtering of the observed signal with continuous-domain functions that lie in an SI subspac...
Electroencephalogram (EEG) signals are known to contain signatures of stimuli that induce brain activities. However, detecting these signatures to classify captured EEG waveforms is one of the most challenging tasks of EEG analysis. This paper proposes a novel time–frequency-based method for EEG analysis and characterization implemented in a comput...
We introduce a novel framework for acquisition of analog signals by combining compressive sensing (CS) and the shift-invariant (SI) reconstruction procedure. We reinterpret the random demodulator as a system that acquires a linear combination of the samples in the conventional SI setting with the box function as the sampling kernel. The SI samples...
This paper introduces a novel framework and corresponding methods for sampling and reconstruction of sparse signals in shift-invariant (SI) spaces. We reinterpret the random demodulator, a system that acquires sparse bandlimited signals, as a system for acquisition of linear combinations of the samples in the SI setting with the box function as the...
There are numerous papers analyzing the theoretical background of compressive sensing (CS), but a few practical implementations exist due to the realization complexity. In this paper, a realization of a system for CS of analog one-dimensional signals in a shift-invariant subspace is proposed. We use statistical compressive sensing that allows effic...
In contrast to conventional cameras which capture a 2D projection of a 3D scene by integrating the angular domain, light field cameras preserve the angular information of individual light rays by capturing a 4D light field of a scene. On the one hand, light field photography enables powerful post-capture capabilities such as refocusing, virtual ape...
In this paper, a dual imaging technique is used for high-precision reconstruction of an observed 3D scene. In contrast to stereo vision, dual imaging systems use a camera and a projector instead of a camera pair. We propose a multiresolution approach based on the sum-to-one transform, coupled with compressive sensing principles, for efficient estim...
This paper introduces a novel spline-like parametric model for an image representation obtained directly from compressive imaging (CI) measurements. As a representation basis we use Chebyshev polynomials. To avoid common problem of blocking artifacts in block-based reconstruction algorithms, a desired number of derivatives are equated on the block...
Compressed sensing (CS) is a technique for signal
sampling below the Nyquist rate, based on the assumption that
the signal is sparse in some transform domain. The acquired
signal is represented in a compressed form that is appropriate
for storage, transmission and further processing. In this paper,
use of the Chebyshev polynomials of the first kind...
This paper proposes a spline-like Chebyshev polynomial
image representation obtained by block-based compressed
sampling (CS) for image analysis and processing. Due to orthogonality and close relation with the discrete cosine transform,
Chebyshev polynomials have near-zero redundancy measure and
possess great compression properties. Consequently, th...
Abstract In this paper, the problem of detection of small signal-to-noise ratio (SNR) variations in noisy signals is addressed in order to provide an efficient and fast method for detection of faulty electroencephalogram (EEG) electrodes which can improve the interpretation of medical data. The method for slight SNR variation assessment, based on t...
An image or volume of interest in positron emission tomography (PET) is reconstructed from pairs of gamma rays emitted from a radioactive substance. Many image reconstruction methods are based on estimation of pixels or voxels on some predefined grid. Such an approach is usually associated with limited resolution of the reconstruction, high computa...
Compressive sensing is a technique for signal sampling below the Nyquist rate based on the assumption that the signal is sparse in some transform domain. The acquired signal is already in a compressed form and is appropriate for storage, transmission and processing. In this extended abstract, use of Chebyshev polynomials on intervals for efficient...
While numerous works analyze the theoretical background of compressive sensing (CS) and provide rich mathematical theory, few practical implementations exist and they mostly share the same disadvantage of being either too complex or too expensive to implement. As a result of the reported work, a simple measurement setup for CS using off-the-shelf c...
In this paper, L1 minimization refers to finding the minimum L1-norm solution to an overdetermined linear system y = X·p. The underdetermined variant of the same problem has recently received much attention, mainly due to the new compressive sensing theory that shows, under wide conditions, the minimum L1-norm solution is also the sparsest solution...
This paper presents our experiences from workshops with gifted primary school students (grades 2–4) especially in programming with robotics sets (Lego Mindstorms EV3) and other technology. As a part of extracurricular enriched program at the Center for Gifted Child Development in Zagreb, Croatia, we organized a number of robotics and ICT workshops....
This paper focuses on pattern matching in the DNA sequence. It was inspired by a previously reported method that proposes encoding both pattern and sequence using prime numbers. Although fast, the method is limited to rather small pattern lengths, due to computing precision problem. Our approach successfully deals with large patterns, due to our im...
