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With the spread of aerial laser bathymetry (ALB), seafloor topographies are being measured more frequently. Nevertheless, data deficiencies occur owing to seawater conditions and other factors. Conventional interpolation methods generally need to produce digital elevation models (DEMs) with sufficient accuracy. If the topographic features are considered as a basis, the DEM should be reproducible based on a combination of such features. The purpose of this study is to develop new DEM generation methods based on sparse modeling. Based on a review of the definitions of sparsity, we developed DEM generation methods based on a discrete cosine transform (DCT), DCT with elastic net, K-singular value decomposition (K-SVD), Fourier regularization, wavelet regularization, and total variation (TV) minimization, and conducted a comparative analysis. The developed methods were applied to artificially deficient DEM and ALB data, and their accuracy was evaluated. Thus, as a conclusion, we can confirm that the K-SVD method is appropriate when the percentage of deficiencies is low, and that the TV minimization method is appropriate when the percentage of deficiencies is high. Based on these results, we also developed a method integrating both methods and achieved an RMSE of 0.128 m.

Sparse orthonormal transform is based on orthogonal sparse coding, which is relatively fast and suitable in image compression such as analytic transforms with better performance. However, because of the constraints on its dictionary, it has performance limitations. This paper proposes an extension of a sparse orthonormal transform based on unions of orthonormal dictionaries for image compression. Unlike unions of orthonormal bases (UONB), which implement an overcomplete dictionary with several orthonormal dictionaries, the proposed method allocates patches to an orthonormal dictionary based on their directions. The dictionaries are constructed into a discrete cosine transform and an orthonormal matrix. To determine a trade-off parameter between the reconstruction error and sparsity, which hinders efficient implementation, the proposed method adapts Bayesian optimization. The framework exhibits an improved performance with fast implementation to determine the optimal parameter. It is verified that the proposed method performs similar to an overcomplete dictionary with a faster speed via experiments.

Group sparse coding (GSC) uses the non-local similarity of images as constraints, which can fully exploit the structure and group sparse features of images. However, it only imposes the sparsity on the group coefficients, which limits the effectiveness of reconstructing real images. Low-rank regularized group sparse coding (LR-GSC) reduces this gap by imposing low-rankness on the group sparse coefficients. However, due to the use of non-local similarity, the edges and details of the images are over-smoothed, resulting in the blocking artifact of the images. In this paper, we propose a low-rank matrix restoration model based on sparse coding and dual weighting. In addition, total variation (TV) regularization is integrated into the proposed model to maintain local structure smoothness and edge features. Finally, to solve the problem of the proposed optimization, an optimization method is developed based on the alternating direction method. Extensive experimental results show that the proposed SDWLR-GSC algorithm outperforms state-of-the-art algorithms for image restoration when the images have large and sparse noise, such as salt and pepper noise.

Hundreds of thousands of images that are widely used in different fields of modern life have appeared in recent years. The process of retrieving the target images from a big database has become a meaningful problem. As one of the classical techniques of computer vision, image retrieval could effectively solve the problem. However, in most cases, high-quality retrieval results are supported by a large number of learning instances. It not only occupies much computing resources but also wastes much human resource. Moreover, much time is wasted in the process of retrieval. To solve the abovementioned problems, we proposed a sparse coding based few learning instances model for retrieval. Concretely, cross-validation sparse coding representation, sparse coding based instance distance and improved KNN model are combined which directly contributes to build up the previous model. It could reduce the number of learning instances significantly through the selection of optimized learning instances while preserving the retrieval accuracy. At last, a database using a large number of images was set up. The experimental results using the database show our method’s superiority in preserving the quality of retrieval with the reduction of learning instances.

A central goal in theoretical neuroscience is to predict the response properties of sensory neurons from first principles. To this end, “efficient coding” posits that sensory neurons encode maximal information about their inputs given internal constraints. There exist, however, many variants of efficient coding (e.g., redundancy reduction, different formulations of predictive coding, robust coding, sparse coding, etc.), differing in their regimes of applicability, in the relevance of signals to be encoded, and in the choice of constraints. It is unclear how these types of efficient coding relate or what is expected when different coding objectives are combined. Here we present a unified framework that encompasses previously proposed efficient coding models and extends to unique regimes. We show that optimizing neural responses to encode predictive information can lead them to either correlate or decorrelate their inputs, depending on the stimulus statistics; in contrast, at low noise, efficiently encoding the past always predicts decorrelation. Later, we investigate coding of naturalistic movies and show that qualitatively different types of visual motion tuning and levels of response sparsity are predicted, depending on whether the objective is to recover the past or predict the future. Our approach promises a way to explain the observed diversity of sensory neural responses, as due to multiple functional goals and constraints fulfilled by different cell types and/or circuits.

