Model observers have been used successfully to predict human observer performance and to evaluate image quality for
detection tasks on various backgrounds in medical applications. This paper will apply the closed-form compression noise
statistics in analytic form to model observers and the derived channelized Hotelling observer (CHO) for decompressed
images. The performance of CHO on decompressed images is validated using JPEG compression algorithm and lumpy background
images. The results show that the derived CHO performance predicts closely its simulated performance.
This paper studies the principle of transform coding and identifies the quantization noise as the sole distortion. It shows that compression noise is a linear transform of quantization noise, which is usually generated during quantization of transform coefficients using uniform scalar quantizers. The quantization noise may not distribute uniformly as distributions and quantization step sizes vary among transform coefficients. This paper derives the marginal, pairwise and joint probability density functions (pdfs) of multi-dimensional quantization noise. It also shows the mean vector and covariance matrix of quantization noise in closed-form. Based on above results, this paper derives closed-form compression noise statistics, which include marginal pdfs, pairwise pdfs and joint pdf, mean vector and covariance matrix of compression noise. This paper shows compression noise has a jointly normal distribution, which enables its calculation to have reasonable computation complexity. The derived statistics of quantization and compression noise are verified by using the JPEG compression algorithm and lumpy background images. Verification results show that derived statistics closely predicts estimated ones. This paper provides a theoretical foundation to derive closed-form model observers and to define closed-form quality measures for compressed medical images.
This paper provides a theoretical foundation for the closed-form expression of model observers on compressed images. In medical applications, model observers, especially the channelized Hotelling observer, have been successfully used to predict human observer performance and to evaluate image quality for detection tasks in various backgrounds. To use model observers, however, requires knowledge of noise statistics. This paper first identifies quantization noise as the sole distortion source in transform coding, one of the most commonly used methods for image compression. Then, it represents transform coding as a 1-D block-based matrix expression, it further derives first and second moments, and the probability density function (pdf) of the compression noise at pixel, block and image levels. The compression noise statistics depend on the transform matrix and the quantization matrix in the transform coding algorithm. Compression noise is jointly normally distributed when the dimension of the transform (the block size) is typical and the contents of image sets vary randomly. Moreover, this paper uses JPEG as a test example to verify the derived statistics. The test simulation results show that the closed-form expression of JPEG quantization and compression noise statistics correctly predicts the estimated ones from actual images.
To achieve higher compression ratios in medical images while preserving quality, a new fractal method is developed, examined, and tested in this paper. The basic idea of fractal image compression is to reduce the similarity redundancy by identifying a given image with the fixed-point of an appropriate partitioned iterated function system (PIFS), that consists of a set of contractive affine transformations. Since conventional PIFS models use only affine transformations to represent similarity for the whole image, the quality of the re-created images is quite limited in some cases. Because the grayscale in most images is dependent on location, it is not sufficient to describe the relationship using linear transforms when there are complex textures present. Effective interpolation polynomials should adapt to the nature of the underlying texture; that is the basis of the new method. The new fractal image-compression algorithm uses adaptive PIFS (APIFS), that is based on variants of affine transformations and lossless compression methods. Polynomials of various orders are used to represent adaptively the similarity of grayscale based on the local details of the image, and the contractive condition for the generalized transformation is shown to hold. In this approach, quadratic and linear models are applied adaptively to the contractive transformations. The variants of the affine transform are used where similarities can be identified, while lossless compression techniques are used for those local areas in which similar domains do not exist or cannot be found. Preliminary experiments indicate that the APIFS model has the potential to increase the useful compression ratio. Experiments with medical images indicate that this new algorithm can be extended to yield a compression ratio of about 30:1 without perceptible degradation.