We present a novel method for restoration of images of nanostructures obtained with a soft-ray microscope that uses a 46.9 nm soft x-ray laser microscope for illumination. To suppress the noise and to preserve the image sharpness, we develop a method based on pixel adaptive zero-order modeling of the observed object. Neighboring areas of each pixel...
Image sharpness assessment is a very important issue in image acquisition and processing. Novel approaches in no-reference image sharpness assessment methods are based on local phase coherence (LPC), rather than edge or frequency content analysis. It has been shown that the LPC based methods are closer to human observer assessments. In this paper,...
Compact representation of signals and images is a key for many applications. Compactness is often achieved through linear transforms with good energy concentration property. We present an adaptive wavelet filter bank with fixed number of vanishing moments, plus additional local adaptation. Proposed adaptation method is conducted at each sample acco...
We present advanced techniques for the restoration of images obtained by soft x-ray laser microscopy. We show two methods. One method is based on adaptive thresholding, while the other uses local Wiener filtering in the wavelet domain to achieve high noise gains. These wavelet based denoising techniques are improved using spatial noise modeling. Th...
In this paper, we present five different approaches of teaching 8-years-old children basic concepts of programming and fundamentals of computing. Using mechanical calculators, children learn some of the basic computer architecture and functionality concepts like the accumulator, counter and register shifting. The marble adding machine teaches binar...
Underperformance in higher frequency signal regions denoising is a common problem for many denoising methods. Wavelet transforms are, generally, less prone to the problem than the pure spatial or frequency domain transforms, but there is still much room for improvements. In this paper, we propose a point-wise adaptive wavelet transform for signal d...
Many microscopy images, or 3D depth maps can be represented using piecewise constant models. They usually contain noise due to sensor imperfectness. In this paper, an improved separable denoising method based on the relative intersection of confidence intervals rule is proposed. The method uses median averaging and is robust to outliers and differe...
In this paper, the relative intersection of confidence intervals (ICI) rule is used to adaptively determine window sizes around each observed point in purpose of denoising. The relative ICI rule defines neighbourhoods of similar statistical properties for every signal sample. If we calculate a mean value on each window, it corresponds to the zero-o...
Separation of different signal components, produced by one or more sources, is a problem encountered in many signal processing applications. This paper proposes a fully automatic undetermined blind source separation method, based on a peak detection and extraction technique from a signal time-frequency distribution (TFD). Information on the local n...
Classroom interactivity is today considered to be one of the most important preconditions for successful lecturing. It is also often considered to be the main drawback of learning from lecture captures. In this article, the issue of live lecture and lecture capture interactivity is addressed from the aspect of students' question posing. During seve...
Lowering the cumulative radiation dose to a patient undergoing fluoroscopic examination requires efficient denoising algorithms. We propose a method, which extensively utilizes temporal dimension in order to maximize denoising efficiency. A set of subsequent images is processed and two estimates of denoised images are calculated. One is based on a...
A time-frequency distribution provides many advantages in the analysis of multicomponent non-stationary signals. The simultaneous signal representation with respect to the time and frequency axis defines the signal amplitude, frequency, bandwidth, and the number of components at each time moment. The Rényi entropy, applied to a time-frequency distr...
Wavelet transforms found widespread application in signal denoising. Many adaptive algorithms were proposed to improve their performance, especially about edges in a signal. In this study, the authors propose a novel denoising method based on adaptive edge-preserving lifting scheme - intersection of confidence intervals-edge preserving lifting sche...
Besides many advantages of wavelet transform, it has several drawbacks, e.g. ringing, shift variance, aliasing and lack of directionality. Some of them can be eliminated by using wavelet packet transform, stationary wavelet transform, complex wavelet transform, adaptive directional lifting-based wavelet transform, or adaptive wavelet filter banks t...
Spectral analysis and wavelet analysis of successive flood waves on the basis of measured water levels help to understand hydrological processes and to improve hydrological modeling. In this paper, we compare Fourier transform, short time Fourier transform and continuous wavelet transforms to describe behavior of River Sava. Urban, agricultural and...
Sparse representation of signals is the key for many applications, such as denoising, compression, or compressive sensing. In this paper, we propose an original adaptive wavelet filter bank that, for a class of signals, provides better compaction of information. Previously reported 1D and 2D point-wise adaptive wavelets were based on minimization o...
Denoising is an important issue in signal processing. Noise, caused by sensors or by quantization effects during digitalization or compression, can significantly influence the processing results. Hence, removing the noise, or extracting the signal with minimal distortion is a valuable objective for many applications. In this paper, we propose a nov...
In this paper, an adaptive separable 2D wavelet transform is proposed. Wavelet transforms are widely used in signal and image processing due to its energy compaction property. Sparser representation corresponds to better performance in compression, denoising, compressive sensing, sparse com-ponent analysis and many other applications. The proposed...
