This study examines the analysis of biomedical signals using the Fourier transform within short-time windows. The imposition of the constant-overlap-add (COLA) constraint on these window functions ensures that the sum of windowed segments faithfully reconstructs the original signal. This work introduces an innovative methodology for designing generalized COLA windows that accommodate any given window function. Furthermore, we address the preservation of signal energy through the orthogonalization of windowed signals during analysis. Our investigation involves the application of the proposed Gaussian COLA windows-based short-time Fourier transform (STFT) and short-time discrete cosine transform (STDCT) in the time-frequency analysis of biomedical signals. Experimental results are presented to illustrate the effectiveness of the proposed method in achieving high-resolution time-frequency representation (TFR), considering both synthetic and real-life data, including electroencephalogram (EEG) signals, heart sounds and cough sounds. Furthermore, these results demonstrate the utility of proposed scheme in a practical healthcare context.

Polysomnography (PSG)-based accurate sleep staging is essential to monitor sleep quality and sleep-related disorders. Despite previous attempts for improving the performance of automatic sleep staging, there are certain limitations: 1) neglecting synchronization patterns in their time-frequency (TF) domain, 2) not utilizing both local and global features within sleep epochs, and 3) neglecting correlation patterns for tracking transitions between sleep stages. To address them, we propose a novel framework based on the polynomial chirplet transform-derived characteristic response vector (PCT-CRV) for the assessment of sleep stages. In this work, we perform the time-domain PCT (TPCT) and frequency-domain PCT (FPCT) to enhance the TF representation of nonstationary PSG signals. From these PCT representations, we construct correlation matrices across their frequency bins within short-time windows to obtain characteristic response vectors (CRVs), which are the sums of eigenvectors, weighted by their corresponding eigenvalues. Subsequently, a comprehensive set of local and global features is derived from PCT-CRVs, which is subjected to various machine learning-based classifiers. Our PCT-CRV excels on three datasets, surpassing existing methods, and outperforming wavelet-based and synchrosqueezed-based CRV methods. Furthermore, to track transitions of sleep stages, we form sub-band PCT-CRVs using eigenvectors with maximum information, depending upon the physics of our problem. We hypothesize that sleep stages are characterized by specific correlation profiles, within different frequency bins. Hence, sub-band PCT-CRVs corresponding to the dominant eigenvectors, would detect transition of sleep stages across all epochs. All these results highlight the efficacy of our method in tracking sleep stage transitions and improving their classification performance.

In many real time scenarios, it becomes necessary to compare complex networks. Graph distances measure the degree of similarity between any two networks. We conjecture that construction of the edge weight matrix of any network should consider the underlying physics of the problem. In addition to that, the selection of eigenvectors chosen for analysis also play an important role in comparing any two networks. In this paper, we explore the most naturally formed networks in various real time applications, such as tracking the transitions of brain states and real time seizure onset detection, and propose a graph distance measure based on the spectral characteristics of the edge weight matrix. We have conducted several experiments to show the efficacy of the proposed graph distance measure. It has an application in comparing any two brain networks while studying brain dynamics. Our results clearly show that the proposed graph distance outperforms the existing graph distances

Background The Graph theory provides the platform that could be used to model complex brain networks mathematically, and it could play a significant role in the diagnosis of various neurodegenerative diseases such as Alzheimer’s. Purpose The main aim of our study is to perform a comparative analysis in terms of various graph theoretic measures of structural brain networks. In particular, the paper evaluates graph theoretical measures by first forming graphs using magnetic resonance imaging (MRI) data. Method In this paper, we study and evaluate graph theoretical measures using MRI data, namely characteristic path length, global efficiency, strength, and clustering coefficient, in a cohort of normal controls ( N = 30), a cohort of mild cognitive impairment (MCI) ( N = 30), and a cohort of Alzheimer’s disease (AD) ( N = 30). In our work, MRI data is preprocessed and cortical thickness is extracted for each brain region. The connectivity matrix is obtained, and thus a graph is formed. We have also performed receiver operating characteristic (ROC) and area under the ROC analyses of all graph theoretical measures to better elucidate and validate the results. Results It is observed that these measures may be used to differentiate Alzheimer’s from normal. In our study, we observed that a very random and disrupted network is obtained in the case of Alzheimer’s in comparison with the normal and MCI cases. The other observations in terms of graph theoretic measures are an increase in characteristic path length, a decrease in global efficiency, a decrease in strength, and a reduction in values of the clustering coefficient in the case of Alzheimer’s. Conclusion The findings suggest that graph theoretical measures and alterations in network topology could be used as quantitative biomarkers of AD.