In image processing, sparse coding has been known to be relevant to both variational and Bayesian approaches. The regularization parameter in variational image restoration is intrinsically connected with the shape parameter of sparse coefficients’ distribution in Bayesian methods. How to set those parameters in a principled yet spatially adaptive fashion turns out to be a challenging problem especially for the class of nonlocal image models. In this work, we propose a structured sparse coding framework to address this issue—more specifically, a nonlocal extension of Gaussian scale mixture (GSM) model is developed using simultaneous sparse coding (SSC) and its applications into image restoration are explored. It is shown that the variances of sparse coefficients (the field of scalar multipliers of Gaussians)—if treated as a latent variable—can be jointly estimated along with the unknown sparse coefficients via the method of alternating optimization. When applied to image restoration, our experimental results have shown that the proposed SSC–GSM technique can both preserve the sharpness of edges and suppress undesirable artifacts. Thanks to its capability of achieving a better spatial adaptation, SSC–GSM based image restoration often delivers reconstructed images with higher subjective/objective qualities than other competing approaches.

Social visual processing in vertebrates employs sophisticated neural mechanisms ranging from categorical face cells to distributed sparse coding systems. In primates, recent evidence supports a “tuning landscape” model where neurons signal distances to prototypes in high-dimensional space rather than functioning as simple category detectors. However, social visual processing in non-mammalian animals remains poorly understood. We recorded single-unit activity from three functionally distinct pigeon brain regions—mesopallium ventrolaterale (MVL), visual Wulst, and nidopallium caudolaterale (NCL)—while birds viewed dynamic videos of conspecifics and control shapes performing courtship, eating, flying, and walking behaviors. Despite finding visually responsive neurons in all regions, we observed no categorical distinction between conspecific and control stimuli. Instead, population analyses revealed discrete temporal modulations corresponding to specific motion features—bowing, wing-flapping, head-bobbing—suggesting feature-based rather than categorical encoding of visual information. Sound-modulated visual units were significantly more prevalent in MVL than Wulst, indicating earlier multimodal integration in the tectofugal pathway than previously recognized. The absence of differential responses in NCL during passive viewing, contrasting with clear modulation in visual areas, suggests that this region is less involved in the automatic analysis of visual features. These findings suggest that avian visual structures use sparse coding principles that are similar to the visual cortex, where populations encode specific features through coordinated but brief neural responses rather than sustained categorical signals.

Both theoretical and experimental evidence indicate that synaptic excitation and inhibition in the cerebral cortex are well-balanced during the resting state and sensory processing. Here, we briefly summarize the evidence for how neural circuits are adjusted to achieve this balance. Then, we discuss how such excitatory and inhibitory balance shapes stimulus representation and information propagation, two basic functions of neural coding. We also point out the benefit of adopting such a balance during neural coding. We conclude that excitatory and inhibitory balance may be a fundamental mechanism underlying efficient coding.

Understanding the extremely variable, complex shape and venation characters of angiosperm leaves is one of the most challenging problems in botany. Machine learning offers opportunities to analyze large numbers of specimens, to discover novel leaf features of angiosperm clades that may have phylogenetic significance, and to use those characters to classify unknowns. Previous computer vision approaches have primarily focused on leaf identification at the species level. It remains an open question whether learning and classification are possible among major evolutionary groups such as families and orders, which usually contain hundreds to thousands of species each and exhibit many times the foliar variation of individual species. Here, we tested whether a computer vision algorithm could use a database of 7,597 leaf images from 2,001 genera to learn features of botanical families and orders, then classify novel images. The images are of cleared leaves, specimens that are chemically bleached, then stained to reveal venation. Machine learning was used to learn a codebook of visual elements representing leaf shape and venation patterns. The resulting automated system learned to classify images into families and orders with a success rate many times greater than chance. Of direct botanical interest, the responses of diagnostic features can be visualized on leaf images as heat maps, which are likely to prompt recognition and evolutionary interpretation of a wealth of novel morphological characters. With assistance from computer vision, leaves are poised to make numerous new contributions to systematic and paleobotanical studies.

A full-rank matrix ${\\bf A}\\in {\\Bbb R}^{n\\times m}$ with n < m generates an underdetermined system of linear equations Ax = b having infinitely many solutions. Suppose we seek the sparsest solution, i.e., the one with the fewest nonzero entries. Can it ever be unique? If so, when? As optimization of sparsity is combinatorial in nature, are there efficient methods for finding the sparsest solution? These questions have been answered positively and constructively in recent years, exposing a wide variety of surprising phenomena, in particular the existence of easily verifiable conditions under which optimally sparse solutions can be found by concrete, effective computational methods. Such theoretical results inspire a bold perspective on some important practical problems in signal and image processing. Several well-known signal and image processing problems can be cast as demanding solutions of undetermined systems of equations. Such problems have previously seemed, to many, intractable, but there is considerable evidence that these problems often have sparse solutions. Hence, advances in finding sparse solutions to undetermined systems have energized research on such signal and image processing problems--to striking effect. In this paper we review the theoretical results on sparse solutions of linear systems, empirical results on sparse modeling of signals and images, and recent applications in inverse problems and compression in image processing. This work lies at the intersection of signal processing and applied mathematics, and arose initially from the wavelets and harmonic analysis research communities. The aim of this paper is to introduce a few key notions and applications connected to sparsity, targeting newcomers interested in either the mathematical aspects of this area or its applications.