In recent years there has been a growing interest in the study of sparse representation of signals. Using an overcomplete dictionary that contains prototype signal-atoms, signals are described by sparse linear combinations of these atoms. Applications that use sparse representation are many and include compression, regularization in inverse problems, feature extraction, and more. Recent activity in this field has concentrated mainly on the study of pursuit algorithms that decompose signals with respect to a given dictionary. Designing dictionaries to better fit the above model can be done by either selecting one from a prespecified set of linear transforms or adapting the dictionary to a set of training signals. Both of these techniques have been considered, but this topic is largely still open. In this paper we propose a novel algorithm for adapting dictionaries in order to achieve sparse signal representations. Given a set of training signals, we seek the dictionary that leads to the best representation for each member in this set, under strict sparsity constraints. We present a new method-the K-SVD algorithm-generalizing the K-means clustering process. K-SVD is an iterative method that alternates between sparse coding of the examples based on the current dictionary and a process of updating the dictionary atoms to better fit the data. The update of the dictionary columns is combined with an update of the sparse representations, thereby accelerating convergence. The K-SVD algorithm is flexible and can work with any pursuit method (e.g., basis pursuit, FOCUSS, or matching pursuit). We analyze this algorithm and demonstrate its results both on synthetic tests and in applications on real image data

https://users.ece.utexas.edu/~sanghavi/courses/papers/KSVD.pdf

$rm K$ -SVD: An Algorithm for Designing Overcomplete Dictionaries for Sparse Representation

One of the aims of the standardization committee has been the development of Part I, which could be used on a royalty- and fee-free basis. This is important for the standard to become widely accepted. The standardization process, which is coordinated by the JTCI/SC29/WG1 of the ISO/IEC has already produced the international standard (IS) for Part I. In this article the structure of Part I of the JPFG 2000 standard is presented and performance comparisons with established standards are reported. This article is intended to serve as a tutorial for the JPEG 2000 standard. The main application areas and their requirements are given. The architecture of the standard follows with the description of the tiling, multicomponent transformations, wavelet transforms, quantization and entropy coding. Some of the most significant features of the standard are presented, such as region-of-interest coding, scalability, visual weighting, error resilience and file format aspects. Finally, some comparative results are reported and the future parts of the standard are discussed.

/pdf/the-jpeg-2000-still-image-compression-standard-2dd3aimci6.pdf

The JPEG 2000 still image compression standard

Sparse representations of signals have drawn considerable interest in recent years. The assumption that natural signals, such as images, admit a sparse decomposition over a redundant dictionary leads to efficient algorithms for handling such sources of data. In particular, the design of well adapted dictionaries for images has been a major challenge. The K-SVD has been recently proposed for this task and shown to perform very well for various grayscale image processing tasks. In this paper, we address the problem of learning dictionaries for color images and extend the K-SVD-based grayscale image denoising algorithm that appears in . This work puts forward ways for handling nonhomogeneous noise and missing information, paving the way to state-of-the-art results in applications such as color image denoising, demosaicing, and inpainting, as demonstrated in this paper.

/pdf/sparse-representation-for-color-image-restoration-zgu54hue6s.pdf

Sparse Representation for Color Image Restoration

[1] The HiRISE camera features a 0.5 m diameter primary mirror, 12 m effective focal length, and a focal plane system that can acquire images containing up to 28 Gb (gigabits) of data in as little as 6 seconds. HiRISE will provide detailed images (0.25 to 1.3 m/pixel) covering ∼1% of the Martian surface during the 2-year Primary Science Phase (PSP) beginning November 2006. Most images will include color data covering 20% of the potential field of view. A top priority is to acquire ∼1000 stereo pairs and apply precision geometric corrections to enable topographic measurements to better than 25 cm vertical precision. We expect to return more than 12 Tb of HiRISE data during the 2-year PSP, and use pixel binning, conversion from 14 to 8 bit values, and a lossless compression system to increase coverage. HiRISE images are acquired via 14 CCD detectors, each with 2 output channels, and with multiple choices for pixel binning and number of Time Delay and Integration lines. HiRISE will support Mars exploration by locating and characterizing past, present, and future landing sites, unsuccessful landing sites, and past and potentially future rover traverses. We will investigate cratering, volcanism, tectonism, hydrology, sedimentary processes, stratigraphy, aeolian processes, mass wasting, landscape evolution, seasonal processes, climate change, spectrophotometry, glacial and periglacial processes, polar geology, and regolith properties. An Internet Web site (HiWeb) will enable anyone in the world to suggest HiRISE targets on Mars and to easily locate, view, and download HiRISE data products.

/pdf/mars-reconnaissance-orbiter-s-high-resolution-imaging-4bjw0ks5y9.pdf

Mars Reconnaissance Orbiter's High Resolution Imaging Science Experiment (HiRISE)

With the increasing use of multimedia technologies, image compression requires higher performance as well as new features. To address this need in the specific area of still image encoding, a new standard is currently being developed, the JPEG2000. It is not only intended to provide rate-distortion and subjective image quality performance superior to existing standards, but also to provide features and functionalities that current standards can either not address efficiently or in many cases cannot address at all. Lossless and lossy compression, embedded lossy to lossless coding, progressive transmission by pixel accuracy and by resolution, robustness to the presence of bit-errors and region-of-interest coding, are some representative features. It is interesting to note that JPEG2000 is being designed to address the requirements of a diversity of applications, e.g. Internet, color facsimile, printing, scanning, digital photography, remote sensing, mobile applications, medical imagery, digital library and E-commerce.

The JPEG2000 still image coding system: an overview

JPEG-2000 is an emerging standard for still image compression. This paper provides a brief history of the JPEG-2000 standardization process, an overview of the standard, and some description of the capabilities provided by the standard. Part I of the JPEG-2000 standard specifies the minimum compliant decoder, while Part II describes optional, value-added extensions. Although the standard specifies only the decoder and bitstream syntax, in this paper we describe JPEG-2000 from the point of view of encoding. We take this approach, as we believe it is more amenable to a compact description more easily understood by most readers.

/pdf/an-overview-of-jpeg-2000-2uy5wu2hxc.pdf

An overview of JPEG-2000

Overview of JPEG-2000

A compression and decompression system in which a reversible wavelet filter are used to generates coefficients from input data, such as image data. The reversible wavelet filter is an efficient transform implemented with integer arithmetic that has exact reconstruction. The present invention uses the reversible wavelet filter in a lossless system (or lossy system) in which an embedded codestream is generated from the coefficients produced by the filter. An entropy coder performs entropy coding on the embedded codestream to produce the compressed data stream.

Method and apparatus for compression using reversible wavelet transforms and an embedded codestream

A method and apparatus for reformatting electronic documents is disclosed. In one embodiment, the method comprises performing layout analysis on an electronic version of a document to locate text zones, assigning attributes for scale and importance to text zones in the electronic version of the document, and reformatting text in the electronic version of the document based on the attributes to create an image.

Michael J. Gormish

Papers

An overview of JPEG-2000

Overview of JPEG-2000

Method and apparatus for compression using reversible wavelet transforms and an embedded codestream

Reformatting documents using document analysis information

Compression/decompression using reversible embedded wavelets