This paper presents a unified framework for linear scale invariant signals, systems, and transforms from a system theoretic perspective. The work is the scale counterpart of the theory related to linear shift invariant systems and transforms. Similar to Fourier and Laplace transforms that are used to study linear shift or time invariant systems, Mellin transform is used to study scale invariant systems. However, unlike the shift invariant theory, the theory related to scale invariant systems and transforms has so far not been presented with a unified approach. In this work, we present this theory from signal processing viewpoint, where we present the development of scale invariant transform as a systematic progression from scale series for scale periodic signals to scale invariant transform for scale aperiodic signals. We also present a few examples to illustrate the utility of the presented theory.

Fourier theory is a popular tool for analyzing various signals and interpreting their spectral contents. It finds applications in a wide variety of subject areas. However, some of the popular signals, such as sinusoidal signals, Dirac delta, signum, and unit step, fail to have a convergent Fourier representation (FR) in the conventional sense. Hence, it becomes imperative to utilize the distribution theory to understand and build a suitable representation for these signals. The signal processing and communication engineering literature does not explain these concepts clearly. As a result, many of the concepts of FR for signals that do not conform to the conventional derivations remain obscure to researchers. We attempt to bridge this gap and provide a comprehensive explanation regarding the existence of FR. Further, we have proposed a new linear space of Gauss--Schwartz (GS) functions and corresponding tempered superexponential (TSE) distributions. It is shown that the Fourier transform (FT) is an isomorphism on the GS space of test functions and hence by duality is an isomorphism on TSE distributions. The space GS is smallest in the sense that its dual space, a set of TSE distributions, is the largest linear space over which FT can be defined by duality.

This study introduces a novel probabilistic pooling convolutional neural network (PP-CNN) classifier designed to enhance image classification. The PP-CNN integrates probabilistic outputs from three distinct architectures utilizing MaxPooling, MinPooling, and MaxMinPooling layers. By averaging these probabilities, the model achieves improved accuracy compared to individual models. Notably, the proposed CNN model employs Positive ReLU activation with MaxPooling, Negative ReLU activation with MinPooling, and both Positive and Negative ReLU activations with MaxMinPooling. This strategy ensures the retention of both positive and negative relevant features, enhancing the classification performance by capturing a broader range of critical information. The proposed model has been comprehensively evaluated for its generalizability on four diverse datasets: CIFAR-10, CIFAR-100, CT scan, and X-ray images. Experimental results demonstrate a consistent improvement in classification accuracy across all datasets, highlighting the versatility and effectiveness of the proposed model. The proposed model applies to various image classification tasks, specifically illustrating its utility by detecting COVID-19 from medical images. This work presents the design, implementation, and performance evaluation of the proposed model, underscoring its potential to significantly improve image classification and diagnostic accuracy in medical imaging applications.

