arXiv subjects

Nikita Moriakov

Publications and source records attributed to Nikita Moriakov.

27 records · Page 2Linked to original sources

arXiv2018

Deep Learning Framework for Digital Breast Tomosynthesis Reconstruction

Digital breast tomosynthesis is rapidly replacing digital mammography as the basic x-ray technique for evaluation of the breasts. However, the sparse sampling and limited angular range gives rise to different artifacts, which manufacturers try to solve in several ways. In this study we propose an extension of the Learned Primal-Dual algorithm for digital breast tomosynthesis. The Learned Primal-Dual algorithm is a deep neural network consisting of several `reconstruction blocks', which take in raw sinogram data as the initial input, perform a forward and a backward pass by taking projections and back-projections, and use a convolutional neural network to produce an intermediate reconstruction result which is then improved further by the successive reconstruction block. We extend the architecture by providing breast thickness measurements as a mask to the neural network and allow it to learn how to use this thickness mask. We have trained the algorithm on digital phantoms and the corresponding noise-free/noisy projections, and then tested the algorithm on digital phantoms for varying level of noise. Reconstruction performance of the algorithms was compared visually, using MSE loss and Structural Similarity Index. Results indicate that the proposed algorithm outperforms the baseline iterative reconstruction algorithm in terms of reconstruction quality for both breast edges and internal structures and is robust to noise.

physics.med-ph↗

arXiv2018

Vendor-independent soft tissue lesion detection using weakly supervised and unsupervised adversarial domain adaptation

Computer-aided detection aims to improve breast cancer screening programs by helping radiologists to evaluate digital mammography (DM) exams. DM exams are generated by devices from different vendors, with diverse characteristics between and even within vendors. Physical properties of these devices and postprocessing of the images can greatly influence the resulting mammogram. This results in the fact that a deep learning model trained on data from one vendor cannot readily be applied to data from another vendor. This paper investigates the use of tailored transfer learning methods based on adversarial learning to tackle this problem. We consider a database of DM exams (mostly bilateral and two views) generated by Hologic and Siemens vendors. We analyze two transfer learning settings: 1) unsupervised transfer, where Hologic data with soft lesion annotation at pixel level and Siemens unlabelled data are used to annotate images in the latter data; 2) weak supervised transfer, where exam level labels for images from the Siemens mammograph are available. We propose tailored variants of recent state-of-the-art methods for transfer learning which take into account the class imbalance and incorporate knowledge provided by the annotations at exam level. Results of experiments indicate the beneficial effect of transfer learning in both transfer settings. Notably, at 0.02 false positives per image, we achieve a sensitivity of 0.37, compared to 0.30 of a baseline with no transfer. Results indicate that using exam level annotations gives an additional increase in sensitivity.

cs.CV↗

arXiv2017

On systems with quasi-discrete spectrum

In this paper we re-examine the theory of systems with quasi-discrete spectrum initiated in the 1960's by Abramov, Hahn, and Parry. In the first part, we give a simpler proof of the Hahn--Parry theorem stating that each minimal topological system with quasi-discrete spectrum is isomorphic to a certain affine automorphism system on some compact Abelian group. Next, we show that a suitable application of Gelfand's theorem renders Abramov's theorem --- the analogue of the Hahn-Parry theorem for measure-preserving systems --- a straightforward corollary of the Hahn-Parry result. In the second part, independent of the first, we present a shortened proof of the fact that each factor of a totally ergodic system with quasi-discrete spectrum (a "QDS-system") has again quasi-discrete spectrum and that such systems have zero entropy. Moreover, we obtain a complete algebraic classification of the factors of a QDS-system. In the third part, we apply the results of the second to the (still open) question whether a Markov quasi-factor of a QDS-system is already a factor of it. We show that this is true when the system satisfies some algebraic constraint on the group of quasi-eigenvalues, which is satisfied, e.g., in the case of the skew shift.

math.DS↗

arXiv2017

On effective Birkhoff's ergodic theorem for computable actions of amenable groups

We introduce computable actions of computable groups and prove the following versions of effective Birkhoff's ergodic theorem. Let $Γ$ be a computable amenable group, then there always exists a canonically computable tempered two-sided Følner sequence $(F_n)_{n \geq 1}$ in $Γ$. For a computable, measure-preserving, ergodic action of $Γ$ on a Cantor space $\{0,1\}^{\mathbb N}$ endowed with a computable probability measure $μ$, it is shown that for every bounded lower semicomputable function $f$ on $\{0,1\}^{\mathbb N}$ and for every Martin-Löf random $ω\in \{0,1\}^{\mathbb N}$ the equality \[ \lim\limits_{n \to \infty} \frac{1}{|F_n|} \sum\limits_{g \in F_n} f(g \cdot ω) = \int\limits f d μ\] holds, where the averages are taken with respect to a canonically computable tempered two-sided Følner sequence $(F_n)_{n \geq 1}$. We also prove the same identity for all lower semicomputable $f$'s in the special case when $Γ$ is a computable group of polynomial growth and $F_n:=\mathrm{B}(n)$ is the Følner sequence of balls around the neutral element of $Γ$.

