Set Of Sparse Coefficients Research Articles

GJTD-LR: A Trainable Grouped Joint Tensor Dictionary With Low-Rank Prior for Single Hyperspectral Image Super-Resolution

Reconstructing a high-resolution hyperspectral image (HR-HSI) by using a single low-resolution hyperspectral image (LR-HSI) is a significant technique for increasing the spatial resolution of HSIs and overcoming the physical limitation of the HSI sensor. Most single HSI super-resolution methods have achieved great success recently. However, owning to the difficulty of acquiring an HSI, the available training samples are relatively few, which will inevitably lead to relatively low performance. To address this issue, in the paper, we propose a novel single HSI super-resolution method by combining a trainable grouped joint tensor dictionary and a low-rank prior (GJTD-LR). First, we design a trainable grouped joint tensor dictionary, which can build an accurate mapping relationship between training HR-HSIs and their corresponding LR-HSIs with relatively few training samples. To be specific, the training HR-HSI and LR-HSI pairs are decomposed into a joint tensor dictionary and a set of sparse coefficients by using tensor-tensor product to fully preserve the spectral correlation. In addition, we apply a grouped strategy to divide the training images into several groups and learn a compact joint dictionary for each group. Second, a tensor low-rank model is forced into the reconstruction model to further capture the spatial correlation. At last, GJTD-LR is optimized by employing alternating direction method of multipliers (ADMM), soft threshold algorithm, singular value decomposition and fourier domain transform. The experimental results on both remote sensed HSIs and indoor HSIs show the superiority of GJTD-LR to some other traditional and advanced single HSI super-resolution methods.

Remote Sensing Image Super-Resolution Using Sparse Representation and Coupled Sparse Autoencoder

Remote sensing image super-resolution (SR) refers to a technique improving the spatial resolution, which in turn benefits to the subsequent image interpretation, e.g., target recognition, classification, and change detection. In popular sparse representation-based methods, due to the complex imaging conditions and unknown degradation process, the sparse coefficients of low-resolution (LR) observed images are hardly consistent with the real high-resolution (HR) counterparts, which leads to unsatisfactory SR results. To address this problem, a novel coupled sparse autoencoder (CSAE) is proposed in this paper to effectively learn the mapping relation between the LR and HR images. Specifically, the LR and HR images are first represented by a set of sparse coefficients, and then, a CSAE is established to learn the mapping relation between them. Since the proposed method leverages the feature representation ability of both sparse decomposition and CSAE, the mapping relation between the LR and HR images can be accurately obtained. Experimentally, the proposed method is compared with several state-of-the-art image SR methods on three real-world remote sensing image datasets with different spatial resolutions. The extensive experimental results demonstrate that the proposed method has gained solid improvements in terms of average peak signal-to-noise ratio and structural similarity measurement on all of the three datasets. Moreover, results also show that with larger upscaling factors, the proposed method achieves more prominent performance than the other competitive methods.

Adaptive RD Optimal Sparse Coding With Quantization for Image Compression

In image and video compression for many multimedia applications, an image/frame is divided into component blocks or patches and is then encoded using some type of transform. Traditional transforms use a complete dictionary of basis functions. A recent technique of growing interest is signal approximation using a linear combination of basis functions from an overcomplete dictionary. The result is a sparse set of coefficients that can represent the original signal and is called sparse coding. This is an NP-hard problem. Orthogonal matching pursuit is a greedy algorithm that is effectively used to address this problem. Keeping in mind the iterative nature of this algorithm, in a recent conference publication, we proposed a rate distortion optimization (RDO) method to select the best sparse representation among iterations up to a target sparsity level. In this paper, we expand the work and consider an adaptive coding scheme that takes advantage of both discrete cosine transform (DCT) and sparse coding. This scheme shows a better performance over plain DCT or sparse coding schemes. We further propose a scheme to increase the coding efficiency of sparse coding by quantizing the sparse coefficients. We investigate an RDO method to select the value of the quantization parameter from a range, balancing distortion, and bit rate. Based on experimental results, we provide a comparison between conventional DCT-based coding, sparse coding scheme, our mixed coding scheme, and the proposed method that includes quantization of the sparse coefficients.

In-band sub-pixel registration of wavelet-encoded images from sparse coefficients

Sub-pixel registration is a crucial step for applications such as super-resolution in remote sensing, motion compensation in magnetic resonance imaging, and nondestructive testing in manufacturing, to name a few. Recently, these technologies have been trending towards wavelet-encoded imaging and sparse/compressive sensing. The former plays a crucial role in reducing imaging artifacts, while the latter significantly increases the acquisition speed. In view of these new emerging needs for applications of wavelet-encoded imaging, we propose a sub-pixel registration method that can achieve direct wavelet domain registration from a sparse set of coefficients. We make the following contributions: (i) We devise a method of decoupling scale, rotation, and translation parameters in the Haar wavelet domain, (ii) we derive explicit mathematical expressions that define in-band sub-pixel registration in terms of wavelet coefficients, (iii) using the derived expressions, we propose an approach to achieve in-band sub-pixel registration, avoiding back and forth transformations. (iv) Our solution remains highly accurate even when a sparse set of coefficients are used, which is due to localization of signals in a sparse set of wavelet coefficients. We demonstrate the accuracy of our method, and show that it outperforms the state of the art on simulated and real data, even when the data are sparse.

