Sparse representation of images using learned dictionaries have been shown to work well for applications like image denoising, impainting, image compression, etc. In this paper dictionary properties are reviewed from a theoretical approach, and experimental results for learned dictionaries are presented. The main dictionary properties are the upper and lower frame (dictionary) bounds, and (mutual) coherence properties based on the angle between dictionary atoms. Both ℓ0 sparsity and ℓ1 sparsity are considered by using a matching pursuit method, order recursive matching Pursuit (ORMP), and a basis pursuit method, i.e. LARS or Lasso. For dictionary learning the following methods are considered: Iterative least squares (ILS-DLA or MOD), recursive least squares (RLS-DLA), K-SVD and online dictionary learning (ODL). Finally, it is shown how these properties relate to an image compression example.
The aim of this study is to provide feature images of digital mammograms in which regions corresponding to masses are enhanced. Subsequently, the feature images can be segmented and classified
into two classes; masses and normal tissue. Our proposed feature extraction method is based on a local energy measure as texture feature. The local energy measure is extracted using a filter optimized with respect to the relative distance between the average feature values. In order to increase the sensitivity of the texture feature extraction scheme each mammogram is preprocessed using wavelet transformation, adaptive histogram equalization, and a morphology based enhancement technique. Initial experiments indicate that our scheme is able to provide useful feature images of digital mammograms. In order to quantify the system performance the feature images of 38 mammograms from the MIAS database -- 19 containing circumscribed masses, and 19 containing spiculated masses -- were segmented using simple gray level thresholding. For the circumscribed masses a true positive (TP) rate of 89% with a corresponding 2.3 false detections (false positives, FPs) per image was achieved. For the spiculated masses the performance was somewhat lower, yielding an overall TP rate of 84% with a corresponding 2.6 FPs per image.
Screening programs produce large amount of mammographic data, and
good compression schemes would be beneficial for both storage and
transmission purposes. In medical data it is crucial that diagnostic important information is preserved. In this work we have implemented two different region-of-interest (ROI) coding methods together with a Set Partitioning in Hierarchical Trees (SPIHT) scheme to be used for compression of mammograms. Region-of-interest coding allows a region of the image to be compressed with higher fidelity than the rest of the image. This is useful in medical data to be able to compress a region containing a possibly cancer area with very high fidelity, but still manage an overall good compression ratio. Both the ROI methods, the basic SPIHT method as well as JPEG compression
standard, the latter two without possibility of ROI coding, are
evaluated by studying the results from a Computer Aided Detection
(CAD) system for microcalcifications tested on the original and
the compressed mammograms. In addition a visual inspection is performed as well as Peak Signal-to-Noise-Ratio (PSNR) calculations. Mammograms from the MIAS database is used. We show that mammograms can be compressed to less than 0.5 (0.3) bpp without any visual degradation and without significantly influence on the performance of the CAD system.
We present a method for detecting circumscribed masses in digital mammograms. Morphological hierarchical watersheds are used in the segmentation process. Oversegmentation is prevented by employing a reconstructive open/close alternating sequential filter to simplify the image. The advantage of this method of simplification is that the object shapes and edges are preserved. The regional maxima of the simplified input image are then extracted and used as internal markers for the hierarchical watershed transform, which is applied to the gradient image of the simplified input image. An image-based classification technique is applied to reduce the number of false positives. The method is applied to 18 mammograms from the MIAS database, containing 20 circumscribed masses in background tissue of varying density. We obtain a high true detection rate using combined with a low number of false positives per image.