In recent years, there has been significant progress in the development of parallel imaging techniques, such as SMASH (1), SENSE (2), SPACE-RIP (3), GRAPPA (4), and PILS (5). These techniques have permitted significant scan time reduction in both MRI and spectroscopic imaging (MRSI) (6, 7). Although these techniques differ in implementation and underlying approximations, they are all based on the principle that the spatially varying sensitivities of the receiver coils complement the role of the magnetic field gradients in spatial encoding. As a result, it is feasible to reduce the sampling density in *k*-space without compromising the spatial resolution or the field of view (FOV).

A key departure of parallel imaging from conventional imaging is that the effects of the coil sensitivities are taken into account during reconstruction. This departure affects the properties of the reconstructed image, since the net encoding functions are no longer orthogonal. For example, the achievable signal-to-noise ratio (SNR) is spatially varying and, as the present work shows, the achievable resolution is also spatially varying.

Parallel imaging reconstruction can be performed very efficiently when *k*-space is sampled along a Cartesian grid. In this case, the effects of *k*-space undersampling are particularly easy to account for. In the image domain, they result in aliasing that occurs among small sets of equidistant voxels. Image reconstruction can then be achieved by individual unfolding of these aliased sets. This is the approach underlying the common SENSE method in the case of Cartesian *k*-space sampling (2). In the following it will be simply be referred as SENSE for easier reading.

Straightforward image-domain unfolding requires relatively little computation. It is important to note, however, that this advantage is the result of a mild approximation. SENSE strictly enforces the elimination of aliasing only in the voxel centers and was therefore dubbed *weak* reconstruction in Ref. (2). The potential downside of weak reconstruction is that appreciable residual aliasing may occur when coil sensitivities vary considerably over the extent of a voxel and its significant side lobes. This is typically not of concern for high-resolution imaging since coil sensitivities vary smoothly at the scale of common voxel sizes. However, it gradually becomes a problem when the scan resolution is reduced and becomes a serious issue at the very low resolutions that are typically used in MRSI.

In the present work, we propose an alternative reconstruction approach that overcomes the described restrictions. The basic idea is to optimize the spatial response function of reconstructed voxels as a whole rather than only at the voxel centers. This is achieved by formulating the encoding equation at an enhanced spatial resolution and taking its minimum-norm solution as the reconstructed image.