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In recent years, tree-structured analysis/reconstruction systems have been extensively studied for use in subband coders for speech. In such systems, it is imperative that the individual channel signals be decimated in such a way that the number of samples coded and transmitted do not exceed the number of samples in the original speech signal. Under this constraint, the systems presented in the past have sought to remove the aliasing distortion while minimizing the overall analysis/reconstruction distortion. In this paper, it, is shown that it is possible to design tree-structured analgsis/reconstruction systems which meet the sampling rate condition and which result in exact reconstruction of the input signal. The conditions for exact reconstruction are developed and presented. Furthermore, it is shown that these conditions are not overly restrictive and high-quality frequency division may be performed in the analysis section. A filter design procedure is presented which allows high-quality filters to be easily designed.

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The problem of interslice magnetic resonance (MR) image reconstruction arises in a broad range of medical applications. In such cases, there is a need to approximate information present in the original subject that is not reflected in contiguously acquired MR images because of hardware sampling limitations. In the context of vascular morphology reconstruction, this information is required in order for subsequent visualization and computational analysis of blood vessels to be most effective. Toward that end we have developed a method of vascular morphology reconstruction based on adaptive control grid interpolation (ACGI) to function as a precursor to visualization and computational analysis. ACGI has previously been implemented in addressing various problems including video coding and tracking. This paper focuses on the novel application of the technique to medical image processing. ACGI combines features of optical flow-based and block-based motion estimation algorithms to enhance insufficiently dense MR data sets accurately with a minimal degree of computational complexity. The resulting enhanced data sets describe vascular geometries. These reconstructions can then be used as visualization tools and in conjunction with computational fluid dynamics (CFD) simulations to offer the pressure and velocity information necessary to quantify power loss. The proposed ACGI methodology is envisioned ultimately to play a role in surgical planning aimed at producing optimal vascular configurations for successful surgical outcomes.

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Abstract-A new technique is presented for interpolating between grey-scale images in a medical data set. Registration between neighboring slices is achieved with a modified control grid interpolation algorithm that selectively accepts displacement field updates in a manner optimized for performance. A cubic interpolator is then applied to pixel intensities correlated by the displacement fields. Special considerations are made for efficiency, interpolation quality, and compression in the implementation of the algorithm. Experimental results show that the new method achieves good quality, while offering dramatic improvement in efficiency relative to the best competing method.