Effective sparse representation of X‐ray medical images

Abstract

Effective sparse representation of X-ray medical images within the context of data reduction is considered. The proposed framework is shown to render an enormous reduction in the cardinality of the data set required to represent this class of images at very good quality. The goal is achieved by (1) creating a dictionary of suitable elements for the image decomposition in the wavelet domain and (2) applying effective greedy strategies for selecting the particular elements, which enable the sparse decomposition of the wavelet coefficients. The particularity of the approach is that it can be implemented at very competitive processing time and low memory requirements.

Sparse representation of 3D images for piecewise dimensionality reduction with high quality reconstruction

“…While a number of techniques for learning dictionaries from training data have been proposed in the literature [35][36][37][38][39][40][41][42], they are not designed for learning large and highly coherent separable dictionaries. Nevertheless, previous works [18,32,33,43] have demonstrated that highly redundant and highly coherent separable dictionaries, which are easy to construct, achieve remarkable levels of sparsity in the representation of 2D images. Such dictionaries are not specific to a particular class of images.…”

“…Consequently, instead of looking for the sparsest solution, one looks for a 'satisfactory solution', i.e., a solution such that the number of k-terms in (2) is considerably smaller than the image dimension. For 2D images this can be effectively achieved by greedy pursuit strategies in the line of the Matching Pursuit (MP) [29] and OMP [30] methods, if dedicated to 2D separable dictionaries [14,18,32,33]. Within a tensor product framework the consideration of OMP in 3D is natural.…”

A competitive scheme for storing sparse representation of X-Ray medical images

“…While the actual size depends on the sparsity of the image, previous studies indicate that in general for block sizes greater than 24 × 24 an alternative implementation is advisable. The alternative implementation, called Self Projected Matching Pursuit (SPMP2D) [ 8 , 21 ] is not only dedicated to tackling large dimensional problems, but also potentially suitable for implementation in Graphic Processing Unit (GPU) programming. However, because for X-Ray medical images a partition into blocks of size 16 × 16 is a good compromise between sparsity and processing time, we have focussed on the implementation of OMP2D as given in Sec.…”

“…In recent work [ 8 ] we have demonstrated that sparse representation, obtained by a large dictionary and greedy algorithms, renders high quality approximation of X-Ray images. The framework was proven to produce approximations which are far more sparser than those arising from traditional transformations such as the Cosine and Wavelet Transforms.…”

“…Nevertheless, for the approximation to be useful within the context of automatic health care systems and remote reporting, it is necessary to ensure that the high levels of the achieved sparsity are not affected by saving the reduced data in a small file. This paper follows on the study in [ 8 ] by presenting a simple scheme to store the sparse approximation of an X-Ray medical image in a file of competitive size with respect to the most commonly used formats, namely JPEG and JPEG2000 (JPEG2).…”