Background: Breast cancer screening techniques have been developing rapidly in the field of imaging systems. One of these techniques is thermography, which is an alternative modality for mammography to detect breast lesions. Thermography utilization has been progressively developing as various models and methods of object processing improvement. Currently, the Fluke TIS20 infrared camera, with a resolution of 320 × 240, has not been used to measure precisely small objects such as early breast cancer lesions. Retrieval and processing of single images lead into imprecise object measurements and false positive results. Objective: Problems have been arisen due to the limitations of the camera resolution, object retrieval techniques and suboptimal image processing. The aim of this study was to detect accurately breast cancer lesions in rats, which were induced by carcinogenic compounds. Material and Methods: In this experimental study, development of models was conducted based on increasing image by optimizing the ability of low-resolution infrared (IR) cameras to identify s mall objects precisely. image pixel density increased by adjusting the distance of the objects from the camera and multiple images of objects gradually shifting were used to measure object dimensions precisely. Results: The results showed that cancerous lesions as small as 1. 27 mm could be detected. This method of lesion detection had a sensitivity and specificity of 93% and 77 % respectively. Conclusion: Small objects (cancerous lesions) were measured by increasing image resolution through splitting pixels into subpixels and combining several images using Partitioned Iterated Function Systems (PIFS).

A generalization of matrix-valued Multiresolution analysis (MMRA) to matrix-valued frames, and the constructions of matrix-valued frames are considered and characterized. A matrix-valued frame Multiresolution analysis is defined in this paper. We provide necessary and sufficient conditions for constructing matrix-valued frames and Riesz bases of translates, and give the calculation method of matrix-valued dual Riesz basis. These conclusions are useful in providing theoretical basis for constructing matrix-valued frames and Riesz basis.

Wavelets and radial basis functions (RBF) have ubiquitously proved very successful to solve different forms of partial differential equations (PDE) using shifted basis functions, and as with the other meshless methods, they have been extensively used in scattered data interpolation. The current paper proposes a framework that successfully reconciles RBF and adaptive wavelet method to solve the Perona-Malik equation in terms of locally shifted functions. We take advantage of the scaling functions that span Multiresolution subspaces to provide resilient grid comprising centers. At the next step, the derivatives are computed and summed over these local feature collocations to generate the solution. We discuss the stability of the solution and depict how convergence could be granted in this context. Finally, the numerical results are provided to illustrate the accuracy and efficiency of the proposed method.