Several real-world signals exhibit semi-periodicity in that the period of repetition varies from pulse to pulse about a mean value instead of being constant. Some examples, including among others, are ECG signals, voiced phonemes in speech, carrier jitter in communication etc. In order to model/generate such signals, one can pass a train of discrete-time delta functions, having zeros between two ones in a semi-periodic manner, through an LTI system with the impulse response matched to the pulse. Strictly speaking, the number of zeros between two ones should be a random variable, with the mean value being an average period of repetition. As a first step towards this objective, we propose a time-varying up-sampling rate (TVUSR-Q) structure, where Q up-samplings, namely up arrow(L1+1),& ctdot;,up arrow(LQ+1) are introduced periodically. We demonstrate that the proposed TVUSR-Q , followed by the LTI system, results in the DT-LTI system/ DT-TVUSR-Q system under distinct up-sampling rate conditions. Since modeling of any real-life signal mentioned earlier would be effected by passing a stochastic input through such a system, we investigate the spectral properties of the outputs under various input conditions. We demonstrate the proposed structure's utility by synthesizing ECG signals. In order to demonstrate the utility of the proposed structure we take a segment of ECG and, after extracting some required information from it, synthesize the same using the proposed DT-TVUSR-15 system. Simulation findings validate the proposed theory.

Mathematics is the mother of all the sciences, engineering and technology, and a normed division algebra of all finite dimensions is the mathematical holy grail. In search of a real three-dimensional, normed, associative, division algebra, Hamilton discovered quaternions that form a non-commutative division algebra of quadruples. Later works showed that there are only four real division algebras with 1, 2, 4, and 8 dimensions. This work overcomes this limitation and introduces generalized hypercomplex numbers of all dimensions that are extensions of the traditional complex numbers. The space of these numbers forms non-distributive normed division algebra that is extendable to all finite dimensions. To obtain these extensions, we defined a unified multiplication, designated as scaling and rotative multiplication, fully compatible with the existing multiplication. Therefore, these numbers and the corresponding algebras reduce to distributive normed algebras for dimensions 1 and 2. Thus, this work presents a generalization of $\mathbb{C}$ in higher dimensions along with interesting insights into the geometry of the vectors in the corresponding spaces.

Convolutional neural networks (CNNs) have become deeper and wider over time. However due to low computational power, mobile devices or embedded systems cannot use very deep models. Filter pruning solves this by eliminating redundant filters. Pruning can be performed in a feature dependent or independent manner. Feature dependent methods require extensive time to determine the filter importance as these methods require generation and processing of feature maps for each example. Additionally, in iterative pruning, filter importance is computed several times based on the current state. This increases algorithm execution time further. However, existing feature independent methods are fast, but they perform poor as they compute importance using only current layer filter weights. However, our analysis suggests that both the current and succeeding layer filters are crucial to determine filter importance. We propose 'Filter Pruning by Successive Layers analysis' (FPSL), a novel feature independent algorithm, that considers the effect of pruning a filter on the generation of feature maps for the first time. Moreover, FPSL does not require layer-wise retraining, rigorous hyperparameter search for fine-tuning, or human intervention to set the pruning percentage per layer. These make FPSL extremely fast, efficient, and adaptive. Thus it follows iterative pruning and retraining. FPSL outperforms the state-of-the-art (SOTA) methods on extensive experiments with different datasets (CIFAR, ImageNet) and architectures (VGG, ResNet, MobileNet). It decreases the computational burden of VGG16 by half but improves CIFAR10 and CIFAR100 accuracy. Even for ImageNet, FPSL reduces 42.7% floating point operations (FLOPs) while maintaining top-1 accuracy for ResNet50.

The clinical applications of EEG Source Localization are seen in the analysis of epilepsy, schizophrenia, Parkinson, stress, and tumor. This paper proposes a novel brain source localization method using a multiway Multivariate Fourier Decomposition Method (MFDM) based technique. Firstly, a multiway array (tensor) is formed using MFDM, a novel way of forming a tensor from EEG signals. Then, this tensor is decomposed into various independent components using Canonical Polyadic Decomposition (CPD). Each independent component is used to reconstruct separate EEG signals corresponding to every independent source. Lastly, localization techniques like SPICE and LIKES are used to obtain the source locations. The results are compared with traditional methods like MNE, sLORETA, LASSO, and Space Time Frequency (STF) based tensor decomposition method. Further, real EEG signals during an arithmetic task are used to support and verify the proposed method in real application.

