Probability Distributions.- Linear Models for Regression.- Linear Models for Classification.- Neural Networks.- Kernel Methods.- Sparse Kernel Machines.- Graphical Models.- Mixture Models and EM.- Approximate Inference.- Sampling Methods.- Continuous Latent Variables.- Sequential Data.- Combining Models.

Pattern Recognition and Machine Learning

Data Mining - Concepts and Techniques.

Compressive Sensing (CS) is a new sensing modality, which compresses the signal being acquired at the time of sensing. Signals can have sparse or compressible representation either in original domain or in some transform domain. Relying on the sparsity of the signals, CS allows us to sample the signal at a rate much below the Nyquist sampling rate. Also, the varied reconstruction algorithms of CS can faithfully reconstruct the original signal back from fewer compressive measurements. This fact has stimulated research interest toward the use of CS in several fields, such as magnetic resonance imaging, high-speed video acquisition, and ultrawideband communication. This paper reviews the basic theoretical concepts underlying CS. To bridge the gap between theory and practicality of CS, different CS acquisition strategies and reconstruction approaches are elaborated systematically in this paper. The major application areas where CS is currently being used are reviewed here. This paper also highlights some of the challenges and research directions in this field.

A Systematic Review of Compressive Sensing: Concepts, Implementations and Applications

Most image encryption algorithms based on low-dimensional chaos systems bear security risks and suffer encryption data expansion when adopting nonlinear transformation directly. To overcome these weaknesses and reduce the possible transmission burden, an efficient image compression–encryption scheme based on hyper-chaotic system and 2D compressive sensing is proposed. The original image is measured by the measurement matrices in two directions to achieve compression and encryption simultaneously, and then the resulting image is re-encrypted by the cycle shift operation controlled by a hyper-chaotic system. Cycle shift operation can change the values of the pixels efficiently. The proposed cryptosystem decreases the volume of data to be transmitted and simplifies the keys distribution simultaneously as a nonlinear encryption system. Simulation results verify the validity and the reliability of the proposed algorithm with acceptable compression and security performance.

Image compression–encryption scheme based on hyper-chaotic system and 2D compressive sensing

The existing ways to encrypt images based on compressive sensing usually treat the whole measurement matrix as the key, which renders the key too large to distribute and memorize or store. To solve this problem, a new image compression–encryption hybrid algorithm is proposed to realize compression and encryption simultaneously, where the key is easily distributed, stored or memorized. The input image is divided into 4 blocks to compress and encrypt, then the pixels of the two adjacent blocks are exchanged randomly by random matrices. The measurement matrices in compressive sensing are constructed by utilizing the circulant matrices and controlling the original row vectors of the circulant matrices with logistic map. And the random matrices used in random pixel exchanging are bound with the measurement matrices. Simulation results verify the effectiveness, security of the proposed algorithm and the acceptable compression performance.

Novel image compression–encryption hybrid algorithm based on key-controlled measurement matrix in compressive sensing

Due to the presence of diverse and disparate patterns, the segmentation of natural images endures crucial as well as a challenging problem in image analysis algorithms The proposed method addresses image segmentation as a subspace clustering of image feature vectors Initially, an image is partitioned into superpixels and further, a feature data matrix is computed using the Local Spectral Histogram (LSH) features from individual superpixels A single-stage optimization model is formulated which incorporates better subspace selection, excellent grouping effect and simultaneous noise robustness for the uncorrelated, correlated and corrupted data by the conjunctive venture of l 1 , l 2 and l 2,1 norm minimization The proposed model is solved using Augmented Lagrangian technique We compared the proposed method with state-of-the-art methods and the results demonstrate the improved performance of our proposed model over the existing counterparts

A Joint Sparse and Correlation Induced Subspace Clustering Method for Segmentation of Natural Images

