1 Introduction

Matter 2 provides a variety of signal processing tools for both uniformly-sampled and nonuniformly-sampled signals in both 1D and 2D, as well as a limited selection of processing tools for signals of arbitrary dimension.

While the primary motivation for implementing these signal processing tools is for use with mass spectrometry imaging experiments, most of the provided functions are broadly applicable to any signal processing domain.

2 Vocabulary

Matter uses a few consistent terms across its available functions when referring to certain aspects of signal processing. These terms will frequently appear as parameters to signal processing functions.

2.1 Dimensionality and domain

Signals may have multiple dimensions. Each dimension corresponds to a domain.

Here is a simple 1-dimensional signal that resembles a mass spectrum:

set.seed(1)
s <- simspec(1)

plot_signal(s, xlab="Index", ylab="Intensity")

A 1-dimensional signal has a single domain.

For a mass spectrum, the domain values are the mass-to-charge ratios, (or m/z-values).

plot_signal(domain(s), s, xlab="m/z", ylab="Intensity")

A 2-dimensional signal has two domains.

For example, for an image (which is a 2D signal), the domain values are the x and y locations of the pixels.

plot_image(volcano)

The dimensionality of a signal is the number of domains.

For example, a mass spectrum collected in tandem with liquid chromatography and ion mobility spectrometry (i.e., LC-IMS-MS) is a 3-dimensional signal. The domains for LC-IMS-MS spectra would include (1) retension times, (2) drift times, and (3) m/z-values.

Note that the values of a signal (e.g., intensities) are not considered as a separate dimension or domain.

2.2 Index and domain

In some cases, it is necessary for Matter to distinguish between the observed domain values for a signal and the effective domain values for a signal.

This is most obvious when we need to represent multiple nonuniformly-sampled signals (that may have been observed at different domain values) with a single set of domain values.

set.seed(1)
s1 <- simspec(1)
s2 <- simspec(1)

# spectra with different m/z-values
head(domain(s1))

## [1] 507.8720 508.0159 508.1598 508.3037 508.4476 508.5915

head(domain(s2))

## [1] 562.5085 562.6585 562.8085 562.9585 563.1085 563.2585

# create a shared vector of m/z-values
mzr <- range(domain(s1), domain(s2))
mz <- seq(from=mzr[1], to=mzr[2], by=0.2)

# create representations with the same m/z-values
s1 <- sparse_vec(s1, index=domain(s1), domain=mz)
s2 <- sparse_vec(s2, index=domain(s2), domain=mz)

In cases like this, Matter refers to the observed domain values as the signal index, and the effective domain values as the signal domain.

3 Filtering and smoothing

3.1 Smoothing in 1D

Matter provides a family of 1D smoothing methods that follow the naming scheme filt1_*:

filt1_ma performs moving average filtering
filt1_conv performs convolutional filtering with custom weights
filt1_gauss performs Gaussian filtering
filt1_bi performs bilateral filtering
filt1_adapt performs adaptive bilateral filtering
filt1_diff performs nonlinear diffusion filtering
filt1_guide performs guided filtering
filt1_pag performs peak-aware guided filtering
filt1_sg performs Savitzky-Golay filtering

We demonstrate the smoothing results on a simulate signal below:

set.seed(1)
s <- simspec(1, sdnoise=0.25, resolution=500)

p1 <- plot_signal(s)
p2 <- plot_signal(filt1_ma(s))
p3 <- plot_signal(filt1_gauss(s))
p4 <- plot_signal(filt1_bi(s))
p5 <- plot_signal(filt1_diff(s))
p6 <- plot_signal(filt1_guide(s))
p7 <- plot_signal(filt1_pag(s))
p8 <- plot_signal(filt1_sg(s))

plt <- as_facets(list(
    "Original"=p1,
    "Moving average"=p2,
    "Gaussian"=p3,
    "Bilateral"=p4,
    "Diffusion"=p5,
    "Guided"=p6,
    "Peak-aware"=p7,
    "Savitsky-Golay"=p8), nrow=4, ncol=2)

plot(plt)

Now we zoom in on the x-axis to better see the differences in the smoothing.

plot(plt, xlim=c(5800, 6100))

3.2 Smoothing in 2D

Matter also provides a family of 2D image smoothing methods that follow the naming scheme filt2_*:

filt2_ma performs moving average filtering
filt2_conv performs convolutional filtering with custom weights
filt2_gauss performs Gaussian filtering
filt2_bi performs bilateral filtering
filt2_adapt performs adaptive bilateral filtering
filt2_diff performs nonlinear diffusion filtering
filt2_guide performs guided filtering

If a multichannel image is provided (e.g., a 3D array), then these functions will smooth each channel independently.

We demonstrate the smoothing results on the volcano dataset with added noise:

set.seed(1)
img <- volcano + rnorm(length(volcano), sd=2.5)

p1 <- plot_image(img)
p2 <- plot_image(filt2_ma(img))
p3 <- plot_image(filt2_gauss(img))
p4 <- plot_image(filt2_bi(img))
p5 <- plot_image(filt2_diff(img))
p6 <- plot_image(filt2_guide(img))

plt <- as_facets(list(
    "Original"=p1,
    "Moving average"=p2,
    "Gaussian"=p3,
    "Bilateral"=p4,
    "Diffusion"=p5,
    "Guided"=p6), nrow=3, ncol=2)

plot(plt)

Matter 2: Signal and image processing

Revised: July 17, 2024

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