For the past few decades source localization, based on EEG modality, has been a very active area of research. EEG signal provides temporal resolution in millisecond range that can capture rapidly changing patterns of brain activity but it has a low spatial resolution as compared to techniques like fMRI, PET, CT scan, etc. So, one of the motives of this research is to improve the spatial resolution of the EEG signal. Many successful attempts have been made to localise the active neural sources using EEG signals with the introduction of techniques like MNE, LORETA, sLORETA, FOCUSS, etc. But these techniques require a large number of electrodes for correct localization of a few sources. This paper aims at providing a new method for the localization of EEG sources with a fewer electrode. This is achieved by exploiting the second-order statistics to enhance the aperture and solve the EEG localization problem. The comparison of the proposed method with the state-of-the-art methods is done by observing the localization error with variation in SNR, number of snapshots (time samples), number of active sources, and number of electrodes. The results show that the proposed method can detect a greater number of sources with fewer electrodes and with higher accuracy as compared to methods available in the literature. Real -time EEG signal during an arithmetic task is considered and the proposed algorithm clearly shows a sparse activity in the frontal region.

Empirical mode decomposition, better known by its acronym EMD, has developed into a scale-based modal decomposition technique that is increasingly scale-based as well as adaptive, versatile, and multipurpose. The EMD algorithm’s ability to detect both the upper and lower envelopes is undoubtedly its most valuable feature. The determination of the sizes of the envelopes comes with a significant amount of additional computational work. In recent years, several different algorithms have been suggested as potential improvements to the EMD method that would make it faster and more effective. The purpose of this research is to present a picture of the development of empirical mode decomposition approaches that is both comprehensive and easy to understand.

A convolutional layer of a traditional convolutional neural network (CNN) does not ensure the extraction of complementary bands of the input data. Thus a significant amount of redundancy is observed among different convolutional filters. Here, we propose a novel architecture design framework called ‘Multi-band CNN’ to efficiently utilize model parameters in a CNN. The framework generates four filters from a single filter by varying their frequency responses, extracting four complementary bands of the input data without increasing the parameter count. This leads to higher parameter utilization and results in a compact network with reduction in trainable parameter count but with close to the same accuracy as the base model. We perform experiments using residual networks (ResNet-32, ResNet-56, and ResNet-110) on datasets like CIFAR-10 and CIFAR-100. Our results show improved classification accuracy for CIFAR-10 when introducing a multi-band layer in the first convolutional layer, while there is no significant drop in accuracy for CIFAR-100. The performance is better when replacing the first convolutional layer instead of the last one, indicating that low-level features generated by sub-band filtering are more beneficial to the network than high-level features provided by filter banks at the final layer. The proposed Multi-band CNN framework offers a potential solution for reducing the number of filters required to train and the computational complexity of generating feature maps in CNNs, while maintaining or even improving classification accuracy.

The behavioral tagging (BT) hypothesis provides crucial insights into the mechanism of long-term memory (LTM) consolidation. Novelty exposure in BT is a decisive step in activating the molecular machinery of memory formation. Several studies have validated BT using different neurobehavioral tasks; however, the novelty given in all studies is open field (OF) exploration. Environment enrichment (EE) is another key experimental paradigm to explore the fundamentals of brain functioning. Recently, several studies have highlighted the importance of EE in enhancing cognition, LTM, and synaptic plasticity. Hence, in the present study, we investigated the effects of different types of novelty on LTM consolidation and plasticity-related protein (PRP) synthesis using the BT phenomenon. Novel object recognition (NOR) was used as the learning task for rodents (male Wistar rats), while OF and EE were two types of novel experiences provided to the rodents. Our results indicated that EE exposure efficiently leads to LTM consolidation through the BT phenomenon. In addition, EE exposure significantly enhances protein kinase Mζ (PKMζ) synthesis in the hippocampus region of the rat brain. However, the OF exposure did not lead to significant PKMζ expression. Further, our results did not find alterations in BDNF expression after EE and OF exposure in the hippocampus. Hence, it is concluded that different types of novelty mediate the BT phenomenon up to the same extent at the behavioral level. However, the implications of different novelties may differ at molecular levels.

