Constrained least-squares restoration and renogram deconvolution: a comparison by simulation

Abstract

Before deconvolution can be used in renography, it is necessary to decide whether the renal function is sufficiently good to allow it. To see if this decision can be circumvented, an iterative constrained least-squares restoration (CLSR) method was implemented in which the point of termination of the iteration occurs when a residual vector has a value less than an estimate of the noise in the original renogram curve. The technique was compared with the matrix algorithm and with direct FFT division. The comparison was achieved by deconvolving simulated renogram data with differing transit time spectra and statistics. As expected, the FFT technique produced results of little value whereas the CLSR and matrix methods produced values of mean transit time (MTT) that differed slightly from the expected results. Analysis indicated that the matrix approach was superior when the percentage noise component was less than 6% and vice versa. No technique produced useful transit time spectra. As the CLSR technique produced better results than the matrix method in simulations with relatively long MTTs and high noise, it seems reasonable to suggest that it might be used for renogram deconvolution without the need for previous inspection of the curves.

Noise reduction of renograms: a new algorithm applied to simulated renograms for evaluation of the renal retention function

“…has been addressed by Tawatchai et al (1994), who applied a large set of different Butterworth ®lters when analysing the vascular phase of the RRF. Sutton & Kempi, 1992, 1993 proposed instead a constrained least-squares restoration (CLSR) deconvolution algorithm based on the FT, and employed a Wiener ®lter to handle the noise. They reported results superior to the outcome of 3-point smoothing, although the 3-point smoothings were not investigated with respect to the number of smoothings.…”

Modeling of the Renal Kinetics of the AT1 Receptor Specific PET Radioligand [11C]KR31173

“…Processes of deconvolution and convolution were carried out in frequency domain as follows. For convolution the response function (time-activity curve; y ( t )) was described as the convolution integral (⊗) of the input function x ( t ) with the impulse response function f ( t ): $\begin{array}{c}y\left(t\right)=x\left(t\right)\otimes f\left(t\right).\end{array}$ Equation (6) represents (5) in frequency domain: $\begin{array}{c}\psi =\xi \varphi .\end{array}$ Frequency-domain deconvolution analysis [12] included regularization by the third difference operator function c = [1, −3,3, −1,0,…, 0]: $\begin{array}{cc}\left(6\right)& \varphi =\frac{{\xi }^{\ast }\psi }{{\xi }^{\ast }\xi +\kappa {\kappa }^{\ast }}.\end{array}$ For this equation κ was the Fourier transform of c , the symbol * represented complex conjugate of the Fourier transforms, and ϕ , ξ , and ψ were the Fourier transforms of f ( t ), x ( t ), and y ( t ) calculated by fast Fourier transformations (FFTs).…”

Logistic Regression Analysis

“…A vascular spike (10,11) on the TAC, frequently observed at 30 sec after injection, i.e., the second curve point, was removed by bounding (10). The TAC were then subjected to three smooths using the smoothing operator (9,12,17). Prior to deconvolution, the data points of the first frame were excluded from calculations (10).…”

“…To address this problem, a variant of the AMA technique (AMA+) in which the AMA parameters were combined with the amplitude from the matrix algorithm was also entered to the study. In all cases, the MaxTT was defined as the time at which the retention function crossed the time-axis and the MTT as the area under the retention curve, divided by its amplitude (10,12).…”