In this paper, we propose novel adaptive wavelet filter bank structures based on the lifting scheme. The filter banks are nonseparable, based on quincunx sampling, with their properties being pixel-wise adapted according to the local image features. Despite being adaptive, the filter banks retain a desirable number of primal and dual vanishing mome...
The linear mixture model (LMM) has recently been used for multi-channel representation of a blurred image. This enables use of multivariate data analysis methods such as independent component analysis (ICA) to solve blind image deconvolution as an instantaneous blind source separation (BSS) requiring no a priori knowledge about the size and origin...
The recently proposed signal denoising method based on the relative intersection of confidence intervals (RICI) rule combined with local polynomial approximation is applied to image denoising, with images being transformed to one-dimensional signals. The obtained results, in the terms of peak signal-to-noise ratio (PSNR), are compared to the result...
In this paper we have analyzed the performance of the recently introduced LPA-RICI signal denoising method. The RICI method is an extension of the classical denoising method based on the intersection of confidence intervals (ICI) rule, whereby an additional criterion, the ratio of intersection of confidence intervals, has been included. The perform...
Sub-band decomposition independent component analysis (SDICA) assumes that wide-band source signals can be dependent but some of their sub-components are independent. Thus, it extends applicability of standard independent component analysis (ICA) through the relaxation of the independence assumption. In this paper, firstly, we introduce novel wavel...
An adaptive lifting scheme is proposed, in which the intersection of confidence intervals (ICI) rule is used to determine the wavelet support. The adaptation is performed on a point-by-point basis and the ICI rule is used to prevent the support from spanning across the edges in a signal, in which the edge is considered to be any sudden change in th...
Blind source separation (BSS) problem is commonly solved by means of independent component analysis (ICA) assuming statistically independent and non-Gaussian sources. The strict independence assumption can be relaxed to existence of subbands where signals are less dependent. In this paper, we use dual tree complex wavelets for the subband decomposi...
Wheezing often accompanies pulmonary pathologies and its detection is considered of great importance for the diagnosis and
management of respiratory diseases. Our aim was to develop a simple and robust algorithm for wheeze detection in respiratory
sound spectra to be used for long-term monitoring and early stage assessment of asthma episode in chil...
In this paper, we present the realization of an adaptive shift invariant wavelet transform defined on the quin-cunx grid. The wavelet transform relies on the lifting scheme which enables us to easily introduce the adapta-tion by splitting the predict stage into two parts. The first part of the predict stage is fixed and guarantees the number of van...
In this paper, we explore the use of nonseparable and adaptive wavelet decompositions for the purpose of image denoising. We apply the classical wavelet shrinkage methods on the wavelet coefficients obtained by using the adaptive wavelet transform defined on the quincunx grid. The wavelet transform is pixel-wise adaptive in all decomposition levels...
In this paper, a novel realization of two-dimensional nonseparable wavelet filter bank with adaptive filter parameters is proposed. Two-dimensional generalization of the previously presented 1-D scheme [4] is based on nonseparable quincunx decimation. 2-D filters are designed directly rather then obtained from 1-D filters using the pyramid scheme....
An efficient realization of a two-channel wavelet filter bank that
maps integers to integers with an adaptive number of zero moments is
presented. Filters with more zero moments result in a better
representation of the smooth parts of the analyzed signal, while fewer
zero moments are better for transients and singularities. The proposed
realization...
In this paper, we compare different adaptation criteria in the proposed two-channel wavelet filter bank with variable number of zero moments. Generally, filters with more zero moments are more appropriate for representing smooth parts of the analyzed signal, while shorter filters are better for transients and singularities. Depending on the criteri...
An efficient realization of a two-channel wavelet filter bank with
adaptive number of zero moments is proposed. The described time variant
wavelet filter bank is more suitable for analysis of non-stationary
signals then fixed banks. Filters with more zero moments result in a
better representation of smooth parts of the analyzed signal, while less
z...
In this paper, an efficient realization of the two-channel wavelet filter bank with adaptive filter parameters is proposed. Described time variant wavelet filter bank is more suitable for analysis of non-stationary signals then fixed banks. Basic convergence and regularity properties of the limit wavelet functions and scales are provided by fixed p...
In this paper, we compare different adaptation criterions of the proposed two dimensional wavelet filter bank with a variable number of zero moments. Two-dimensional generalization of the previously reported 1-D algorithm is based on nonseparable quincunx scheme. 2-D filters were designed directly, rather then obtained from 1-D filters using pyrami...