An accurate mathematical ECG model helps comprehend the heart’s workings, which in turn helps identify various heart-related abnormalities. A typical ECG waveform consists of recurrent QRS complexes at almost regular intervals. In the most general scenario, the amplitude, the period after which it repeats, and the shape of the QRS complex may change from pulse to pulse. This paper proposes a mathematical model for the ECG signals capable of capturing these features. Since statistical analysis of the the general model is more complex, we make certain assumptions to make the problem analytically tractable. With these assumptions at our disposal, we provide closed-form expressions for time-varying covariance/spectra of the process generated by the proposed model. In order to demonstrate the approximation capability of the model, that is, the ability to model ECG signals, we synthesize ECG signals for different health states by first extracting the QRS complex of that health state and using the mean time period also extracted from the realization of the same health state. We find that the degree of non-stationarity of the real-world ECG and the one generated by the model match closely. In reality, the signal for each state appears to be a close match. Based on our experimental findings, we observe that the measure of the degree of non-stationarity interestingly falls in different ranges, depending upon the type of heart-related abnormality. This observation makes our conjecture that this measure can serve as a biomarker for various related abnormalities.

How humans recognise faces and objects effortlessly, has become a great point of interest. To understand the underlying process, one of the approaches is to study the facial features, in particular ordinal contrast relations around the eye region, which plays a crucial role in face recognition and perception. Recently the graph-theoretic approaches to electroencephalogram (EEG) analysis are found to be effective in understating the underlying process of human brain while performing various tasks. We have explored this approach in face recognition and perception to know the importance of contrast features around the eye region. We studied functional brain networks, formed using EEG responses, corresponding to four types of visual stimuli with varying contrast relationships: Positive faces, chimeric faces (photo-negated faces, preserving the polarity of contrast relationships around eyes), photo-negated faces and only eyes. We observed the variations in brain networks of each type of stimuli by finding the distribution of graph distances across brain networks of all subjects. Moreover, our statistical analysis shows that positive and chimeric faces are equally easy to recognise in contrast to difficult recognition of negative faces and only eyes.

In standard neural network training, the gradients in the backward pass are determined by the forward pass. As a result, the two stages are coupled. This is how most neural networks are trained currently. However, gradient modification in the backward pass has seldom been studied in the literature. In this paper we explore decoupled training, where we alter the gradients in the backward pass. We propose a simple yet powerful method called PowerGrad Transform, that alters the gradients before the weight update in the backward pass and significantly enhances the predictive performance of the neural network. PowerGrad Transform trains the network to arrive at a better optima at convergence. It is computationally extremely efficient, virtually adding no additional cost to either memory or compute, but results in improved final accuracies on both the training and test sets. PowerGrad Transform is easy to integrate into existing training routines, requiring just a few lines of code. PowerGrad Transform accelerates training and makes it possible for the network to better fit the training data. With decoupled training, PowerGrad Transform improves baseline accuracies for ResNet-50 by 0.73 and by more than 1.0 classification task.

Many methods have been proposed in the literature for diagnosis of Alzheimer's disease (AD) in the early stages, among which the graph-based methods have been more popular, because of their capability to utilize the relational information among different brain regions. Here, we design a novel graph signal processing based integrated AD detection model using multimodal deep learning that simultaneously utilizes both the static and the dynamic brain connectivity based features extracted from resting-state fMRI (rs-fMRI) data to detect AD in the early stages. First, our earlier proposed state-space model (SSM) based graph connectivity dynamics characterization method is used to design a modified dynamic connectivity based AD detection model. After verifying its utility, this dynamic connectivity based model is integrated with our earlier designed static connectivity based AD detection model using the intermediate level integration approach of the multimodal deep learning, to construct our proposed integrated AD detection model. To verify the effectiveness of the designed AD detection models, the models are applied on the rs-fMRI data, extracted from ADNI dataset. Superior performance of our proposed AD diagnosis method corroborates its utility in AD detection application.