math.DS↗

arXiv2016

Hochman's upcrossing theorem for groups of polynomial growth

Consider a stochastic process $(S_{[a_i,b_i]})_{[a_i,b_i] \subset \mathbb{N}}$, which is indexed by the collection of all nonempty intervals $[a_i,b_i] \subset \mathbb{N}$ and which is stationary under translations of the intervals. It was shown by M. Hochman that, for any $k \geq 1$ and any interval $(α,β) \subset \mathbb{R}$, one can give an `almost-exponential' bound on the size of the set where the associated process $(S_{[1,n]})_{n \geq 1}$ has at least $k$ fluctuations over $(α,β)$. It was also noticed that a similar techniques can be applied in $\mathbb{Z}^d$ case. In this article we extend Hochman's upcrossing theorem to groups of polynomial growth.

math.DS↗

arXiv2016

Fluctuations of Ergodic Averages for Actions of Groups of Polynomial Growth

It was shown by S. Kalikow and B. Weiss that, given a measure-preserving action of $\mathbb{Z}^d$ on a probability space $X$ and a nonnegative measurable function $f$ on $X$, the probability that the sequence of ergodic averages $$ \frac 1 {(2k+1)^d} \sum\limits_{g \in [-k,\dots,k]^d} f(g \cdot x) $$ has at least $n$ fluctuations across an interval $(α,β)$ can be bounded from above by $c_1 c_2^n$ for some universal constants $c_1 \in \mathbb{R}$ and $c_2 \in (0,1)$, which depend only on $d,α,β$. The purpose of this article is to generalize this result to measure-preserving actions of groups of polynomial growth. As the main tool we develop a generalization of effective Vitali covering theorem for groups of polynomial growth.

math.DS↗

arXiv2015

Computable Følner monotilings and a theorem of Brudno II

A theorem of A.A. Brudno says that the Kolmogorov-Sinai entropy of a subshift X over $\mathbb{N}$ with respect to an ergodic measure $μ$ equals the asymptotic Kolmogorov complexity of almost every word $ω$ in X. The purpose of this article is to extend this result to subshifts over computable groups that admit computable regular symmetric Følner monotilings, which we introduce in this work. These monotilings are a special type of computable Følner monotilings, which we defined earlier in order to extend the initial results of Brudno. For every $d \in \mathbb{N}$, the groups $\mathbb{Z}^d$ and the groups of unipotent upper-triangular matrices of dimension $d+1$ with integer entries admit particularly nice computable regular symmetric Følner monotilings for which we can provide the required computing algorithms `explicitly'.

math.DS↗

arXiv2015

Categories of measurement functors. Entropy of discrete amenable group representations on abstract categories. Entropy as a bifunctor into $[0,\infty]$

The main purpose of this article is to provide a common generalization of the notions of a topological and Kolmogorov-Sinai entropy for arbitrary representations of discrete amenable groups on objects of (abstract) categories. This is performed by introducing the notion of a measurement functor from the category of representations of a fixed amenable group $Γ$ on objects of an abstract category C to the category of representations of $Γ$ on distributive lattices with localization. We develop the entropy theory of representations of $Γ$ on these lattices, and then define the entropy of a representation of $Γ$ on objects of the category C with respect to a given measurement functor. For a fixed measurement functor, this entropy decreases along arrows of the category of representations. For a fixed category, entropies defined via different measurement functors decrease pointwise along natural transformations of measurement functors. We conclude that entropy is a bifunctor to the poset of extended positive reals. As an application of the theory, we show that both topological and Kolmogorov-Sinai entropies are instances of entropies arising from certain measurement functors.

math.DS↗

arXiv2015

Computable Følner monotilings and a theorem of Brudno I

The purpose of this article is to extend the earliest results of A.A. Brudno, connecting topological entropy of a subshift X over $\mathbb{N}$ to the Kolmogorov complexity of words in X, to subshifts over computable groups that posses computable Følner monotilings, which we introduce in this work. The classical examples of such groups are the groups $\mathbb{Z}^d$ and the groups of upper-triangular matrices with integer entries. Following the work of B. Weiss we show that the class of such groups is closed under group extensions.

math.DS↗