High-speed all-optical Haar wavelet transform for real-time image compression.

We present a high-speed single pixel flow imager based on an all-optical Haar wavelet transform of moving objects. Spectrally-encoded wavelet measurement patterns are produced by chirp processing of broad-bandwidth mode-locked laser pulses. A complete wavelet pattern set serially illuminates the object via a spectral disperser. This high-rate structured illumination transforms the scene into a set of sparse coefficients. We show that complex scenes can be compressed to less than 30% of their Nyquist rate by thresholding and storing the most significant wavelet coefficients. Moreover by employing temporal multiplexing of the patterns we are able to achieve pixel rates in excess of 360 MPixels/s.

Tuned depth signal analysis on merged transform domain for view synthesis in free viewpoint systems

Completely embedded in the 3D era, depth maps coding becomes a must in order to favour 3D admission to different fields of application, ranging from video games to medical imaging. This study presents a novel depth coding approach that, after a decimation step favouring the foreground, decomposes depth maps onto a set of sparse coefficients and redundant mixed discrete cosine and B-splines atoms highly correlated to depth maps piece-wise linear nature. Depth decomposition searches the best rate/distortion tradeoff through minimisation of an adaptive cost function, where its weight parameter is manipulated according to depth homogeneity. The bigger the parameter is, the more the sparsity is favoured at the expense of synthesis quality. Furthermore, handled distortion measure of the cost function quantifies the effect of depth maps coding on rendered views quality. The experiments show the relevance of the proposed method, able to obtain considerable tradeoffs between bitrate and synthesised views distortion.

Action recognition via structured codebook construction

Bag-of-words models have been widely used to obtain the global representation for action recognition. However, these models ignored the structure information, such as the spatial and temporal contextual information for action representation. In this paper, we propose a novel structured codebook construction method to encode spatial and temporal contextual information among local features for video representation. Given a set of training videos, our method first extracts local motion and appearance features. Next, we encode the spatial and temporal contextual information among local features by constructing correlation matrices for local spatio-temporal features. Then, we discover the common patterns of movements to construct the structured codebook. After that, actions can be represented by a set of sparse coefficients with respect to the structured codebook. Finally, a simple linear SVM classifier is applied to predict the action class based on the action representation. Our method has two main advantages compared to traditional methods. First, our method automatically discovers the mid-level common patterns of movements that capture rich spatial and temporal contextual information. Second, our method is robust to unwanted background local features mainly because most unwanted background local features cannot be sparsely represented by the common patterns and they are treated as residual errors that are not encoded into the action representation. We evaluate the proposed method on two popular benchmarks: KTH action dataset and UCF sports dataset. Experimental results demonstrate the advantages of our structured codebook construction.

Compressed History Matching: Exploiting Transform-Domain Sparsity for Regularization of Nonlinear Dynamic Data Integration Problems

In this paper, we present a new approach for estimating spatially-distributed reservoir properties from scattered nonlinear dynamic well measurements by promoting sparsity in an appropriate transform domain where the unknown properties are believed to have a sparse approximation. The method is inspired by recent advances in sparse signal reconstruction that is formalized under the celebrated compressed sensing paradigm. Here, we use a truncated low-frequency discrete cosine transform (DCT) is redundant to approximate the spatial parameters with a sparse set of coefficients that are identified and estimated using available observations while imposing sparsity on the solution. The intrinsic continuity in geological features lends itself to sparse representations using selected low frequency DCT basis elements. By recasting the inversion in the DCT domain, the problem is transformed into identification of significant basis elements and estimation of the values of their corresponding coefficients. To find these significant DCT coefficients, a relatively large number of DCT basis vectors (without any preferred orientation) are initially included in the approximation. Available measurements are combined with a sparsity-promoting penalty on the DCT coefficients to identify coefficients with significant contribution and eliminate the insignificant ones. Specifically, minimization of a least-squares objective function augmented by an l1-norm of DCT coefficients is used to implement this scheme. The sparsity regularization approach using the l1-norm minimization leads to a better-posed inverse problem that improves the non-uniqueness of the history matching solutions and promotes solutions that are, according to the prior belief, sparse in the transform domain. The approach is related to basis pursuit (BP) and least absolute selection and shrinkage operator (LASSO) methods, and it extends the application of compressed sensing to inverse modeling with nonlinear dynamic observations. While the method appears to be generally applicable for solving dynamic inverse problems involving spatially-distributed parameters with sparse representation in any linear complementary basis, in this paper its suitability is demonstrated using low frequency DCT basis and synthetic waterflooding experiments.

Image compression by sparse PCA coding in curvelet domain

This paper uses the newly developed concept of ‘sparsity’ in signal processing to the context of Image Compression. The first step of the scheme is to use a sparsifying transform on the image. The sparse set of coefficients is encoded via Sparse PCA. Wavelet Transform had been used profusely for image compression tasks. But the choice is not the ideal one. The partial reconstruction error from wavelet coefficients is an order of magnitude higher than the ideal error rate. In this paper image compression is carried in the curvelet domain—a better choice compared to wavelets, at least theoretically, since the reconstruction error rate with curvelet coefficients is of the same asymptotic order as that of the ideal error rate. The compression scheme is tested on the Lena and Barbara image as well as the USPS and Yale Face databases.