Incomplete observations in the data are always troublesome to data clustering algorithms. In fact, most of the well-received techniques are not designed to encounter such imperative scenarios. Hence, clustering of images under incomplete samples is an inquisitive yet unaddressed area of research. Therefore, the aim of this article is to design a single-stage optimization procedure for clustering as well as simultaneous reconstruction of images without breaking the intrinsic spatial structure. The method employs the self-expressiveness property of submodules, and images are stacked as the lateral slices of a three-dimensional tensor. The proposed optimization method is designed to extract a sparse t-linear combination tensor with low multirank constraint, consisting of a unique set of linear coefficients in the form of mode-3 fibers and the spectral clustering is performed on these fibers. Simultaneously, the recovery of lost samples is accomplished by twisting the entire lateral slices of the data tensor and applying a low-rank approximation on each slice. The prominence of the proposed method lies in the simultaneous execution of data clustering and reconstruction of incomplete observations in a single step. Experimental results reveal the excellence of the proposed method over state-of-the-art clustering algorithms in the context of incomplete imaging data.

A Unified Tensor Framework for Clustering and Simultaneous Reconstruction of Incomplete Imaging Data

Clustering of multidimensional data has found applications in different fields. Among the existing methods, spectral clustering techniques have gained great attention due to its superior performance and low computational complexity. The clustering accuracy in spectral clustering methods depends on the affinity matrix learned from the data. Traditional clustering techniques fail to capture the spatial aspects of the images since they vectorize the images. In the proposed approach, the images are stacked as lateral slices of a three-way tensor. Further, a two-way optimization problem is formulated to extract a sparse t-linear combination tensor. Weighted Tensor Nuclear Norm (WTNN) is introduced in the optimization problem for enhancing tensor sparsity, and thereby improving the clustering accuracy. The performance of the proposed method is evaluated on three popular datasets. The evaluation shows that the proposed method has superior performance over the state-of-the-art methods.

A Two-Way Optimization Framework for Clustering of Images using Weighted Tensor Nuclear Norm Approximation

In this paper, we focus on denoising of additively corrupted volumetric magnetic resonance (MR) images for improved clinical diagnosis and further processing. We have considered three dimensional MR images as third-order tensors. MR image denoising is solved as a low-rank tensor approximation problem, where the non-local similarity and correlation existing in volumetric MR images are exploited. The corrupted images are divided into 3D patches and similar patches form a group matrix. The group matrices exhibit low-rank property and is decomposed with tensor singular value decomposition (t-SVD) technique, and reweighted iterative thresholding is performed on core coefficients for removing the noise. The proposed method is compared with the state-of-the-art methods and has shown improved performance.

Denoising of Volumetric MR Image Using Low-Rank Approximation on Tensor SVD Framework

Insufficient illumination causes poor discernibility of visuals captured under low light environment. Often, computer vision algorithms designed to process visuals taken under normal light struggle to handle visuals with low visibility. The present work proposes a low rank approximation (LRA) based optimization model in producing the brightness enhanced version from the input low light image. The work adopts $$l_{1/2}$$
 nuclear norm and sparsity minimization combined with total variation (TV) regularization to estimate the illumination map required to reconstruct the clear image. The $$l_{1/2}$$
 nuclear norm serves primarily for smoothing the coarse illumination map, while TV regularization helps to preserve the prominent edge information. Additionally, $$l_{1/2}$$
 regularization aids to retain the sparse structural details. The intelligence of the proposed method is bounded in the efficient formulation of a unified optimization model for the estimation of illumination map with low rank and sparsity concepts which is never reported in the direction of low light image enhancement. Furthermore, extensive experiments confirm that the proposed method outperforms the current state of art methods in low light image enhancement.

Sudhish N. George

Papers

A Joint Sparse and Correlation Induced Subspace Clustering Method for Segmentation of Natural Images

A Unified Tensor Framework for Clustering and Simultaneous Reconstruction of Incomplete Imaging Data

A Two-Way Optimization Framework for Clustering of Images using Weighted Tensor Nuclear Norm Approximation

Denoising of Volumetric MR Image Using Low-Rank Approximation on Tensor SVD Framework

$$l_{1/2}$$ regularized joint low rank and sparse recovery technique for illumination map estimation in low light image enhancement