Wavelet-based image compression provides substantial improvements in picture quality at higher compression ratios. Haar wavelet transform based compression is one of the methods that can be applied for compressing images. An ideal image compression system must yield good quality compressed images with good compression ratio, while maintaining minimal time cost. With Wavelet transform based compression, the quality of compressed images is usually high, and the choice of an ideal compression ratio is difficult to make as it varies depending on the content of the image. Therefore, it is of great advantage to have a system that can determine an optimum compression ratio upon presenting it with an image. We propose that neural networks can be trained to establish the non-linear relationship between the image intensity and its compression ratios in search for an optimum ratio. This paper suggests that a neural network could be trained to recognize an optimum ratio for Haar wavelet compression of an image upon presenting the image to the network. Two neural networks receiving different input image sizes are developed in this work and a comparison between their performances in finding optimum Haar-based compression is presented.

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Image compression using neural networks and haar wavelet

A system, apparatus, and method related to content adaptive partitioning for prediction and coding for next generation video (NGV) coding are described. NGV coding differs from standards-based approaches as it naturally incorporates significant content-based adaptivity in video coding process to achieve higher compression. On the other hand, NGV exploits interframe differences due to motion and other types of interframe difference (gain, blur, registration) that naturally exist in typical video scenes.

Video codec architecture for next generation video

In this paper, we propose a new reciprocal-orthogonal parametric discrete Fourier transform (DFT) by appropriately replacing some specific twiddle factors in the kernel of the classical DFT by independent parameters that can be chosen arbitrarily from the complex plane. A new class of parametric unitary transforms can be obtained from the proposed transform by choosing all its independent parameters from the unit circle. One of the special cases of this class is then exploited for developing a new one-parameter involutory discrete Hartley transform (DHT). The proposed parametric DFT and DHT can be computed using the existing fast algorithms of the DFT and DHT, respectively, with computational complexities similar to those of the latter. Indeed, for some special cases, the proposed transforms require less number of operations. In view of the fact that the transforms of small sizes are used in some image and video compression techniques and employed as building blocks for larger size transform algorithms, we develop new algorithms for the proposed small-size transforms. The proposed parametric DFT and DHT, in view of the introduction of the independent parameters, offer more flexibility in achieving better performance compared to the classical DFT and DHT. As examples of possible applications of the proposed transforms, image compression, Wiener filtering, and spectral analysis are considered.

New Parametric Discrete Fourier and Hartley Transforms, and Algorithms for Fast Computation

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CT image denoising using locally adaptive shrinkage rule in tetrolet domain

A method for video coding according to the present invention comprises: the steps of receiving prediction error data or coding partition or a partition of original pixel data for transform coding; performing a closed-form parametric transform on the prediction error data or coding partition or the partition of original pixel data to generate transform coefficients; quantizing the transform coefficients to generate quantized transform coefficients; and entropy encoding data associated with the quantized transform coefficient into a bitstream.

Content adaptive parametric transforms for coding for next generation video

A new image compression scheme is presented, based on a fast orthogonal parametrically adaptive Haar-like transform, which is a discrete orthogonal transform such that it may be computed with a fast algorithm in structure similar to the classical fast Haar transform, and such that its matrix contains one or more predefined row(s) of an arbitrary order. The nature of the proposed image compression scheme is such that its performance (in terms of PSNR versus compression ratio) cannot be worse than that of the classical DCT (discrete cosine transform) based scheme. Simulations show that a significant performance improvement can be achieved for certain types of images such as medical X-ray images.

An image compression scheme based on parametric Haar-like transform

In this paper a methodology to design VLSI architectures for parametric transform families is proposed. A parametric transform family consists of discrete orthogonal transforms such that they all may be computed with a fast algorithm of similar structure where parameters defining the transform within the family are used. In our previous work, an algorithm to synthesize transforms with predefined basis functions was introduced and efficiently applied to image compression. The methodology proposed in this paper allows of designing VLSI architectures that may not only switch from one transform of a family to another by setting parameters, but also to actually set these parameters so that the matrix of the resulting transform has predefined basis functions

On unified architectures for synthesizing and implementation of fast parametric transforms

A class of parametric transforms that are based on unified representation of transform matrices in the form of sparse matrix products is described. Different families of transforms are defined within the introduced class. All transforms of one family can be computed with fast algorithms similar in structure to each other. In particular, the family of Haar-like transforms consists of discrete orthogonal transforms of arbitrary order such that they all may be computed with a fast algorithm that is in structure similar to classical fast Haar transform. A method for parameter selection is proposed that allows synthesizing specific transforms with matrices containing predefined row(s). The potential of the proposed class of Haar-like parametric transforms to improve the performance of fixed block transforms in image compression is investigated. With this purpose, two image compression schemes are proposed where a number of Haar-like transforms are synthesized each adapted to a certain set of blocks within an image.The nature of the proposed schemes is such that their performance (in terms of PSNR versus compression ratio) cannot be worse than a scheme based on classical discrete cosine transform (DCT). Simulations show that a significant performance improvement can be achieved for certain types of images such as medical X-ray images and compound images.

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On a Class of Parametric Transforms and Its Application to Image Compression

In our recent work, a class of parametric transforms, including family of Haar-like transforms, was introduced and studied in application to image compression. Parametric Haar-like transform (PHT) is a discrete orthogonal transform such that it may be computed with a fast algorithm in a structure similar to that of classical fast Haar transform and such that its matrix contains arbitrary predefined vector in its first row. The aim of this paper is to study a potential use of parametric Haar-like transforms in image denoising. A PHT-based post-processing method is proposed which may improve a denoising method based on fixed transforms. In particular, it is shown that the proposed method may significantly improve the performance of wavelet thresholding based image denoising.

Parametric Haar-Like Transforms in Image Denoising

The paper introduces a signal adaptive Haar-like transform for ternary functions. The term adaptive means, given the signal, we design a transform after a brief analysis of signal features such as appearance of identical patterns or periods of constancy. The proposed transform possesses a fast FFT-like computation algorithm similar to fast algorithms for the classical Haar transform on finite dyadic groups as well as the generalized Haar transforms for multiple-valued functions. The proposed transform is utilized in reduction of the number of nonzero coefficients in spectral representation of ternary functions. The method shows good results, especially, when the given ternary signal contains intervals of constancy or repeated patterns having relatively high frequency of appearance.

Susanna Minasyan

Papers

An image compression scheme based on parametric Haar-like transform

On unified architectures for synthesizing and implementation of fast parametric transforms

On a Class of Parametric Transforms and Its Application to Image Compression

Parametric Haar-Like Transforms in Image Denoising

Ternary Haar-Like Transform and Its Application in Spectral Representation of Ternary-Valued Functions